Fitts's Law is a mathematical model of human motor control proposed by Paul Fitts in 1954 that predicts movement time (MT) from target distance (A) and target width (W). Expressed as MT = a + b × log2(2A/W), it demonstrates a logarithmic relationship where higher index of difficulty (ID = log2(2A/W)) requires longer movement time. It is widely applied as the theoretical foundation for HCI design and aim training.
Mathematical Foundation of Fitts's Law
Fitts's Law is grounded in information theory, modeling pointing movements as an information transmission channel. The Index of Difficulty (ID) is calculated as log2(2A/W), measured in bits. Movement time increases linearly with ID, and the reciprocal of the slope (1/b) corresponds to Fitts' index of performance, in bits per second. The law has been applied to input devices such as the mouse, as well as to studies of foot tapping and head movement.
Relationship to Aim Testing
An aim test asks you to point at and click on-screen targets quickly, which is the kind of pointing movement Fitts's Law describes. Under Fitts's Law, smaller and more distant targets raise the difficulty, and movement time grows logarithmically.
Optimizing the Speed-Accuracy Tradeoff
Fitts's Law describes the speed-accuracy tradeoff in motor control. Faster movements increase motor noise (variability), raising the probability of missing targets. One account divides an aiming movement into an initial ballistic phase that brings the cursor near the target and a final feedback-controlled correction phase.