Fitts's Law¶

Predict how long an aimed reach takes as a logarithmic function of target distance over target width — MT = a + b·log₂(2D/W) — treating the movement as transmission across a finite-throughput motor channel.

Core Idea¶

Fitts's law (1954) is the empirical regularity that the time to move an effector to acquire a target is a logarithmic function of the ratio of target distance to width: MT = a + b·log₂(2D/W). Here log₂(2D/W) is the index of difficulty, a is response-initiation overhead, and b is the inverse throughput of the movement channel, derived from Shannon channel-capacity theory. The trade-off is logarithmic, not linear.

Scope of Application¶

The law applies wherever its one precondition holds: a single aimed effector-to-target reach to a tolerance-bounded spatial target.

Human-computer interaction — predicting pointing time for mice, touchscreens, styli, and eye trackers.
Motor-control psychology — the founding model of the speed-accuracy trade-off in aimed movement.
Robotics and teleoperation — end-effector positioning and haptic-interface design.
Sport science — aiming and reaching tasks with practitioner-specific constants.
Accessibility engineering — a motor impairment surfacing as an elevated slope b, corrected by inflating width.

Clarity¶

Before Fitts's law the speed-accuracy trade-off was a qualitative observation with no way to say how much harder a small far target was. The law makes difficulty measurable, collapsing distance and tolerance into one index, log₂(2D/W). Its sharpest move is fixing the shape as logarithmic, correcting the intuition that a button twice as wide is twice as easy, and supplying a bits-per-second comparison currency.

Manages Complexity¶

An enormous grid — every distance-and-width pair, effector, modality, and population a distinct condition — collapses along three axes at once: the two geometric variables fuse into one index of difficulty, each device reduces to two constants (a and b), and every channel gets a common currency (1/b in bits per second). The analyst then tracks only the index, the two constants, and which term dominates.

Abstract Reasoning¶

The law licenses a predictive move (compute movement time before anyone moves and rank unbuilt layouts), an interventionist move (read the leverage point off which term dominates — edge-parking driving effective width to infinity), and a diagnostic move (fit a and b to separate overhead from channel throughput). A boundary-drawing move keeps these inside the aimed-movement regime and marks the logarithmic floor as untrainable.

Knowledge Transfer¶

Fitts's law is a quantitative law, so it transfers literally wherever its precondition holds — a single aimed reach — with a and b re-fit but the logarithm intact across mice, styli, eye trackers, robotic end-effectors, and reaching tasks; these are one substrate type, not analogies. It ceases to apply, rather than weakening into metaphor, when difficulty comes from choosing among options (Hick's law). The cross-domain principle it instantiates is the parent information_theory_channel_capacity and the power_law/log-scaling family.

Relationships to Other Abstractions¶

Current abstraction Fitts's Law Domain-specific

Parents (1) — more general patterns this builds on

Fitts's Law is a decomposition of Channel Capacity Prime

Fitts's Law is Channel Capacity applied to aimed movement, treating target acquisition as transmission of spatial information through a noisy finite-throughput motor channel.

Hierarchy path (1) — routes to 1 parentless root

Fitts's Law → Channel Capacity

Neighborhood in Abstraction Space¶

Fitts's Law sits in a sparse region of the domain-specific corpus (68^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Psychophysical Laws of Perception (10 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12