Fitts's Law

Fitts’s Law

The model of pointing: the time to move a pointer (mouse cursor, fingertip) to a target grows with the distance to it and shrinks as the target gets larger, and only logarithmically in the ratio — so target size buys more than proximity does. The single most-used law in UI layout. The sibling laws and the pattern-level mapping live in UI Interaction Laws.

Formula

Let $D$ = distance to target center (also written $A$, amplitude), $W$ = target width along the axis of motion, $MT$ = movement time, $a$/$b$ = empirical constants (device + user + setup).

Fitts’s original 1954 index of difficulty: $ID = \log_2(2D/W)$ bits.
MacKenzie’s 1992 “Shannon” reformulation (modern standard, ISO 9241-9): $ID = \log_2(D/W + 1)$ bits — fits data better and never goes negative (the original can go negative for close, large targets).
Movement time is linear in difficulty: $MT = a + b\cdot ID$.
$a$ = fixed overhead (reaction + press), target-independent. $b$ = seconds per bit, the device’s cost of difficulty.

⚠️ Naming caution: the form $\log_2(2D/W)$ is often called “Shannon” but is actually Fitts’s original index. The genuine Shannon (MacKenzie 1992) form is $\log_2(D/W + 1)$. They agree when $D \gg W$.

Throughput

$TP = ID_e / MT$ in bits/s, where the effective width $W_e = 4.133\,\sigma$ is re-measured from the actual scatter of users’ endpoints ($\sigma$ = std. dev. of hits). This “adjust for the errors they really made” step lets throughput fairly compare devices. Mouse ≈ 3.7–4.9 bits/s; direct finger touch often higher (~6–11 bits/s).

2-D targets: use the dimension along the line of approach, or the smaller of width/height (min model, MacKenzie & Buxton 1992). Wide-thin buttons are easy horizontally, fiddly vertically.
Small-target error floor: below some size, aiming noise dominates and error rates climb — the empirical basis for minimum-size guidelines.

Corollaries designers use

Bigger + closer = faster; prefer size over proximity (the log).
Screen edges and corners are effectively infinite targets: the pointer stops at the edge, so $W\to\infty$ along that axis and $ID\to 0$, $MT\to a$. Corners are infinite on both axes — the prime pixels / magic corners, the four fastest points on screen. Powers the macOS menu bar (top edge) and Windows Start (corner); Tognazzini reports the edge-pinned Mac menu bar is ~5× faster than a Windows in-window menu bar.
Magic pixel / one-pixel tax: the benefit needs the target to truly reach the edge; a single non-clickable pixel of gap costs ~20–30% (Tognazzini).
Context menu → $D\approx 0$: opens at the cursor, so travel vanishes and $MT\to a$. Fastest non-keyboard acquisition; cost is discoverability.
Fittsize: reduce the number of acquisitions, not only size/distance.

Building blocks as Fitts artifacts

Minimum tap targets (the small-target floor as policy, ~9 mm physical): Apple 44 pt, Material 48 dp, WCAG 2.5.8 24 CSS px (AA, with a spacing exception), WCAG 2.5.5 44 CSS px (AAA). Hit target ≠ visual size — pad a small icon out to the minimum.
FAB: large (56 dp), fixed position (muscle memory), near the thumb zone.
Segmented control: contiguous targets, no gaps → tiny $D$, no dead space.
Dock magnification: dynamic $W$; debated, since a growing icon can shift under the pointer and violate the fixed-target assumption.
Toolbar vs overflow (“⋯”/kebab): visible = one acquisition; hidden = an extra one, same tax as the hamburger. Surface frequent, bury rare.

UI Interaction Laws — the steering law, the thumb zone, the command-palette bypass, and which law governs which pattern.