# Fitts's law

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Fitts's law (often cited as Fitts' law) is a model of human movement in human-computer interaction and ergonomics which predicts that the time required to rapidly move to a target area is a function of the distance to and the size of the target. Fitts's law is used to model the act of pointing, either by physically touching an object with a hand or finger, or virtually, by pointing to an object on a computer display using a pointing device. It was proposed by Paul Fitts in 1954.

## Contents

### Model

Fitts's law has been formulated mathematically in several different ways. One common form is the Shannon formulation (proposed by Scott MacKenzie, professor of York University, and named for its resemblance to the Shannon–Hartley theorem) for movement along a single dimension:

where:

• T is the average time taken to complete the movement. (Traditionally, researchers have used the symbol MT for this, to mean movement time.)
• a represents the start/stop time of the device (intercept) and b stands for the inherent speed of the device (slope). These constants can be determined experimentally by fitting a straight line to measured data.
• D is the distance from the starting point to the center of the target. (Traditionally, researchers have used the symbol A for this, to mean the amplitude of the movement.)
• W is the width of the target measured along the axis of motion. W can also be thought of as the allowed error tolerance in the final position, since the final point of the motion must fall within ±W2 of the target's center.

From the equation, we see a speed–accuracy trade off associated with pointing, whereby targets that are smaller and/or further away require more time to acquire.

### Success and implications

Fitts's law is an unusually successful and well-studied model. Experiments that reproduce Fitts's results and/or that demonstrate the applicability of Fitts's law in somewhat different situations are not difficult to perform. The measured data in such experiments often fit a straight line with a correlation coefficient of 0.95 or higher, a sign that the model is very accurate.

Although Fitts only published two articles on his law (Fitts 1954, Fitts and Peterson 1964), there are hundreds of subsequent studies related to it in the human-computer interaction (HCI) literature, and quite possibly thousands of studies published in the larger psychomovement literature. The first HCI application of Fitts's law was by Card, English, and Burr (1978), who used the index of performance (IP), defined as 1b, to compare performance of different input devices, with the mouse coming out on top. This early work, according to Stuart Card's biography, "was a major factor leading to the mouse's commercial introduction by Xerox".[1]