Motor control and aiming: Fitts's law and the fit of the body to the interface

Fitts's law stands out among design rules because it rests on a measured relation. Point at a target, and the time the movement takes grows with the distance and shrinks as the target widens. The relation is close enough to a straight line that one equation predicts most of the data. The rule sizes buttons, ranks input devices and settles arguments about layout. The eight units before it described a mind that perceives, attends, remembers and decides. This one closes the loop through the hand. The regularity is real and the trade-off behind it is stable. The constants, however, were measured on one body doing one task on one apparatus. The strongest counter is that the law is robust enough to be standardised: Soukoreff and MacKenzie (2004) recommend throughput as the dependent measure and a fixed reporting protocol, against which one device can be ranked against another. A precise time read into a touch target, a direction the model was not fitted on, or a hand unlike the one in the study goes beyond what the evidence licenses.

Separate the law as a description from the explanations of it, and treat the constants as measurements belonging to a task.

The law is a regularity, and its explanation is a separate matter

Fitts (1954) had participants move a stylus back and forth between two targets on a tablet, varying the distance between them and their width. He found that movement time rose with the logarithm of distance over width, while the information handled per unit of time stayed roughly constant. The relation held across several versions of the task, so the law was not an artefact of one procedure. MacKenzie (1992) compared the competing formulations against pointing data. They differ systematically and change the times they predict, and he recommended the Shannon formulation for design use. The law is a family of equations rather than one number, so quoting a time means naming an equation.

Work the trade-off on one pair of targets. A button 100 pixels away and 20 wide has an index of difficulty of about 2.6 bits on the Shannon formulation. Double the distance to 200, and the index rises by about 0.9 of a bit. Halve the distance, or double the width, and it falls by about 0.8, so the two changes buy the same time. The case shows the shape of the trade-off. It does not give a time in milliseconds, which needs the fitted constants for the device in front of you.

The constants were measured on one apparatus, and they move with the task

Card, English and Burr (1978) compared four devices for selecting text on a screen. The mouse was fastest on every measure and had the lowest error rate. A Fitts's law fit accounted for the variation in the mouse and the joystick, with a slope close to the best seen in other eye-hand tasks. So the law does travel to a new device, but the constants were re-estimated rather than carried over.

MacKenzie and Ware (1993) added lag between the pointer's movement and the display. At the highest lag they tested, 225 milliseconds, movement times rose by 64 per cent and error rates by 214 per cent against the no-lag condition. A model in which lag multiplies the index of difficulty accounted for 94 per cent of the variance, beating one in which lag merely adds a constant. Lag changes the movement itself rather than merely delaying its result. A slow connection or a low-end device supplies the same lag, so the cost is a condition of the network as well.

Read into touch and unusual targets, a number outruns the evidence

Chakraborty and Yadav (2022) reviewed four decades of attempts to apply the law to touch, collecting studies that reported positive, null and negative results. They concluded that the body of work is small, and that there is no consensus on whether the law holds for touch. Zhang (2023) ran two experiments on a 24-inch touch screen, one tilted and one horizontal. The study found a periodic effect of movement direction that the standard index of difficulty does not capture, so a model fitted on left-to-right movement mispredicts elsewhere. Zhang (2025) extended the touch work to a 65-inch screen, where the shoulder joins the movement. Conventional Fitts's law there explained at most 80 per cent of the variance, because performance was driven by amplitude rather than by the ratio of distance to width. The paper proposes an amended index of difficulty, with a calibration term read as a property of the pointing dynamics, and raises the fit above 0.97 for finger and pen input. Accot and Zhai (2003) had shown earlier that a two-dimensional target is not a wider version of a one-dimensional one. For width to height ratios between one and two, a Euclidean model with one free weight fitted better than the models then in use.

Work the target shape. A toolbar button is 44 pixels wide and 24 high, so it is wider than it is tall. Accot and Zhai (2003) found that for width-to-height ratios between one and two the amplitude of the movement dominated, and not the narrow dimension. Reading the width as the difficulty of a two-dimensional target therefore mis-sizes it. The case shows that a target is not a wider version of a bar. It does not give the updated index for a 44 by 24 button, which needs the fitted model rather than a rule of thumb.

Contested question: what sets the movement time, and what can one number mean?

The literature disagrees on a psychological question and a practical one. The psychological question is what the curve is a curve of. Fitts's own account treated the movement as the transmission of information through a limited channel, which is why the index of difficulty is measured in bits. Crossman and Goodeve (1983) derived the law from a different premise, a hand under continuous feedback control. Their velocity-control model fitted the motion time data equally well, and they argued from recorded trajectories for intermittent correction by impulses recurring about ten times a second. Schmidt and colleagues (1979) proposed a third mechanism, in which accuracy is limited by variability in the motor output that grows with the force and the distance of the movement. Meyer and colleagues (1988) modelled the movement as a primary submovement and an optional correction, both programmed to minimise total time at a high hit rate. They found the submovement durations, and not only the average totals, followed a square-root form of the law. The four mechanisms fit the same average data, so the curve does not choose among them, and the practical dispute turns on the definition of throughput, which is a modelling choice rather than a finding.

• Information capacity. The task demands information, in bits, and the channel supplies it at a roughly fixed rate (Fitts, 1954; MacKenzie, 1992).
• Intermittent feedback control. The hand is corrected in impulses about ten times a second (Crossman and Goodeve, 1983).
• Motor-output variability. Error grows with the force and the distance, so speed is bought with accuracy (Schmidt et al., 1979).
• Optimised submovements. A primary movement plus an optional correction minimise total time at a high hit rate (Meyer et al., 1988).

The practical question is whether one number can stand for a device. Soukoreff and MacKenzie (2004) reviewed 24 published Fitts's law models of the mouse and 9 studies using the ISO 9241-9 protocol. They made seven recommendations for reporting, among them the Shannon formulation, difficulties from 2 to 8 bits, and a recorded scatter of movement end points. They recommend throughput, the ratio of difficulty to time, as the dependent measure. Zhai (2004), in the same issue, argued the opposite. On his view throughput so defined is ill-defined. It changes with the range of difficulties used, and cannot be generalised beyond the distances and widths tested. Index of difficulty over movement time equals a constant only when the intercept is zero. He would keep slope and intercept apart, the intercept giving the non-informational cost and the slope the informational part. What would settle it is a reanalysis with the intercept reported and the range of difficulties varied on purpose. Until then a quoted throughput should carry its protocol and its range.

While the dispute is open, a designer can act on what both readings allow. Use the law to rank options and bound expectations, and re-measure the constants for the device, the direction and the hand in front of you, because an ageing hand is a different body. Treat a quoted millisecond figure as an estimate valid for the task that produced it, and prefer a large close target to a small distant one, because that trade-off is stable across the accounts.

Where the argument is heading

The direction of travel is away from one universal constant and towards models that declare their conditions. Chakraborty and Yadav (2022) call for a common protocol so that touch results can be compared. Zhang (2023, 2025) is an instance of the work such a protocol would enable, a model extended first to direction and then to the scale of the display rather than a further estimate of a single slope. Soukoreff and MacKenzie (2004) tie the practice to the ISO 9241-9 standard and to a fixed way of reporting error.

The sources this unit rests on

• Accot, J. and Zhai, S. (2003). Refining Fitts' law models for bivariate pointing. Proceedings of CHI '03, 193-200. doi:10.1145/642611.642646 Extended Fitts's law to two-dimensional targets and found that for width-to-height ratios between one and two the amplitude of the movement dominated the directional constraint, with a Euclidean model of one free weight fitting better than earlier models.
• Card, S. K., English, W. K. and Burr, B. J. (1978). Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT. Ergonomics, 21(8), 601-613. doi:10.1080/00140137808931762 Compared four devices for text selection and found the mouse fastest on every measure and lowest in errors, with a Fitts's law fit accounting for the mouse and the joystick.
• Chakraborty, P. and Yadav, S. (2022). Applicability of Fitts' law to interaction with touchscreen: review of experimental results. Theoretical Issues in Ergonomics Science, 24(5), 532-546. doi:10.1080/1463922x.2022.2114034 Reviewed studies reporting positive, null and negative results on whether Fitts's law applies to touchscreen interaction, with the modifications proposed for the model. It found the body of work small and the verdict unsettled.
• Crossman, E. R. F. W. and Goodeve, P. J. (1983). Feedback control of hand-movement and Fitts' law. Quarterly Journal of Experimental Psychology A, 35(2), 251-278. doi:10.1080/14640748308402133 Derived Fitts's law from a hand under continuous feedback control, found it fitted the motion time data equally well, and argued from recorded trajectories for intermittent correction by impulses recurring about ten times a second.
• Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47(6), 381-391. doi:10.1037/h0055392 Had participants move a stylus between targets of varying distance and width and found movement time rose with the logarithm of distance over width while the information handled per unit of time stayed roughly constant. It is the founding measurement, and its stylus-and-tablet task is what the unit's caution is about.
• MacKenzie, I. S. (1992). Fitts' law as a research and design tool in human-computer interaction. Human-Computer Interaction, 7(1), 91-139. doi:10.1207/s15327051hci0701_3 Compared the competing formulations of Fitts's law, showed they differ systematically and change the predicted times, and recommended the Shannon index of difficulty for design.
• MacKenzie, I. S. and Ware, C. (1993). Lag as a determinant of human performance in interactive systems. Proceedings of INTERCHI '93, 488-493. doi:10.1145/169059.169431 Added lag between pointer movement and display and found that at 225 milliseconds movement times rose by 64 per cent and error rates by 214 per cent, a model of lag as a multiplier on difficulty fitting better than an additive one.
• Meyer, D. E., Abrams, R. A., Kornblum, S., Wright, C. E. and Smith, J. E. K. (1988). Optimality in human motor performance: ideal control of rapid aimed movements. Psychological Review, 95(3), 340-370. doi:10.1037/0033-295x.95.3.340 Modelled a rapid aimed movement as a primary submovement and an optional correction programmed to minimise total time at a high hit rate, and found the submovement durations themselves followed a square-root form of the law derived from the model.
• Schmidt, R. A., Zelaznik, H., Hawkins, B., Frank, J. S. and Quinn, J. T. (1979). Motor-output variability: a theory for the accuracy of rapid motor acts. Psychological Review, 86(5), 415-451. doi:10.1037/0033-295x.86.5.415 Proposed that the accuracy of a rapid movement is limited by variability in the motor output that grows with the force and the distance moved, supported across three movement tasks.
• Soukoreff, R. W. and MacKenzie, I. S. (2004). Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI. International Journal of Human-Computer Studies, 61(6), 751-789. doi:10.1016/j.ijhcs.2004.09.001 Reviewed 24 published Fitts's law models of the mouse and 9 studies using the ISO 9241-9 protocol, and made seven recommendations for reporting, including the Shannon formulation, difficulties from 2 to 8 bits and throughput as the dependent measure.
• Zhai, S. (2004). Characterizing computer input with Fitts' law parameters: the information and non-information aspects of pointing. International Journal of Human-Computer Studies, 61(6), 791-809. doi:10.1016/j.ijhcs.2004.09.006 Argued that throughput defined as index of difficulty over movement time is ill-defined, shifts with the range of difficulties used and cannot be generalised beyond the tested distances and sizes, and proposed reporting the slope and the intercept separately.
• Zhang, X. (2025). Characterizing amplitude-dominated performance: a refinement of Fitts' law for target acquisition on large-format touchscreens. Proceedings of the ACM on Human-Computer Interaction, 9(8), 210-232. doi:10.1145/3773067 Had participants point at a 65-inch touchscreen with finger and pen and found conventional Fitts's law explained at most 80 per cent of the variance, because amplitude dominated. An amended index of difficulty with a calibrated constant raised the fit above 0.97.
• Zhang, X. (2023). Understanding the effects of movement direction on 2D touch pointing tasks. Proceedings of the ACM on Human-Computer Interaction, 7(ISS), 444-462. doi:10.1145/3626482 Ran two two-dimensional pointing experiments on a 24-inch touch screen, tilted and horizontal, and confirmed a periodic effect of movement direction that the standard index of difficulty does not capture.