Ratio¶
Core Idea¶
A ratio is an ordered quantitative comparison formed by dividing a numerator by a nonzero denominator. The quotient answers a specific question: how much of the numerator obtains per unit of the reference quantity? That apparently simple operation carries more structure than the bare number shows. The numerator and denominator occupy different roles; reversing them changes the claim. Their units determine whether the quotient is dimensionless or becomes a rate, density, concentration, or other compound quantity. Their population, exposure, and time window determine which observations belong in the comparison.
The prime is the relation, not any particular notation. A colon, fraction, percentage, “per” expression, index, or verbal comparison can all express a ratio. Common multiplication of numerator and denominator leaves the quotient invariant, so relative magnitude survives changes in the overall scale of the system. That invariance makes ratios powerful for comparison—and makes denominator choice dangerous when it is hidden.
How would you explain it like I'm…
How Many for Each
How Much Per One
Ratio as Per-Unit Comparison
Structural Signature¶
- The numerator — the focal amount whose relative magnitude is being stated.
- The nonzero denominator — the reference amount, population, exposure, duration, area, or comparison unit.
- The ordered division — the operation that maps the pair to a quotient; reversal generally produces a different relation.
- The units — like-dimensional terms may cancel, while unlike dimensions produce compound units such as kilometers per hour.
- The scope alignment — numerator and denominator refer to compatible populations, places, and periods.
- The common-scale invariance — multiplying both terms by the same nonzero factor preserves the quotient.
- The denominator sensitivity — changing the reference can radically change interpretation while the numerator remains fixed.
What It Is Not¶
Ratio is not a generic comparison, because comparison can be qualitative or ordinal and need not perform division. It is not an additive difference, because subtraction asks how far apart two quantities are rather than how many units of one obtain per unit of the other. It is not inherently a percentage, probability, risk, or rate; those are constrained or framed members of the broader family.
Nor does the quotient erase its inputs. A reported value of 0.8 is not self-interpreting. It could be a dimensionless share, 0.8 failures per hour, 0.8 dollars per unit, or 0.8 meters of rise per meter of run. The ratio's referents and units remain part of its identity.
Broad Use¶
- Physics and engineering: velocity, density, strain, efficiency, gear ratios, and signal-to-noise ratios.
- Medicine and epidemiology: incidence per person-time, case-fatality ratios, dosage per body mass, and staffing ratios.
- Economics and finance: leverage, debt-to-income, exchange rates, productivity, and price-to-earnings.
- Demography and public policy: per-capita expenditure, tax burden relative to income, and events per population at risk.
- Computing: compression ratio, throughput per core, cache-hit rate, and errors per request.
- Ecology and chemistry: predator-to-prey ratios, stoichiometric ratios, concentration, and biomass per area.
Clarity¶
The prime exposes the reference base hidden behind statements such as “more crime,” “higher productivity,” or “twice the risk.” Ten events may be rare or common depending on whether the denominator is twelve opportunities or twelve million. Once the denominator is named, disagreements can be localized: people may agree on the numerator yet be comparing different exposed populations, time windows, or units.
Manages Complexity¶
Ratio reduces a large family of relative metrics to a stable audit: identify the two quantities, assign their roles, check that the denominator is nonzero, preserve the resulting units, and align scope. This makes quantities from differently sized systems comparable without pretending their absolute totals match. It also makes the chief failure mode visible: a convenient denominator can normalize away scale while importing a misleading reference class.
Abstract Reasoning¶
Ratio supports multiplicative rather than additive inference. A quotient of 3 means three numerator units per denominator unit; it does not mean the numerator exceeds the denominator by three. The common-scale invariant lets the reasoner move between 2:5, 20:50, and 0.4 without losing the relation. Dimensional analysis then constrains valid transformations: dollars divided by hours cannot be silently compared with dollars divided by people.
The abstraction also supports counterfactual denominator analysis. Holding the numerator fixed while varying the legitimate reference quantities shows whether a claim is robust or rests on a chosen base. That move is central to auditing per-capita statistics, failure rates, risk statements, and performance metrics.
Knowledge Transfer¶
The same diagnostic travels literally across domains: What is the focal amount? Relative to what? Are the quantities measured over the same population and period? What units remain after division? Would a different legitimate denominator reverse the conclusion? A public-health analyst's exposure-denominator discipline transfers directly to reliability engineering, finance, education metrics, and ML evaluation.
Examples¶
Formal/Abstract¶
Let quantities be a and nonzero b. Their ratio is a/b. For any nonzero scale factor k, (ka)/(kb) = a/b; the relation survives common rescaling. Reversing the roles yields b/a, which is generally the reciprocal rather than the same comparison.
Applied¶
Two factories each record 50 defects. Factory A produced 1,000 units; Factory B produced 100,000. Equal numerators conceal ratios of 0.05 and 0.0005—5% versus 0.05%. The denominator changes the operational diagnosis from a severe quality problem to a comparatively rare failure rate.
Structural Tensions¶
- Reference relevance: a mathematically valid denominator may be substantively irrelevant to the question.
- Scope mismatch: numerator and denominator drawn from different populations or windows create a polished but incoherent quotient.
- Small denominators: ratios become unstable when a small reference magnifies minor numerator changes.
- Aggregation: a ratio of totals and an average of subgroup ratios answer different questions and can reverse rankings.
- Unit cancellation: dimensionless output can hide that unlike constructs were made commensurable by a contested measurement choice.
Structural–Framed Character¶
Ratio sits at the structural end of the structural–framed spectrum: it is a bare mathematical relation, unchanged by the field that uses it. A focal quantity is divided by a nonzero reference quantity, and the quotient answers how much of the first obtains per unit of the second.
The diagnostics line up cleanly. No home lexicon accompanies it: the same questions — what is the focal amount, what is the reference, which observations and time window count, what units result — apply identically to a mass density in physics and to an incidence figure in epidemiology. It has no normative default; a ratio counts as high or low only against a purpose supplied from outside. Its origin is arithmetic, definable without any agent or institution. Forming one recognizes a comparison the quantities already support rather than importing a perspective. On every diagnostic, it reads structural.
Substrate Independence¶
Ratio is maximally substrate-independent: any domain with quantitative magnitudes can instantiate the ordered division relation. The operation and its failure modes remain the same whether the quantities are distances, events, money, organisms, bytes, or probabilities.
Relationships to Other Abstractions¶
Current abstraction Ratio Prime
Parents (1) — outgoing typed relations
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Ratio is a kind of Comparison Prime
Ratio is comparison specialized to a multiplicative or per-unit relation obtained by dividing an ordered numerator by a nonzero denominator.Comparison supplies the genus of placing quantities in one declared frame. Ratio adds ordered quantitative roles, a nonzero reference denominator, division, and a quotient interpreted multiplicatively or per unit.
Children (118) — abstractions linked here by typed relations
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Absorbed Dose Domain-specific is a kind of Ratio
Absorbed dose specializes a ratio as ionizing-radiation energy imparted per absorber mass.Every absorbed dose is mean energy imparted by ionizing radiation divided by a specified positive receiving mass, or the local limit of those finite-mass quotients. Ratio admits other numerator and denominator kinds; radiation deposition and absorber selection provide the narrower differentia.
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Aggregate Modulus Domain-specific is a kind of Ratio
Aggregate Modulus is a strict kind of Ratio: it is the equilibrium axial-stress to axial-strain ratio under confined-compression conditions.Every reviewed Aggregate Modulus instance satisfies Ratio because it is the equilibrium axial-stress to axial-strain ratio under confined-compression conditions. The child adds the domain-specific restrictions stated in its frozen identity. Ratio is broader and can occur without the restrictions that define Aggregate Modulus.
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Arc elasticity Domain-specific is a kind of Ratio
Arc elasticity is a strict kind of Ratio: A measure of one variable's proportional responsiveness to another between two observations, commonly calculated as the ratio of their midpoint percentage changes.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its specialist carrier, conventions, operations, and failure boundaries.
- Arterial resistivity index Domain-specific is a kind of Ratio
Arterial RI is a strict Ratio: it divides the systolic–diastolic velocity difference by peak systolic velocity within one arterial waveform.RI has a focal numerator PSV−EDV, a nonzero ordered denominator PSV, unit cancellation, aligned vessel and cardiac-cycle scope, common-scale invariance, and denominator sensitivity; Doppler physiology supplies the child's differentia.
- Attack rate Domain-specific is a kind of Ratio
Attack rate is a strict kind of Ratio: In epidemiology, the attack rate is the proportion of an at-risk population that contracts the disease during a specified time interval.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Average variable cost Domain-specific is a kind of Ratio
The numerator is variable production cost over a stated short-run horizon, the nonzero denominator is the corresponding positive output quantity, and ordered division yields variable-cost currency per unit of output.Multiplying both quantities by a common nonzero scale factor preserves the quotient, while reversing the roles or substituting fixed or total cost changes the economic claim. Scope alignment requires that cost and output cover the same firm, product, interval, and production level. A positive diagnostic can name `VC`, `Q`, their units, horizon, and the resulting `VC/Q`; a collapse test sets `Q` to zero, mixes incompatible periods, or replaces the numerator with a different cost class. Stripping away the shutdown interpretation leaves Ratio's ordered numerator–reference–division–unit structure intact, while removing that quotient destroys AVC even if the firm still has costs. Average variable cost therefore strictly specializes Ratio through its variable-cost classification and short-run operating threshold.
- Basic Earnings Per Share Domain-specific is a kind of Ratio
Basic Earnings Per Share is a domain-specific kind of Ratio: Earnings available to common shareholders divided by weighted-average basic shares outstanding.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds the source-domain carrier, recognition rule, and failure conditions. The defining source account begins: Basic earnings per share (basic EPS) allocates a reporting period's earnings available to common shareholders across the weighted-average number of common shares outstanding during that period.
- Bodenstein number Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the flow geometry, characteristic length and velocity, axial dispersion or diffusion coefficient, unit consistency, exact convention and interpretation range.It remains its own entry because its identity is fixed by the flow geometry, characteristic length and velocity, axial dispersion or diffusion coefficient, unit consistency, exact convention and interpretation range.
- Body Fluid to Serum Concentration Ratio Domain-specific is a kind of Ratio
The fluid-to-serum concentration quotient is a Ratio with a specified analyte, compatible concentration units and paired clinical specimens.Each admitted case identifies the body-fluid numerator and nonzero serum reference, preserves fluid-over-serum order, divides compatible concentrations, aligns the specimen scope and remains sensitive to denominator choice. Common conversion of both concentrations leaves the dimensionless quotient unchanged. Other ratios have none of the body-fluid, serum or clinical-analyte restrictions.
- Buffett indicator Domain-specific is a kind of Ratio
What makes it its own entry: the domain-specific identity determined by the equity universe, GDP measure, date alignment, jurisdiction, units, revisions, and historical comparison method are explicit and the ratio is not treated as a standalone forecast.What makes it its own entry: the domain-specific identity determined by the equity universe, GDP measure, date alignment, jurisdiction, units, revisions, and historical comparison method are explicit and the ratio is not treated as a standalone forecast.
- Capacity factor Domain-specific is a kind of Ratio
Capacity factor is the ratio of actual energy output to maximum possible output over a period.Capacity factor is the ratio of actual energy output to maximum possible output over a period.
- Capacity utilization Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the production unit and period, actual output, capacity definition, installed capital and labor assumptions, product mix, maintenance and downtime, bottleneck, quality yield, units and prices, seasonal adjustment, uncertainty, and aggregation weights.It remains its own entry because its identity is fixed by the production unit and period, actual output, capacity definition, installed capital and labor assumptions, product mix, maintenance and downtime, bottleneck, quality yield, units and prices, seasonal adjustment, uncertainty, and aggregation weights.
- Capital intensity Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the production unit and period, capital concept and valuation, labor or output denominator, units and price basis, depreciation and utilization treatment, aggregation weights, ratio direction and comparison benchmark.It remains its own entry because its identity is fixed by the production unit and period, capital concept and valuation, labor or output denominator, units and price basis, depreciation and utilization treatment, aggregation weights, ratio direction and comparison benchmark.
- Cash-flow-to-debt ratio Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the reporting entity and consolidation, accounting standard and period, cash-flow numerator and adjustments, debt instruments included and measurement date, leases and cash netting, currency, annualization, ratio direction, negative values, seasonality, peer basis, trend, covenant definition and uncertainty.It remains its own entry because its identity is fixed by the reporting entity and consolidation, accounting standard and period, cash-flow numerator and adjustments, debt instruments included and measurement date, leases and cash netting, currency, annualization, ratio direction, negative values, seasonality, peer basis, trend, covenant definition and uncertainty.
- Coefficient of performance Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the system and boundary, heating or cooling mode, useful heat-transfer rate or energy, work or electrical input, time basis, operating temperatures, auxiliary loads, steady or seasonal convention, dimensionless ratio and uncertainty.It remains its own entry because its identity is fixed by the system and boundary, heating or cooling mode, useful heat-transfer rate or energy, work or electrical input, time basis, operating temperatures, auxiliary loads, steady or seasonal convention, dimensionless ratio and uncertainty.
- Coefficient of variation Domain-specific is a kind of Ratio
The candidate literally instantiates prime:ratio; What makes it its own entry: A dimensionless relative-dispersion statistic equal to standard deviation divided by mean, interpreted only where the measurement scale and nonzero mean make the ratio meaningful.The candidate literally instantiates prime:ratio; What makes it its own entry: A dimensionless relative-dispersion statistic equal to standard deviation divided by mean, interpreted only where the measurement scale and nonzero mean make the ratio meaningful.
- Consumer leverage ratio Domain-specific is a kind of Ratio
Consumer leverage ratio is a strict kind of Ratio: The ratio of household debt outstanding to annual disposable personal income for a matched population and period.The live Ratio prime requires an ordered numerator, nonzero reference denominator, division and declared units/scope. CLR names outstanding household debt, annual disposable personal income, their quotient, and a matched population/time frame. It specializes ratio by economic accounting roles; the frozen prime:ratio parent is therefore preserved. DSR changes the numerator to payments and is a sibling ratio, not an alias.
- Cost per mille Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the advertiser and campaign, medium and placement, cost components and currency, period, impression definition and counting system, thousand-unit scaling, served and viewable status, invalid traffic, estimated audiences, frequency and duplication, attribution, uncertainty, and comparability limits.It remains its own entry because its identity is fixed by the advertiser and campaign, medium and placement, cost components and currency, period, impression definition and counting system, thousand-unit scaling, served and viewable status, invalid traffic, estimated audiences, frequency and duplication, attribution, uncertainty, and comparability limits.
- Crest Factor Domain-specific is a kind of Ratio
Crest factor is an ordered quotient of a waveform's peak amplitude by its nonzero RMS amplitude.The live Ratio prime requires an ordered numerator, nonzero reference denominator, matched scope and interpretable units. Crest factor specializes those roles to the absolute peak and effective amplitude of one waveform over one declared observation interval; equal amplitude units cancel.
- Cyclically adjusted price-to-earnings ratio Domain-specific is a kind of Ratio
Cyclically adjusted price-to-earnings ratio is a strict kind of Ratio: The cyclically adjusted price-to-earnings ratio (CAPE, Shiller P/E, or P/E 10 ratio) is a stock valuation measure usually applied to the US S&P 500 equity market.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Data center infrastructure efficiency Domain-specific is a kind of Ratio
IT-equipment power is the ordered numerator and nonzero total-facility power is the reference denominator; division followed by percentage scaling states how much IT load obtains per unit of facility input.Both terms share power units, so the quotient is dimensionless, and meaningful comparison requires the same facility boundary, meter points, load classification, and observation interval. Common rescaling of both readings preserves DCIE, while denominator additions or boundary changes alter its meaning even if the numerator is unchanged; reversing the ordered pair produces PUE rather than the same metric. Removing data-center names leaves Ratio's numerator, denominator, ordered division, unit behavior, scope alignment, common-scale invariance, and denominator sensitivity; removing that ordered quotient leaves power measurements but no DCIE.
- Debt service coverage ratio Domain-specific is a kind of Ratio
Debt service coverage ratio is a strict kind of Ratio: its frozen identity entails the parent's defining structure while adding domain-specific restrictions.Every reviewed Debt service coverage ratio instance satisfies Ratio because the child identity—The debt service coverage ratio (DSCR), also known as the debt coverage ratio (DCR), is a financial ratio that measures an entity's ability to generate sufficient cash to cover its debt obligations, including interest, principal, and lease payments—entails the parent identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named. Ratio can occur without the domain, mechanism, population, or boundary conditions that distinguish Debt service coverage ratio.
- Debt-to-income ratio Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the borrower and application date, front-end or back-end convention, gross monthly income definition and documentation, included housing and debt obligations, exclusions, calculation period, percentage and governing underwriting rule.It remains its own entry because its identity is fixed by the borrower and application date, front-end or back-end convention, gross monthly income definition and documentation, included housing and debt obligations, exclusions, calculation period, percentage and governing underwriting rule.
- Dividend cover Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the reporting entity and period, attributable earnings definition, ordinary and special dividends, declared or paid timing, share class, continuing operations and exceptional items, currency, sign and zero cases, data provenance, and trailing or forecast convention.It remains its own entry because its identity is fixed by the reporting entity and period, attributable earnings definition, ordinary and special dividends, declared or paid timing, share class, continuing operations and exceptional items, currency, sign and zero cases, data provenance, and trailing or forecast convention.
- Dynamic Amplification Factor Domain-specific is a kind of Ratio
A DAF is a ratio specialized to matched dynamic and static or steady structural responses.Every DAF divides a specified peak dynamic response by a nonzero matched reference response, satisfying the live Ratio identity. Ratio applies in many other domains and to many other quantities; matched structural response under dynamic and static or steady conditions is the narrower DAF differentia.
- Eckert Number Domain-specific is a kind of Ratio
Eckert Number is a strict kind of Ratio: The dimensionless group Ec=U²/(cₚΔT), comparing a flow's characteristic kinetic-energy scale with the sensible-enthalpy scale of a stated temperature difference.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, computation or normalization, interpretation, and failure boundaries.
- Ecological stoichiometry Domain-specific is a kind of Ratio
Ecological Stoichiometry instantiates Ratio because elemental proportions are the invariant comparative quantities connecting organism composition, resources, and ecosystem fluxes.Ecological Stoichiometry instantiates Ratio because elemental proportions are the invariant comparative quantities connecting organism composition, resources, and ecosystem fluxes.
- Electrical admittance Domain-specific is a kind of Ratio
Electrical admittance is the ordered current-to-voltage ratio for a specified linear electrical response, with a nonzero reference voltage for direct division.Ratio supplies an ordered numerator, nonzero reference denominator, division, units, and aligned scope. Electrical admittance specializes those roles to matched electrical current and voltage phasors of one named branch or load at a stated frequency, current orientation and linear model. Its coefficient Y equals I/V where V is nonzero and has conductance and susceptance components; a model can define the same coefficient at zero applied voltage without evaluating a zero-denominator quotient. Thus every eligible finite admittance is an electrical ratio in its defining nonzero-voltage relation, while many ratios have no electrical carrier or linear complex response. The electrical differentia remains identity-bearing, and this kind-of relation does not require a measurement procedure or a declared symbolic basis.
- Emission intensity Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the pollutant species and global-warming potential if aggregated, source and organizational boundary, lifecycle stage, geography and period, direct and indirect scope, gross and net treatment, activity denominator and units, allocation and coproduct method, measurement or estimation, uncertainty, comparability, and total-emission rebound.It remains its own entry because its identity is fixed by the pollutant species and global-warming potential if aggregated, source and organizational boundary, lifecycle stage, geography and period, direct and indirect scope, gross and net treatment, activity denominator and units, allocation and coproduct method, measurement or estimation, uncertainty, comparability, and total-emission rebound.
- Energy Conversion Efficiency Domain-specific is a kind of Ratio
Energy conversion efficiency is Ratio specialized to matched useful converted-energy output divided by energy input.The output is the numerator and all relevant entering energy is the nonzero denominator at one declared boundary and operating basis. The quotient retains Ratio's ordered division, units and scope discipline while adding a physical conversion and purpose-defined useful energy form.
- Enterprise Value-to-Sales Ratio Domain-specific is a kind of Ratio
EV/Sales strictly instantiates **Ratio**: EV is the ordered numerator, nonzero sales the reference denominator, division yields a per-unit quotient, and currency/period/scope determine interpretation.`prime:ratio` is the broader abstraction this entry instantiates. It also uses **Comparison** to read a company against peers or history and **Value Commensuration** to put heterogeneous enterprises into one revenue-scaled frame. Those are already broader operations and need not be additional direct parents because Ratio supplies the exact immediate genus. Tobin's q and the Lerner Index are neighboring domain-specific ratios, not parents. Tobin's q compares market value with replacement cost and carries a unity-threshold investment theory. The Lerner Index normalizes price over marginal cost to measure market power. EV/Sales has neither threshold nor those causal interpretations. Modigliani–Miller is a capital-structure benchmark relevant to valuation reasoning, but it does not define the observed EV/revenue multiple.
- Envy ratio Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the transaction and capitalization date, investor and management cash investments, fully diluted equity percentages and instruments, price-per-percentage calculations, resulting ratio and treatment of sweet equity or contingent awards.It remains its own entry because its identity is fixed by the transaction and capitalization date, investor and management cash investments, fully diluted equity percentages and instruments, price-per-percentage calculations, resulting ratio and treatment of sweet equity or contingent awards.
- Ericksen Number Domain-specific is a kind of Ratio
Ericksen number is an ordered quotient of a declared viscous flow scale by a nonzero orientational-elastic reference scale.The numerator and denominator have distinct physical roles, the denominator must be nonzero, and reversing them changes the comparison. Ratios can have units, and dimensionless quantities need not be ratios, so this parent is independent of the dimensionless-quantity parent.
- EV/EBITDA Domain-specific is a kind of Ratio
EV/EBITDA is a domain-specific kind of Ratio: EV/EBITDA is a valuation multiple dividing enterprise value by earnings before interest, taxes, depreciation, and amortization to compare the market value of operating businesses across financing and accounting structures.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds the source-domain carrier, recognition rule, and failure conditions. The defining source account begins: EV/EBITDA is a valuation multiple that divides a firm's enterprise value by earnings before interest, taxes, depreciation, and amortization.
- EV/GCI Domain-specific is a kind of Ratio
**Ratio** is the broader abstraction this entry instantiates.EV/GCI is a strict specialization with an ordered numerator, nonzero denominator, quotient, units, scope, and denominator sensitivity. **Comparison** explains relative ranking. **Measurement** governs the adjustment and reproducibility chain. **Normalization** explains capital-structure and scale control. **Benchmarking** supplies peer interpretation. **Tobin's q** and **Price-to-Book** are sibling domain-specific valuation ratios. Only Ratio is proposed as a DAG edge.
- False Positive Rate Domain-specific is a kind of Ratio
A defined FPR divides false-positive cases by all actual negatives under the same binary rule.FP is the ordered numerator and FP+TN is the nonzero denominator. Both counts refer to the same reference-negative class, rule and evaluation interval; division cancels their units, preserves the value when both counts scale together, and changes the measure when the denominator changes. These fulfill the full live Ratio signature. FPR adds reference truth and a binary-decision partition, whereas Ratio covers many quantities outside classification.
- Financial ratio Domain-specific is a kind of Ratio
Financial ratio is a strict kind of Ratio: Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Forecast Attainment Domain-specific is a kind of Ratio
**The aggregate numerator** is the realized total and **the aggregate denominator** is the nonzero total from **the preserved forecast snapshot**; ordered division yields **the attainment ratio**.**The aligned scope** fixes carrier, units, products, locations, customers, and period so the quotient answers how much realization occurred per unit forecast. Multiplying both aligned totals by the same unit-conversion factor preserves attainment, while changing the lagged denominator or its scope can change the conclusion without changing actuals. Zero forecasts route to **the exception policy**, preserving Ratio's nonzero-denominator boundary. Remove the ordered actual-to-forecast division and the metric ceases to be Forecast Attainment, while Ratio remains broader because it does not require forecast versioning, a lag policy, or planning interpretation.
- Gender Parity Index Domain-specific is a kind of Ratio
The matched female indicator is the numerator, the corresponding nonzero male indicator is the denominator, and ordered division yields the index.Their common indicator, population, place, period, and measurement rule provide scope alignment; common rescaling preserves the quotient; reversal produces the reciprocal and changes the directional reading; and a zero or unstable denominator limits interpretation. Remove that ordered division and no Gender Parity Index remains. Preserve Ratio without the female-to-male orientation, unity reference, declared parity convention, and substantive equality boundary, and the broader parent remains.
- Hemiperfect number Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the positive integer n, positive-divisor convention, sigma function, abundancy ratio in lowest terms, odd numerator k and evidence or bounds for any least-member claim.It remains its own entry because its identity is fixed by the positive integer n, positive-divisor convention, sigma function, abundancy ratio in lowest terms, odd numerator k and evidence or bounds for any least-member claim.
- Import ratio Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the country, reporting dates, import flow interval, gross or usable reserve definition, currency conversion, seasonality, inversion convention, and treatment of services and external liabilities.It remains its own entry because its identity is fixed by the country, reporting dates, import flow interval, gross or usable reserve definition, currency conversion, seasonality, inversion convention, and treatment of services and external liabilities.
- Incremental Capital–Output Ratio Domain-specific is a kind of Ratio
Defined ICOR divides an incremental capital or investment measure by a nonzero output increment, specializing Ratio.The staged ICOR is a quotient of a declared incremental capital measure and an incremental output measure. Every defined instance is therefore a ratio, while most ratios do not compare those economic increments. The child remains undefined when its denominator is zero; a broad parent does not validate a causal productivity or growth-law interpretation.
- Inherent steady-state availability Domain-specific is a kind of Ratio
Inherent steady-state availability is the ordered MTBF-to-total-cycle-time ratio for a repairable item under corrective-only downtime accounting.Ratio supplies an ordered numerator, nonzero denominator, compatible units, aligned scope and a quotient interpreted per unit of reference time. Inherent steady-state availability specializes those roles to mean operating time between failures divided by that same MTBF plus matching mean corrective repair time for one repairable item, giving a limiting operating fraction under the stated model. Every admitted finite instance is such a ratio when the sum is positive; a price or current-to-voltage ratio lacks the failure, repair and limiting-horizon differentia. Its strict Comparison ancestor is met by the matched-duration comparison, while a predictive radar-receiver design calculation need not meet Performance Measure's enacted observation or Measurement chain.
- Ka/Ks ratio Domain-specific is a kind of Ratio
The statistic is a normalized ratio between two modeled substitution rates.What makes it its own entry: codon-opportunity-normalized comparison of amino-acid-changing and synonymous evolution, with model and averaging limitations.
- Kt/V Domain-specific is a kind of Ratio
Urea Kt/V is a specialized quotient of equivalent urea-cleared volume by urea distribution volume.Every urea Kt/V report divides K times a declared treatment interval by a nonzero urea distribution volume, so it instantiates the live Ratio relation. Its urea marker, dialysis estimators and schedule give the child a narrower identity. Clearance rate is an input, not the full index; the live domain-specific Clearance node's bodily-elimination framing does not cover every extracorporeal operation.
- Land equivalent ratio Domain-specific is a kind of Ratio
Land-equivalent ratio compares monoculture land required with intercropped land for equal yield.Land-equivalent ratio compares monoculture land required with intercropped land for equal yield.
- Law of reciprocal proportions Domain-specific is a kind of Ratio
The law literally compares two normalized combining-mass quotients; chemical identity, the common third element, and simple-integer stoichiometric compatibility provide its autonomous specialization.What makes it its own entry: the three-element reciprocal comparison through a common reference element, not the fixed composition of one compound, the existence of several compounds between one pair, or conservation of total reaction mass.
- Law of sines Domain-specific is a kind of Ratio
The theorem literally equates ratios between side lengths and nonzero sines; What makes it its own entry: the invariant equality of opposite side-to-sine ratios for one triangle, together with circumcircle meaning and branch ambiguity; generic trigonometric inversion, similarity, or any ratio involving sines does not reproduce it.The theorem literally equates ratios between side lengths and nonzero sines; What makes it its own entry: the invariant equality of opposite side-to-sine ratios for one triangle, together with circumcircle meaning and branch ambiguity; generic trigonometric inversion, similarity, or any ratio involving sines does not reproduce it.
- Leaf Area Index Domain-specific is a kind of Ratio
**Ratio** is instantiated by leaf area divided by ground area.**Measurement** is presupposed because both direct and indirect pathways operationalize a convention-defined measurand. **Albedo** and radiative-transfer abstractions are related in applications but are neither definitions nor necessary parents.
- Lerman ratio Domain-specific is a kind of Ratio
The Lerman ratio compares an actual income increase with the nominal benefit provided.The Lerman ratio compares an actual income increase with the nominal benefit provided.
- Lighting Ratio Domain-specific is a kind of Ratio
Lighting ratio is a domain-specific measured ratio.The numerator and nonzero reference denominator are measured illumination quantities under an explicit photographic convention. Other ratios lack the subject-side lighting roles.
- Linear energy transfer Domain-specific is a kind of Ratio
What makes it its own entry: the domain-specific identity determined by particle type and energy, material, path definition, averaging, secondary-electron cutoff, and restricted or unrestricted LET convention are all stated.What makes it its own entry: the domain-specific identity determined by particle type and energy, material, path definition, averaging, secondary-electron cutoff, and restricted or unrestricted LET convention are all stated.
- Logarithmic frequency ratio Domain-specific is a kind of Ratio
Logarithmic frequency ratio is a strict kind of Ratio: The logarithmic frequency ratio (also known as frequency level) of two frequencies is the logarithm of their ratio, and may be expressed using the unit octave (symbol: oct) corresponding to the ratio 2 or the unit decade (symbol: dec) corresponding to the ratio 10.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Major Limma Domain-specific is a kind of Ratio
For an upward interval, the upper pitch frequency is the numerator and the nonzero lower pitch frequency is the denominator; ordered division fixes their quotient at exactly `135/128`.The terms share frequency units, so the quotient is dimensionless, while the musical scope declares that this number compares a directed pitch pair. Multiplying both frequencies by the same nonzero transposition factor leaves the quotient unchanged, and interval inversion reverses the ordered roles to `128/135`. If the relation is only a rounded value near 92 cents, an unqualified limma, or a pitch pair with another quotient, the Major Limma identity and this Ratio instantiation collapse. Ratio remains broader because it does not require pitch, octave-aware interval arithmetic, just intonation, cents, or musical notation.
- Market share Domain-specific is a kind of Ratio
Every market share is an aligned part-to-market-total ratio; it adds a competitive-market boundary and a supplier or product as the focal part.A valid market share divides one supplier's or product's in-market measured amount by a positive matching market total. The numerator and denominator are ordered, have compatible units, and align in product or category, geography, and period or as-of date. Their units cancel, common nonzero rescaling leaves the share unchanged, and changing the market denominator can change the result while the focal amount stays fixed. These instantiate all seven live Ratio signature roles; the defined economic market and focal participant are stable extra conditions. Ratios such as defects per unit or debt to income lack that market differentia. Ratio is the nearest live genus; Comparison is already inherited through Ratio, while Market concentration and Market power name downstream or different identities.
- Mass-to-Light Ratio Domain-specific is a kind of Ratio
Astronomical mass-to-light ratio is a ratio specialized to mass per emitted light.The live Ratio prime requires an ordered numerator and nonzero denominator with stated units and scope. Here mass occupies the numerator and band-defined astronomical luminosity the denominator, with a declared component and aperture. Photometric System defines observing conventions but does not subsume the mass quotient.
- Mechanical Advantage Domain-specific is a kind of Ratio
Mechanical advantage is a specialized output-to-input mechanical ratio.Both the useful force ratio and the rotary torque ratio divide a like-dimensional output by a nonzero like-dimensional input. Ratio supplies ordered numerator, reference denominator, units, and scope; Mechanical Advantage adds coupled mechanical ports and separate ideal work constraints. A ratio can exist without any machine.
- Meshedness coefficient Domain-specific is a kind of Ratio
Meshedness coefficient is a strict kind of Ratio: its frozen identity entails the parent's defining structure while adding domain-specific restrictions.Every reviewed Meshedness coefficient instance satisfies Ratio because the child identity—In graph theory, the meshedness coefficient is a graph invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar graphs with the same number of vertices—entails the parent identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named. Ratio can occur without the domain, mechanism, population, or boundary conditions that distinguish Meshedness coefficient.
- Molar Concentration Domain-specific is a kind of Ratio
Molar Concentration is a strict kind of Ratio: it divides amount of substance by mixture volume under named units and temperature conditions.Every reviewed Molar Concentration instance satisfies Ratio because it divides amount of substance by mixture volume under named units and temperature conditions. The child adds the domain-specific restrictions stated in its frozen identity. Ratio is broader and can occur without the restrictions that define Molar Concentration.
- Multiply perfect number Domain-specific is a kind of Ratio
What makes it its own entry: the domain-specific identity determined by positive integer n, divisor convention, divisor-sum function, and integer multiplier k satisfy the exact equation σ(n)=kn.What makes it its own entry: the domain-specific identity determined by positive integer n, divisor convention, divisor-sum function, and integer multiplier k satisfy the exact equation σ(n)=kn.
- Net income per employee Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the company and reporting period, net-income definition and currency, consolidated scope, employee-count definition and averaging, formula, comparison group and adjustments for outsourcing and exceptional items.It remains its own entry because its identity is fixed by the company and reporting period, net-income definition and currency, consolidated scope, employee-count definition and averaging, formula, comparison group and adjustments for outsourcing and exceptional items.
- Nusselt number Domain-specific is a kind of Ratio
Nusselt number is a strict kind of Ratio: The dimensionless heat-transfer group Nu_L = hL/k, relating a surface's convective coefficient to fluid thermal conductivity across a stated characteristic length.The frozen strict parent remains valid. Nu=hL/k can be written h/(k/L): h is the convective surface-transfer coefficient and k/L is a same-unit fluid-conductive reference. The quotient is meaningful only with a declared geometry length, conductivity, and local or average scope, exactly as the live ratio prime requires. Nusselt adds the heat-transfer carrier and fluid-side reference not required by arbitrary ratios.
- One-seventh area triangle Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the nondegenerate parent triangle, cyclic side-division convention, three cevians, central intersection triangle and exact one-to-seven area relation.It remains its own entry because its identity is fixed by the nondegenerate parent triangle, cyclic side-division convention, three cevians, central intersection triangle and exact one-to-seven area relation.
- Price-to-Book Ratio Domain-specific is a kind of Ratio
The numerator is the market value of the relevant common-equity claim, the nonzero denominator is its accounting book value, and ordered division yields market-value units per book-value unit.Company-level and per-share forms preserve the quotient under common rescaling when share class and count align; dates, currencies, accounting bases, and claim scope provide the required alignment; and changing or reversing the denominator changes the interpretation. Removing the equity-valuation accent leaves Ratio's ordered quantities, division, unit behavior, scope alignment, common-scale invariance, and denominator sensitivity. Removing the aligned market-over-book division destroys P/B even if both values remain available. This full mapping establishes strict subsumption under Ratio.
- Packing density Domain-specific is a kind of Ratio
Packing density is the ratio of occupied measure to total measure in a containing space.Packing density is the ratio of occupied measure to total measure in a containing space.
- Peak signal-to-noise ratio Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the reference and test signals, spatial and temporal alignment, sample domain and color space, transfer function, bit depth and peak value, clipping, mean-squared-error definition and channel aggregation, logarithm and decibel convention, infinite value for zero error, masks or regions, comparability and perceptual limits.It remains its own entry because its identity is fixed by the reference and test signals, spatial and temporal alignment, sample domain and color space, transfer function, bit depth and peak value, clipping, mean-squared-error definition and channel aggregation, logarithm and decibel convention, infinite value for zero error, masks or regions, comparability and perceptual limits.
- Physiological Density Domain-specific is a kind of Ratio
Physiological Density is a strict kind of Ratio: it divides population by arable-land area under a declared geographic scope.Every reviewed Physiological Density instance satisfies Ratio because it divides population by arable-land area under a declared geographic scope. The child adds the domain-specific restrictions stated in its frozen identity. Ratio is broader and can occur without the restrictions that define Physiological Density.
- Power-to-weight Ratio Domain-specific is a kind of Ratio
Power-to-weight ratio is a ratio restricted to a specified physical power numerator and declared nonzero mass denominator.Each instance divides power by a positive mass to express power per unit mass, with ordered quantities, compound units, and aligned scope. Ratio supplies the general division relation; physical power, mass boundary, and operating basis specialize it. A reciprocal mass-per-power measure is a different ordered quotient.
- Process performance index Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the process and characteristic, observation window and sampling, upper and lower specification limits, target if any, mean and overall standard-deviation estimator, one- or two-sided formula, subgrouping, process stability, distribution and dependence, confidence interval, negative values and acceptance criterion.It remains its own entry because its identity is fixed by the process and characteristic, observation window and sampling, upper and lower specification limits, target if any, mean and overall standard-deviation estimator, one- or two-sided formula, subgrouping, process stability, distribution and dependence, confidence interval, negative values and acceptance criterion.
- Proportionality (mathematics) Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the variables and domain, direct or inverse form, constant and units, equation, zero and sign conventions, correspondence of observations and evidence that the ratio or product remains invariant.It remains its own entry because its identity is fixed by the variables and domain, direct or inverse form, constant and units, equation, zero and sign conventions, correspondence of observations and evidence that the ratio or product remains invariant.
- Put/Call Ratio Domain-specific is a kind of Ratio
The put-call ratio is the ratio of put activity to call activity used as a market-sentiment indicator.The put-call ratio is the ratio of put activity to call activity used as a market-sentiment indicator.
- Quadrant Count Ratio Domain-specific is a kind of Ratio
**`ratio` — proposed strict subsumption parent.** Its readout is an ordered numerator—the signed count difference—divided by the nonzero total paired count (N), with both roles and scope required for interpretation.**`ratio` — proposed strict subsumption parent.** Its readout is an ordered numerator—the signed count difference—divided by the nonzero total paired count (N), with both roles and scope required for interpretation.
- Radiation Efficiency Domain-specific is a kind of Ratio
Antenna radiation efficiency is the ordered ratio of total radiated RF power to net RF power accepted at its terminals under one condition.The live ratio prime requires numerator, nonzero denominator, ordered division, units, and scope alignment. Radiated and accepted power fill those exact roles for one antenna, frequency, and excitation. The specialized physical boundary makes this a strict child. The live efficiency prime instead requires feasible alternatives and dominance frontier, which the metric does not entail.
- Rapid Shallow Breathing Index Domain-specific is a kind of Ratio
RSBI is a strict Ratio: respiratory frequency is divided by nonzero tidal volume under one aligned sampling protocol.The ordered numerator and denominator, compound units, patient/time scope alignment, common-scale behavior, and denominator sensitivity instantiate Ratio; respiratory assessment supplies the differentia.
- Real net output ratio Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the firm and reporting period, production boundary, internal production value, externally produced goods and services, valuation and transfer-price rules, denominator reconciliation, ratio and units and comparison across firms or time.It remains its own entry because its identity is fixed by the firm and reporting period, production boundary, internal production value, externally produced goods and services, valuation and transfer-price rules, denominator reconciliation, ratio and units and comparison across firms or time.
- Relative Atomic Mass Domain-specific is a kind of Ratio
(A_{\mathrm r}) is exactly a mass divided by the nonzero atomic mass constant; this is the broader abstraction this entry instantiates.(A_{\mathrm r}) is exactly a mass divided by the nonzero atomic mass constant; this is the broader abstraction this entry instantiates.
- Relative humidity Domain-specific is a kind of Ratio
Relative humidity is a strict kind of Ratio: Relative humidity is the ratio, usually expressed as a percentage, of actual water-vapor partial pressure to equilibrium saturation vapor pressure at the same temperature.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Response-rate ratio Domain-specific is a kind of Ratio
Response-rate ratio is a strict kind of Ratio: Response-rate ratio is a measure of efficacy of therapy in clinical trials.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Return on invested capital Domain-specific is a kind of Ratio
Return on invested capital is a strict kind of Ratio: A company-level ratio of after-tax operating profit to average invested capital, used to assess operating return on deployed capital.The frozen strict prime:ratio edge is valid under the broader abstraction's ordered-division signature. ROIC has a focal numerator (after-tax operating profit), a nonzero reference denominator (average invested capital), aligned company period and units, and a quotient interpreted as operating return per unit of deployed capital. Generic ratios need not involve corporate accounting or this particular profit/capital pairing. The live financial_ratio node is a possible intermediate genus, but the existing strict parent is preserved for this repair.
- Reynolds Number Domain-specific is a kind of Ratio
**Ratio** is the strict parent because Re compares one characteristic contribution with another by division and remains meaningful only with numerator, denominator, and frame named.Turbulence is related but not taxonomically upstream: many low- and high-Re laminar flows exist under special conditions.
- Rugosity Domain-specific is a kind of Ratio
**Ratio** is the broader abstraction this entry instantiates by strict subsumption.Rugosity is an ordered quotient of like-dimensional geometric quantities, so units cancel while numerator, denominator, support, and convention remain semantically load-bearing. **Measurement** supplies the target–instrument–procedure–uncertainty chain. **Scale** explains dependence on resolution and extent. **Comparison** supports cross-surface ranking once procedures align. **Porosity** is a nearby but distinct internal-void property. **Fractal Geometry** and the **Coastline Paradox** concern scaling across resolutions, not the single-scale excess-extent ratio.
- Slip Ratio (Gas–Liquid Flow) Domain-specific is a kind of Ratio
Slip ratio is the gas-phase intrinsic velocity divided by the nonzero liquid-phase intrinsic velocity in one flow frame.Live Ratio supplies the ordered-division genus. This child fixes numerator and denominator to gas and liquid phase-intrinsic mean velocities in a shared location, direction and averaging convention; its unity benchmark and connection to void fraction are specific to gas–liquid two-phase flow. The edge does not imply a universal slip correlation or operational use.
- Specific quantity Domain-specific is a kind of Ratio
Specific quantity is a domain-specific kind of Ratio: An intensive physical quantity expressed per unit mass of a system.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds the source-domain carrier, recognition rule, and failure conditions. The defining source account begins: A specific quantity is normally an extensive physical quantity normalized by mass, turning a size-dependent total into an intensive or comparison-oriented value.
- Spectral line ratios Domain-specific is a kind of Ratio
Spectral line ratios is a strict kind of Ratio: The analysis of line intensity ratios is an important tool to obtain information about laboratory and space plasmas.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Stable Isotope Ratio Domain-specific is a kind of Ratio
A stable-isotope abundance quotient is an ordered Ratio specialized to a same-element stable isotope pair in one material.The heavy and light isotope atom amounts in material P supply Ratio's ordered numerator and nonzero denominator. Dividing aligned atom amounts cancels units, common scaling preserves R, and reversing the pair changes the quotient. Ordinary ratios need not involve stable isotopes, establishing strict subsumption; delta reference reporting remains optional.
- Stefan Number Domain-specific is a kind of Ratio
Stefan Number **specializes Ratio**, the broader abstraction.It is a division of commensurate nonzero-reference quantities whose numerator, denominator, units, and scope must be named. The child adds the compulsory sensible/latent enthalpy roles, phase-change reference, convention lock, and model consequences. It relates to **Thermodynamic Equilibrium** because `T_m` or another transition reference is often an equilibrium temperature, but Stefan number can be used in nonequilibrium interface motion and is not a subtype of equilibrium. It relates to **Second Law of Thermodynamics** through phase-transition direction and entropy, but the ratio is fundamentally an energy-scale nondimensionalization, not an entropy-production law. It relates to **Phase Diagram** for mixtures whose transition temperatures and phase ranges must be selected, yet a phase diagram does not supply the ratio.
- Stress triaxiality Domain-specific is a kind of Ratio
The candidate literally instantiates prime:ratio; What makes it its own entry: The dimensionless ratio of mean hydrostatic stress to von Mises equivalent stress, characterizing the pressure-like component of a multiaxial stress state.The candidate literally instantiates prime:ratio; What makes it its own entry: The dimensionless ratio of mean hydrostatic stress to von Mises equivalent stress, characterizing the pressure-like component of a multiaxial stress state.
- Stuart Number Domain-specific is a kind of Ratio
Stuart Number divides a magnetic-force scale by an inertial-force scale.Under declared nonzero speed and matched scales, the ordered Lorentz-force/inertia quotient realizes Ratio while adding a specific MHD numerator, denominator and regime.
- Superpartient Ratio Domain-specific is a kind of Ratio
**Ratio** is the broader abstraction this entry instantiates.Every superpartient ratio is a ratio comparing two positive quantities by division, with additional reduction, ordering, quotient, and remainder constraints. It is a strict specialization of the live prime. **Classification** explains the taxonomy. **Division Algorithm** supplies the quotient–remainder test. **Coprimality** supplies canonical root terms. **Scale Invariance** explains why `10:6` and `5:3` have the same classification. **Music Interval** is an application context rather than a universal parent. Only Ratio is proposed as a DAG edge. Superposition is dismissed as a lexical retrieval collision.
- Surface-area-to-volume ratio Domain-specific is a kind of Ratio
Surface-area-to-volume ratio is a strict kind of Ratio: The surface-area-to-volume ratio or surface-to-volume ratio (denoted as SA:V, SA/V, or sa/vol) is the ratio between surface area and volume of an object or collection of objects.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- T-statistic Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the estimand and estimator, null value, standard-error estimator, ratio formula and sign, model assumptions, degrees of freedom, reference distribution, test direction and uncertainty interpretation.It remains its own entry because its identity is fixed by the estimand and estimator, null value, standard-error estimator, ratio formula and sign, model assumptions, degrees of freedom, reference distribution, test direction and uncertainty interpretation.
- Testosterone-to-Cortisol Ratio Domain-specific is a kind of Ratio
**Ratio** is the broader abstraction this entry instantiates.T:C is an ordered division of testosterone by a nonzero cortisol reference and inherits unit, scope, denominator, and reversal constraints. **Measurement** is constitutive because each input depends on specimen, instrument, assay, timing, and uncertainty. **Proxy–Target Fidelity** governs any claim that T:C stands in for training strain, recovery, performance, or aggression. **Correlation** describes observed association but is not the measure itself. One strict specialization edge to Ratio is sufficient. Additional edges would encode components or evidential uses rather than the smallest genus.
- Thyroid hormone binding ratio Domain-specific is a kind of Ratio
Thyroid hormone binding ratio is a strict kind of Ratio: A reference-normalized thyroid-hormone uptake result indicating serum binding capacity indirectly.The live Ratio prime requires a numerator, nonzero reference denominator, quotient, units, and scope. THBR names a patient uptake signal divided by normal-reference uptake under one assay, yielding a dimensionless quotient whose interpretation depends on the serum binding context. This exactly instantiates the broader ratio and adds thyroid-specific assay meaning; direct TBG measurement and raw uptake are separate neighbors.
- Torque density Domain-specific is a kind of Ratio
Volumetric torque density is a ratio with torque as numerator and declared positive device volume as denominator.The live Ratio prime defines an ordered numerator divided by a nonzero reference, with units and scope named. Volumetric torque density exactly instantiates those roles: measured or specified torque is numerator, positive device volume is denominator, N·m/L is the unit, and test/volume boundaries define scope. The child narrows the general ratio to mechanical torque capacity per physical volume. The parent does not need to entail torque-specific behavior for child-to-parent subsumption.
- Transmission coefficient Domain-specific is a kind of Ratio
It remains its own entry because its identity is fixed by the incident and transmitted quantities, amplitude-versus-flux convention, normalization, impedances or wave numbers, direction, polarization or mode, frequency, and boundary conditions.It remains its own entry because its identity is fixed by the incident and transmitted quantities, amplitude-versus-flux convention, normalization, impedances or wave numbers, direction, polarization or mode, frequency, and boundary conditions.
- TRIN (Arms Index) Domain-specific is a kind of Ratio
TRIN (Arms Index) is a strict kind of Ratio: An intraday market-breadth indicator equal to the ratio of advancing to declining issues divided by the ratio of advancing to declining share volume for the same universe and interval.TRIN is necessarily a quotient of two named nonzero breadth ratios.
- Type-Token Ratio Domain-specific is a kind of Ratio
Type-Token Ratio is a ratio specialized to distinct lexical types as numerator and total word tokens as the nonzero reference denominator.The measure inherits Ratio's ordered numerator-denominator comparison and quotient interpretation. It fixes the numerator to the number of distinct word types, the denominator to the total token count, and the scope to one explicitly tokenized language sample, adding lexical-diversity interpretation and the length-confound warning.
- Volume concentration Domain-specific is a kind of Ratio
Volume concentration is a strict kind of Ratio: The constituent volume divided by final mixture volume under declared state conditions, reported as a fraction, percentage, or explicit volume-per-volume basis.Ratio supplies comparison by division with typed numerator and denominator; Volume Concentration adds constituent and final-mixture volumes, state conditions, and chemical reporting rules.
- Volume of Distribution Domain-specific is a kind of Ratio
amount divided by nonzero concentration produces the apparent-volume scale and requires explicit units and scope.amount divided by nonzero concentration produces the apparent-volume scale and requires explicit units and scope.
- Working Capital Turnover Ratio Domain-specific is a kind of Ratio
Working Capital Turnover Ratio is a strict kind of Ratio: Net sales for a period divided by average working capital for the same period, reporting sales generated per unit of net current-asset investment.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, operation, evidence conditions, and failure boundaries.
- Number Density Prime is a kind of Ratio
Every number density is a Ratio specialized to a countable population per associated spatial extent.Direct N/V and N/A put a declared count over a positive, co-scoped volume or area, yielding reciprocal-spatial units. A selection-corrected sum of inverse accessible volumes estimates that count-per-volume target; its algorithm need not be one raw N/V division. Ratio supplies ordered numerator, nonzero reference extent, per-unit interpretation, dimensional units, common-scale invariance for the target, and denominator sensitivity. Its strict Comparison ancestor is met by co-framing count and spatial exposure to read their multiplicative relation. Number Density adds counted-object membership and spatial support, while Ratio also covers non-count and non-spatial quotients.
- Productivity Prime is a kind of Ratio
Productivity is the Ratio species whose numerator is produced output and whose denominator is a declared input, resource, capacity, area, or time basis.Every Productivity instance compares two scoped quantities by division and reports how much output obtains per unit of the denominator, satisfying Ratio. Productivity adds a production system, an output convention, an input or exposure basis, an interval, and aggregation rules. Ratios can compare quantities unrelated to production, so the reverse entailment fails.
- Relative Change Prime is a kind of Ratio
Relative Change is a strict kind of Ratio: Relative change measures a quantity's difference from a declared reference value as a ratio to that reference, preserving proportional change while suppressing absolute scale.The parent supplies the necessary broader identity—Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.—while the candidate adds its domain carrier, relation, and rejection conditions.
- Abbe Number Domain-specific presupposes Ratio
Abbe number presupposes an aligned, nonzero-denominator refractivity-to-dispersion ratio.With the medium and spectral convention fixed, V=(n_center−1)/(n_short−n_long) divides a numerator by a nonzero denominator measured on the same material state. This realizes live Ratio's ordered scope-aligned comparison. Ratio alone does not supply wavelength-indexed refractive indices, spectral-line choices, or the optical interpretation. The live prime Dispersion has additional actual-propagation commitments and is not asserted as a strict parent from terminology alone.
- Absolute Advantage Domain-specific includes Ratio
Absolute Advantage contains producer-specific output-per-input ratios whose aligned quotients are compared for the same good.Ratio supplies an internal constituent: Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named. Absolute Advantage requires that role within this mechanism: A per-good comparison of output per unit input between two producers — establishing that productivity differences exist (the precondition for gains from trade) while deliberately not settling who should specialize in what. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.
- Comparative Genomic Hybridization Domain-specific presupposes Ratio
The test-to-reference signal ratio is the measurement that turns two hybridization channels into relative copy-number evidence; removing it destroys CGH's comparative identity.Measurement, comparison, normalization, and signal detection are related. Frozen `domain_specific:radiation_hybrid_mapping` is false coverage because marker-retention mapping does not implement the test/reference dosage ratio.
- Cost Efficiency Domain-specific presupposes Ratio
Cost efficiency presupposes a work-comparison ratio.Parallel cost efficiency assesses processor-work against a sequential baseline using a ratio or equivalent multiplicative comparison. The verdict is not itself the quotient, and fixed-factor asymptotic optimality need not satisfy the live Efficiency prime's undominated-frontier criterion.
- GC Skew Domain-specific presupposes Ratio
Normalized GC skew presupposes a nonzero-denominator ratio.At a fixed oriented sequence segment, local GC skew is (G-C)/(G+C) with G+C>0. This is an ordered division of a signed base-count difference by its same-segment G/C reference total, satisfying live Ratio's required scope and denominator semantics. Ratio alone does not supply nucleotide identities, sequence orientation or the interpretation of genomic profiles. Raw cumulative excess is a separate related transform, not a counterexample to the local index's ratio structure.
- Hatta number Domain-specific includes Ratio
An ordered reaction-to-transport ratio is an internal constituent of the model-defined Hatta calculation.A declared reactive gas–liquid model supplies a kinetic/diffusive reaction term and a nonzero physical liquid-side transfer reference. Their aligned ordered quotient is internal to the Hatta calculation; its positive root is reported as Ha. First-order and pseudo-first-order film forms in Perry and the unlike O2–S(IV) bubbling model in Chen et al. each explicitly contain this quotient, while differing in reagents and kinetic inputs. Ratio and its Comparison ancestor supply order, division, aligned scope and relative magnitude; the Hatta identity adds the liquid-side reactive-absorption setting, conditional kinetic law and qualified regime interpretation. Removing the quotient destroys the named comparison. A bare Ratio can exist without Hatta, and the Ratio is inside this calculation rather than an external precondition.
- Missing Denominator Domain-specific presupposes Ratio
Missing Denominator presupposes an intended ratio because the reported numerator is defective only when a reference quantity is required to form its quotient.Ratio supplies the prerequisite condition: Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named. Missing Denominator operates against that background: Expose a count that only looks like information by firing one substrate-independent question — out of how many? — since a numerator reported without its reference population wears the shape of a rate while blocking every quantitative inference the reader needs. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.
- Power (Physics) Domain-specific presupposes Ratio
A physical work or energy amount per time requires an ordered amount-to-duration rate relation, or its instantaneous limit.Average power relates a specified work or energy amount to a nonzero duration; instantaneous power is the limit of such finite rates, not division by zero. Ratio supplies the amount/reference ordering, unit-bearing division, and scope discipline. Power adds the physical process and accounting boundary and is a rate quantity rather than the generic comparison operation. A zero-work rate remains defined without an Energy Transfer process, so no strict edge to that neighbor is asserted.
- Pressure Domain-specific presupposes Ratio
Signed normal force per positive area supplies the ordered per-area relation in mechanical pressure.Pressure is the signed normal force divided by positive area, or an equivalent scalar already expressed per area by the isotropic component of a continuum stress tensor. Negative absolute tensile pressure and a gauge difference retain that signed per-area structure. Ratio supplies the constitutive per-unit relation; Physical Quantity supplies a distinct measurable-kind genus.
- Quasicircle Domain-specific presupposes Ratio
The uniform turning condition presupposes a same-endpoint ratio of smaller connecting-subarc diameter to nonzero chord length.The intrinsic quasicircle criterion divides the smaller connecting-subarc diameter by the positive chord length for every distinct endpoint pair on one planar Jordan curve. The ordered numerator and denominator have the same length units and pairwise scope; their dimensionless quotient is unchanged by common Euclidean scaling and can grow sharply as the chord shrinks. Thus all seven roles of Ratio occur. Ratio inherits Comparison in the live graph, and that ancestor applies literally because the two lengths are aligned within one Euclidean frame before their relative quotient is read. A generic finite bound need not be on a quotient, and a quotient need not have a finite uniform bound, so Ratio and Boundedness contribute independent prerequisites. An ambient-map witness may prove membership without calculating the quotient, but the equivalent intrinsic property still obtains.
- Total return index Domain-specific includes Ratio
The finite-return chaining rule contains an ordered current/prior index-level ratio.The admitted method defines income-inclusive period return and chains it into an index level. On active finite-return updates with a nonzero prior level, I_t/I_(t-1)=1+R_t is a dimensionless ordered current/prior ratio. The current and prior levels share one declared method and period frame; reversal changes the relation, while common rebasing preserves it. The Ratio parent is a necessary internal constituent of the child (parent_in_child), not a genus for the weighted income-accounting and chaining method. Ratio inherits Comparison through co-framed current and prior levels. A zero-prior-level observation requires method-specific continuation or restart treatment; this edge does not decide whether every such observation remains in the named series.
- Type M Error Domain-specific includes Ratio
Type M contains an exaggeration ratio whose numerator is expected significant effect magnitude and whose denominator is true effect magnitude.Ratio supplies an internal constituent: Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named. Type M Error requires that role within this mechanism: Quantify how much a significant effect's reported magnitude is exaggerated by the significance filter under low power, via the exaggeration ratio — the expected significant estimate divided by the true effect — computable from the design before any data exist. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.
- Water potential Domain-specific includes Ratio
The defining energy-to-pressure normalization contains an ordered Ratio of water chemical-potential difference to nonzero water molar volume.The numerator is the referenced water chemical-potential difference in energy per mole; the denominator is the model-appropriate nonzero water molar volume under compatible reference, temperature and unit conventions. Ordered division yields energy per volume, hence pressure, with scope and units retained. The quotient survives common rescaling of both molar representations, but reversing the terms or replacing the reference volume changes its meaning. This whole Ratio operation is an identity-bearing constituent of the water-state quantity, not a requirement to measure it. Water potential adds the water bearer, pure-water zero, sign and model conventions. A Ratio can exist without those water-specific commitments.
- Weber's Law Domain-specific includes Ratio
The Weber fraction is literally the ordered ratio of just-noticeable change to nonzero baseline stimulus magnitude.Weber's law is defined by k = delta I divided by I. Ratio supplies the numerator, nonzero reference denominator, division, units, and scale interpretation internal to that expression; the domain law adds perceptual detectability, modality constancy, and a bounded sensory regime.
- Proportion and Scale Prime is a decomposition of Ratio
Removing the art-and-design frame leaves the ordered ratio relation among relative dimensions and their reference quantity.Proportion and scale adds compositions, visual harmony, viewer-relative sizing, and aesthetic or functional judgment to the portable ratio relation; common rescaling preserves the underlying quotient.
Hierarchy path (1) — routes to 1 parentless root
- Ratio → is a kind of Comparison
Neighborhood in Abstraction Space¶
Ratio sits in a sparse region of abstraction space (94th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely rather than landing on a neighbor.
Family — Quantitative Relationships & Scaling (6 primes)
Nearest neighbors
- Proportion and Scale — 0.69
- Order of Magnitude — 0.68
- Rank-Dependent Value — 0.68
- Statistical syllogism — 0.67
- Frame of Reference — 0.67
Computed from structural-signature embeddings · 2026-10-25
Not to Be Confused With¶
- Comparison is the genus and can be qualitative, ordinal, additive, or multiplicative; ratio fixes the comparison to ordered division.
- Proportion and Scale uses ratios of dimensions inside an art-and-design frame; removing that frame leaves this prime.
- Probability is a normalized measure on events and lies between zero and one; many ratios satisfy neither condition.
- Normalization is a rescaling purpose that may use division but can also use norms, maxima, standard deviations, or affine transforms.
- Dimensional Analysis governs which unit-bearing expressions are coherent; ratio is one operation whose output dimensional analysis audits.
Solution Archetypes¶
No catalogued solution archetypes reference this prime yet.