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.

Version: v4 · 2026-09-19 · History · 3 corrections
Domain-specific #: 409
Domain group: Social Sciences
Origin domain: Psychology & Behavioral Sciences
Subdomain: Motor Control and HCI → Psychology & Behavioral Sciences

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.

How would you explain it like I'm…

Far and Tiny Takes Longer

When you reach to tap something, it takes longer if it is far away or very tiny. But making it twice as far doesn't take twice as long. It only adds a little extra bit of time each time you double it.

The Pointing Time Rule

Fitts's Law says the time to point at a target depends on two things: how far away it is and how big it is. Far and small targets take longer than close and big ones. The surprising part is how the time grows. If you double the distance, you don't double the time; you add about the same small extra amount each time you double. Computer designers use this, for example by making buttons bigger or putting them at the edge of the screen, where the mouse stops and can't overshoot.

Logarithmic Speed-Accuracy Law

Fitts's Law predicts movement time for aiming at a target: MT = a + b·log₂(2D/W), where D is the distance to the target and W is its width. The log term is called the index of difficulty, measured in bits. Because the relationship is logarithmic rather than linear, doubling the distance adds a constant chunk of time, and doubling the width removes a constant chunk, instead of halving the time. The constants a and b are fitted from experiments: a covers the overhead of getting started, and b is the time cost per bit. The law holds for fingers, mice, styluses, touchscreens, VR controllers and even gaze-driven cursors, with a and b adjusted. That is why screen-edge targets, which act as if they were infinitely wide, are so fast to hit.

Fitts's Law is an empirical regularity in aimed movement: MT = a + b·log₂(2D/W). D is the centre-to-centre distance and W is the target width, meaning the spatial tolerance for acquiring it. The intercept a captures response-initiation overhead. The slope b is a cost in seconds per bit, and its reciprocal is a rate in bits per second. The index of difficulty, ID = log₂(2D/W), comes from treating the movement as sending spatial information through a noisy motor channel, by analogy with Shannon's channel capacity. That framing is an interpretive lens used to motivate the law, not an established mechanism. The key claim is that the speed-accuracy trade-off is logarithmic. Fitts's original index of performance was ID/MT computed condition by condition. Reading 1/b as throughput is a later convention, and it matches Fitts's measure only if a = 0. For that reason, modern work reports effective throughput, IDe/MT. In HCI the law justifies edge-placed targets, which have effectively infinite width, enlarging small targets before moving them closer, and comparing devices by throughput.

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) — outgoing typed relations

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 → is a decomposition of Channel Capacity

Neighborhood in Abstraction Space¶

Fitts's Law sits in a moderately populated region (58^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Usability & Interaction Design Failures (13 abstractions)

Nearest neighbors

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