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In ergonomics, Fitts' law (or Fitts's law) is a principle of human movement published in 1954 by Paul Fitts which predicts the time required to move from a starting position to a final target area. The kind of motion it describes is aimed and rapid. The time needed to acquire a target is a function of the distance to the target, and the size of the target. Fitt's law is used to model the act of pointing, both in the real world, e.g. with a hand or finger, and on a computer, e.g. with a mouse.
Mathematically, Fitts' law has been formulated a few different ways. One common form is the Shannon formulation (due to its resemblance to Shannon's theorem), which, for movement along a single dimension, states
where
From the equation, we see a speed-accuracy tradeoff associated with pointing, whereby targets that are smaller and/or further away require more time to acquire.
The logarithm in Fitts' law is called the index of difficulty ID for the target, and has units of bits. We can rewrite the law as
Thus the units for b are time/bit, e.g. milliseconds/bit. The reciprocal of b is the index of performance IP = 1/b, with units bits/time.
The values for a, b, and IP change as the conditions under which pointing is done are changed. For example, a mouse and stylus may both be used for pointing, but have different constants a, b, IP associated with them. Since IP is the reciprocal of the slope of the line T = a+b ID, it follows that IP is a measure of how quickly pointing tasks can be completed (in bits/time), independent of the particular targets involved.
Slightly different from Shannon's formulation is the original formulation by Fitts
The factor of 2 here is not particularly important; this form of the ID can be rewritten with the factor of 2 absorbed as changes in the constants a, b. The "+1" in the Shannon form, however, does make it different from Fitts' original form. The Shannon form has the advantage that the ID is always non-negative, and has been shown to better fit measured data.
Fitts' law is an unusually successful and well-studied model. Experiments that reproduce Fitts' results, and/or demonstrate the applicability of Fitts' law in somewhat different situations, are not difficult to perform. The measured data in such experiments often fits a straight line with a correlation coefficient of 0.95 or higher, a sign that the model is very accurate.
Although Fitts himself only published two articles on his law (Fitts 1954, Fitts and Peterson 1964), there have been 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 application of Fitts' law to HCI was by Card et al. (1978), who used the index of performance IP to compare the performance of different input devices. Fitts' law has been shown to apply under a variety of conditions, with many different limbs (hands, feet, head-mounted sights, eye gaze), manipulanda (i.e. input devices), physical environments (including underwater!), and user populations (young, old, retarded, and drugged participants). Note that the constants a, b, IP have different values under each of these conditions.
Since the advent of graphical user interfaces, Fitts' law has been applied to tasks where the user must position the mouse pointer over an on-screen target, such as a button or other widget. Fitts' law can be used to model both point-and-click and drag-and-drop actions (note that dragging has a lower IP associated with it, because the increased muscle tension makes pointing more difficult). Despite the appeal of the model, it should be remembered that in its original and strictest form:
If, as generally claimed, the law does hold true for pointing with the mouse, some consequences for user interface design are
Fitts' law remains one of the only hard, reliable predictive models in human-computer interaction, joined more recently by Accot's steering law, which itself is derived from Fitts' law.
See also Hick's law
Fitts' law can be derived from various models of motion. A very simple model, involving discrete, deterministic responses, is considered here. Although this model is overly simplistic, it provides some intuition for Fitts' law.
Assume that the user moves toward the target in a sequence of submovements. Each submovement requires a constant time t to execute, and moves a constant fraction 1-r of the remaining distance to the centre of the target, where 0 < r < 1. Thus, if the user is initially at a distance D from the target, the remaining distance after the first submovement is rD, and the remaining distance after the nth submovement is rnD. (In other words, the distance left to the target's centre is a function that decays exponentially over time.) Let N be the (possibly fractional) number of submovements required to fall within the target. Then,
Solving for N,
| N | <math>= \log_r \frac{W}{2D}<math> | |
| <math>= \frac{1}{log_2 r} \log_2 \frac{W}{2D}<math> | (because logxy = (logzy)/(logzx)) | |
| <math>= \frac{1}{log_2 1/r} \log_2 \frac{2D}{W}<math> | (because logxy = - logx1/y) |
The time required for all submovements is
By defining appropriate constants a and b, this can be rewritten as
The above derivation is similar to one given in Card, Moran, and Newell (1983). For a critique of the deterministic iterative-corrections model, see Meyer et al. (1990).
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