Koomey's law¶

The empirical trajectory by which computations delivered per joule dissipated have doubled about every 1.57 years (slowing to ~2.6 after Dennard scaling broke in 2005), tracking the energy cost of a logical operation toward the Landauer floor.

Version: v2 · 2026-09-19 · History
Domain-specific #: 604
Domain group: Applied Sciences & Engineering
Origin domain: Computer Science & Software Engineering
Subdomains: Information Technology, Computing Hardware → Computer Science & Software Engineering

Core Idea¶

Koomey's law is the observation that computations delivered per joule dissipated doubled roughly every 1.57 years from the mid-1940s to about 2000, slowing to about 2.6 years after Dennard scaling broke down around 2005. Where Moore's law tracks transistor density, Koomey's law tracks the energy cost of a logical operation — how cheaply each switching event can be performed. During Dennard scaling the mechanism was feature shrinkage and voltage reduction; after, it shifted to architectural specialization. It has a hard thermodynamic floor: Landauer's kT ln 2 per irreversible bit erasure.

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More Thinking per Battery

Computers keep learning to do their thinking using less energy. It's like a toy car that goes farther and farther on the same little battery each year. For a long time, the amount of work from one bit of energy doubled every year and a half or so. Lately it has been growing more slowly.

Twice the Work, Same Energy

Koomey's law is the pattern that the number of calculations a computer can do with the same amount of energy keeps doubling. From the 1940s to about 2000 it doubled roughly every year and a half, and later it slowed to about every two and a half years. Moore's law is about how many tiny switches fit on a chip, but Koomey's law is about how little energy each switch-flip costs. This matters for things that run on batteries, like phones and smartwatches. Physics sets a minimum energy for erasing a bit of information, so the trend has to stop someday.

Energy-per-Computation Doubling Law

Koomey's law, published by Jonathan Koomey in 2010, observes that computations per joule doubled about every 1.57 years from the mid-1940s to around 2000, then slowed to about every 2.6 years. Moore's law tracks how many transistors fit on a chip; Koomey's law tracks the energy cost of each logical operation. Early gains came from shrinking transistors, which allowed lower voltages and less energy per switch, plus smarter chip designs. When voltages stopped dropping around 2005 because of leakage currents, progress relied more on specialized and parallel designs, so it slowed. Landauer's principle sets a minimum energy for erasing a bit, giving the trend a physical floor. The law decides what battery-powered devices can do, since their limit is energy, not transistor count.

Koomey's law is an empirical trend: computations per joule dissipated doubled about every 1.57 years from the mid-1940s to about 2000. The doubling time stretched to about 2.6 years after Dennard scaling broke down around 2005. It measures energy per logical operation, an axis distinct from Moore's law's transistor density. In the Dennard era, shrinking features lowered capacitance and supply voltage. Switching energy scales roughly as CV^2, so energy per operation fell, while pipelining, caching, and microarchitectural gains extracted more work per joule. Below about 100 nm, leakage currents halted voltage reduction. Gains then came from specialization, parallelism, and dark-silicon management. Landauer's principle gives a hard floor of kT ln 2 per irreversible bit erasure, about 2.8 × 10^-21 J at room temperature; extrapolation reaches it around 2050–2100 depending on the doubling time. The law sets feasibility for battery-limited computing, from phones and wearables to edge inference: a workload becomes deployable when energy per operation drops below the available battery energy divided by the operations required.

Scope of Application¶

Koomey's law lives entirely within computing — across the hardware, infrastructure, and systems subfields where the energy cost of a logical operation is the design variable.

Semiconductor roadmapping — the curve set as a per-generation efficiency target (ITRS, IRDS).
Data-center and IT-infrastructure planning — efficiency versus workload growth setting aggregate demand.
Mobile, wearable, and embedded design — the feasibility threshold for battery-limited products.
AI cost-of-training and edge inference — dating when a model class ships at watt-scale power.
Computer-architecture analysis and ICT environmental policy — the orthogonal energy-per-operation axis.

Clarity¶

Naming Koomey's law separates how much computing a chip delivers from how cheaply per joule it delivers it. Against the count-and-speed axis a stalled-clock era looks like progress halting; the energy axis shows it still improving by orders of magnitude. It makes the 2005 regime break legible as an efficiency slope change and locates the trajectory against a thermodynamic floor rather than lithographic ceilings.

Manages Complexity¶

The full stack of what makes a battery-powered product feasible — node, voltage, microarchitecture, cooling, workload, battery — collapses into one exponential in computations per joule, summarized by two scalars: current energy-per-operation and doubling time. Projecting the curve reads off feasible-now, feasible-in-N-doublings, or never, with a known regime break at 2005 and a fixed Landauer endpoint.

Abstract Reasoning¶

It supports feasibility forecasting (convert "is this buildable?" into a date), slope-selection and regime diagnosis around the 2005 break, axis-decomposition (separate "stopped getting faster" from "stopped getting efficient"), floor-bounded extrapolation against Landauer's kT ln 2, and an aggregate-consumption inference coupling efficiency to workload growth.

Knowledge Transfer¶

Within computing Koomey's law transfers as a working trend-line wherever the energy axis of silicon is the binding constraint — the same observable, floor, and slope-selection discipline carry across roadmapping, data-center planning, embedded design, and AI projection. Beyond computing, "a Koomey's law for X" is analogy, borrowing the shape while dropping Dennard scaling and the thermodynamic bound. The genuinely portable skeleton was never Koomey-specific: it is carried by exponential_growth, Learning Curve Effects (Wright's law), and physical_limits, with Landauer's bound merely computing's value of the floor.

Relationships to Other Abstractions¶

Current abstraction Koomey's law Domain-specific

Parents (2) — outgoing typed relations

Koomey's law includes Irreducible Floor Prime

Koomey's Law contains an Irreducible Floor because Landauer's thermodynamic cost per irreversible bit erasure bounds the total efficiency gain remaining under the law's computational premise.
Koomey's law is a decomposition of Exponentiation Prime

Koomey's Law extracts Exponentiation because computations delivered per joule follow an empirical doubling-time trajectory whose slope can be measured separately before and after a regime break.

Hierarchy paths (3) — routes to 3 parentless roots

Koomey's law → includes Irreducible Floor → is a kind of Constraint

Show alternative paths (2)

Neighborhood in Abstraction Space¶

Koomey's law sits in a sparse region of the domain-specific corpus (82^nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2769 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25