Fitts’s law

In 1954 the psychologist Paul Fitts asked people to tap back and forth between two metal plates with a stylus, as fast as they could, and changed how wide the plates were and how far apart.

He found that the time grew with a single number: the distance divided by the width. Double the distance or halve the width and the movement gets harder by the same fixed step. He borrowed the idea from information theory, the mathematics of sending messages down a wire, and measured difficulty in bits. The form used today, time = a + b × log₂ (distance ÷ width + 1), was set out by Scott MacKenzie² in 1992.

In 1978 Stuart Card and colleagues at Xerox used it to compare ways of pointing at a screen, and the mouse beat the joystick and the arrow keys, years before most people had seen one. Its slope, they noted, was close to that of the hand pointing on its own.

The time grows with the logarithm, a curve that climbs steeply at first and then flattens. So doubling a small button helps a great deal, and doubling a large one helps very little.

The edges of a screen are a lovely consequence. The pointer stops when it reaches one, so a target along the edge cannot be overshot: the designer Bruce Tognazzini calls it “infinitely deep”⁴. That is why the Mac’s menu bar, fixed to the top of the screen, is faster to hit than a menu inside a window. Pie menus, which open in a ring around the pointer, put every item the same short distance away; in a 1988 study they were about 15% faster than a list.

The numbers a and b are not universal. They change from person to person and device to device, by as much as four times between studies, which is why this page fits the line to you. For anyone with a tremor or an unsteady hand, the slope is steeper still, and a phone number set in small type is harder to hit than it looks.

Fitts’s law describes the reach for the button, and nothing before or after it.

It does not include the time spent reading the options, deciding which one you want, or recovering from a mistake. On touchscreens, a fingertip is less precise than a pointer, and the plain law breaks down for small targets; a version called FFitts law⁶ (2013) accounts for the finger. And when the pointer has to travel along a path, as through a cascading menu, a different rule applies, the steering law⁷, and the time grows much faster with every step narrower the path gets.