Fitts's law

Fitts's law predicts the time (MT) to move to a target of width W at distance D, given by MT = a + b log₂(2D/W), where a and b are empirical constants. The logarithmic term, called the index of difficulty (ID), captures the trade-off between speed and accuracy. The law is derived from information theory, treating the movement as a signal with limited channel capacity. It applies to both one-dimensional and two-dimensional pointing tasks, and it has been validated across many input devices, including mice, touchscreens, and trackballs.

In user interface design, Fitts's law guides the placement and sizing of interactive elements. Larger targets and shorter distances reduce movement time, so designers make important buttons big and place them near the user's current position. The law also explains why menu items at the edges of a screen are easier to click: the screen edge effectively extends the target's width infinitely, a phenomenon known as the 'magic corner.' Touchscreen guidelines, such as Apple's 44-point minimum touch target, are directly influenced by Fitts's law.

Researchers have proposed several extensions to the original model. The two-part model (Welford) and the Shannon formulation (MacKenzie) adjust the ID to better fit empirical data. The law has been extended to 3D movements, eye-gaze pointing, and even foot-operated controls. In addition, the 'steering law' (Accot and Zhai) applies Fitts's law to path-following tasks, such as navigating a menu or drawing a line. These variations maintain the core principle that movement time is a function of task difficulty.

Fitts's law has roots in military research: Paul Fitts developed the model while studying aircraft cockpit controls for the U.S. Air Force. The original 1954 paper used a stylus tapping task, not a computer mouse. The law also applies to non-computer tasks, such as reaching for a cup or pressing a button. In accessibility, it informs the design of switch-accessible interfaces and eye-tracking systems. A notable edge case is that the law breaks down for very small targets due to tremor and for very large distances due to fatigue.

Index of difficulty

A measure of task difficulty in Fitts's law, calculated as log₂(2D/W).

Throughput

A performance metric derived from Fitts's law, measured in bits per second.

Steering law

An extension of Fitts's law for path-following tasks, proposed by Accot and Zhai.