In ergonomics, Fitts' law is a model of human movement, predicting the time required to rapidly move from a starting position to a final target area, as a function of the distance to the target and the size of the target. Fitts' law is used to model the act of pointing, both in the real world, for example, with a hand or finger and on computers, for example, with a mouse. It was published by Paul Fitts in 1954. To meet Wikipedias quality standards, this article or section may require cleanup. ... An abstract model (or conceptual model) is a theoretical construct that represents physical, biological or social processes, with a set of variables and a set of logical and quantitative relationships between them. ... A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ... Operating a mechanical 1: Pulling the mouse turns the ball. ... Paul M. Fitts (1912 – 1965) was a psychologist at Ohio State University (later at the University of Michigan). ... 1954 (MCMLIV) was a common year starting on Friday of the Gregorian calendar. ...

The model

Mathematically, Fitts' law has been formulated in several different ways. One common form is the Shannon formulation (proposed by Scott MacKenzie, and named for its resemblance to the Shannon-Hartley theorem) for movement along a single dimension: In information theory, the Shannon-Hartley theorem states the maximum amount of error-free digital data (that is, information) that can be transmitted over a communication link with a specified bandwidth in the presence of noise interference. ...

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 and b are empirical constants, and can be determined 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 ± W/2 of the target's centre.

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.

Success and implications of Fitts' law

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 fit a straight line with a correlation coefficient of 0.95 or higher, a sign that the model is very accurate. In mathematics, and in particular statistics, the Pearson product-moment correlation coefficient (r) is a measure of how well a linear equation describes the relation between two variables X and Y measured on the same object or organism. ...

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. Fitts' law's first HCI application was by Card, English, and Burr (1978), who used the index of performance (IP), defined as 1/b, 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].) Fitts' law has been shown to apply under a variety of conditions, with many different limbs (hands, feet, head-mounted sights, eye gaze), manipulanda (input devices), physical environments (including underwater!), and user populations (young, old, special educational needs, and drugged participants). Note that the constants a, b, IP have different values under each of these conditions. Human–computer interaction (HCI) or, alternatively, computer–human interaction (symbolized as Χ χ Chi, the 22nd letter of the Greek alphabet) is the study of interaction between people (users) and computers. ... A number of devices, called input devices, are used for entering data into a machine, typically a computer. ... Xerox Corporation (NYSE: XRX) (pronounced ) is an American document management company, which manufactures and sells a range of color and black-and-white printers, multifunction systems, photo copiers, digital production printing presses, and related consulting services and supplies. ...

Since the advent of graphical user interfaces, Fitts' law has been applied to tasks where the user must position the mouse cursor over an on-screen target, such as a button or other widget. Fitts' law can 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 model's appeal, it should be remembered that in its original and strictest form: PUI redirects here. ... A typical arrow-like mouse cursor. ... A widget (or control) is an interface component that a computer user interacts with, such as a window or a text box. ... Point and click describes the simple action of a computer user moving a cursor to a certain location on a screen (point) and then clicking a mouse button, usually the left one (click), or other pointing device. ... Drag-and-drop refers to the act of (or support for the act of) clicking on a virtual object and dragging it to, or onto, another virtual object. ...

• It applies only to movement in a single dimension and not to movement in two dimensions (though it is successfully extended to two dimensions in the Accot-Zhai steering law);
• It describes simple motor response of, say, the human hand, failing to account for software acceleration usually implemented for a mouse cursor;
• It describes untrained movements, not movements that are executed after months or years of practice (though some argue that Fitts' law models behaviour that is so low level that extensive training doesn't make much difference).

If, as generally claimed, the law does hold true for pointing with the mouse, some consequences for user-interface design include: The Accot-Zhai steering law, also known as Accots law (Accot is pronounced ah-caught in English and ah-koh in French) or the steering law, is a model of human movement. ... The user interface is the part of a system exposed to users. ...

• Buttons and other widgets to be selected in GUIs should be a reasonable size; it is very difficult to click on small ones.
• Edges (e.g. the menubar in Mac OS) and corners of the computer display (e.g. "Start" button in Windows XP) are particularly easy to acquire because the pointer remains at the screen edge regardless of how much further the mouse is moved, thus can be considered as having infinite width.
• Popup menus can usually be opened faster than pull-down menus, since the user avoids travel.
• Pie menu items typically are selected faster and have a lower error rate than linear menu items, for two reasons: because pie menu items are all the same, small distance from the centre of the menu; and because their wedge-shaped target areas (which usually extend to the edge of the screen) are very large.

Fitts' law remains one of the few hard, reliable human-computer interaction predictive models, joined more recently by the Accot-Zhai steering law, which is derived from Fitts' law. This article or section does not cite its references or sources. ... A computer display A computer display or computer monitor is an output device that is part of a computers display system. ... Windows XP is a line of operating systems developed by Microsoft Corporation for use on general-purpose computer systems, including home and business desktops, notebook computers, and media centers. ... In computing and telecommunications, a menu is a list of commands presented to an operator by a computer or communications system. ... A pie menu. ... In computing and telecommunications, a menu is a list of commands presented to an operator by a computer or communications system. ... Human–computer interaction (HCI) or, alternatively, computer–human interaction (symbolized as Χ χ Chi, the 22nd letter of the Greek alphabet) is the study of interaction between people (users) and computers. ... The Accot-Zhai steering law, also known as Accots law (Accot is pronounced ah-caught in English and ah-koh in French) or the steering law, is a model of human movement. ...

See also Hick's law, which models user decision making time. Hicks law, or the Hick-Hyman law, is a human-computer interaction model that describes the time it takes for a user to make a decision as a function of the possible choices he or she has. ...

Some mathematical details

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

T = a + bID

Thus, the units for b are time/bit, e.g. milliseconds/bit. The constant a can be thought of as incorporating reaction time and/or the time required to click a button.

The values for a and b 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 and b associated with them. Modern stylus, used for touch-screen enabled devices such as the Nintendo DS and personal digital assistants Styli used in writing in the Fourteenth Century. ...

An index of performance IP (also called throughput TP), in bits/time, can be defined to characterize how quickly pointing can be done, independent of the particular targets involved. There are two conventions for defining IP: one is IP = 1/b (which has the disadvantage of ignoring the effect of a), the other is IP = ID_average/MT_average (which has the disadvantage of depending on an arbitrarily chosen "average" ID). For a discussion of these two conventions, see Zhai (2002). Whatever definition is used, measuring the IP of different input devices allows the devices to be compared with respect to their pointing capability.

Slightly different from the Shannon 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, especially for low values of the ratio D/W. The Shannon form has the advantage that the ID is always non-negative, and has been shown to better fit measured data.

A derivation of Fitts' 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, A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

Solving for N:

N
		(because logxy = (logzy)/(logzx))
		(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).

References

• Original work
  • Paul M. Fitts (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, volume 47, number 6, June 1954, pp. 381-391. (Reprinted in Journal of Experimental Psychology: General, 121(3):262--269, 1992).
  • Paul M. Fitts and James R. Peterson (1964). Information capacity of discrete motor responses. Journal of Experimental Psychology, 67(2):103--112, February 1964.
• Selected subsequent work
  • The first application of Fitts' law to HCI
    • Stuart K. Card, William K. English, and Betty J. Burr (1978). Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT. Ergonomics, 21(8):601--613, 1978.
  • Extending Fitts' law to 2 dimensions (bivariate targets)
    • I. Scott MacKenzie and William A. S. Buxton (1992). Extending Fitts' law to two-dimensional tasks. Proceedings of ACM CHI 1992 Conference on Human Factors in Computing Systems, pp. 219--226. http://doi.acm.org/10.1145/142750.142794
    • A. Murata. Extending effective target width in Fitts' law to a two-dimensional pointing task. International Journal of Human-Computer Interaction, 11(2):137--152, 1999.
    • Johnny Accot and Shumin Zhai (2003). Refining Fitts' law models for bivariate pointing. Proceedings of ACM CHI 2003 Conference on Human Factors in Computing Systems, pp. 193--200. http://doi.acm.org/10.1145/642611.642646
  • Extending Fitts' law to goal passing and crossing
    • Johnny Accot and Shumin Zhai (2002). More than dotting the i's --- foundations for crossing-based interfaces. Proceedings of ACM CHI 2002 Conference on Human Factors in Computing Systems, pp. 73--80. http://doi.acm.org/10.1145/503376.503390
• Overviews
  • Stuart K. Card, Thomas P. Moran, Allen Newell (1983). The Psychology of Human-Computer Interaction.
  • I. Scott MacKenzie (1992). Fitts' law as a research and design tool in human-computer interaction. Human-Computer Interaction, volume 7, 1992, pp. 91-139.
  • Meyer, D. E., Smith, J. E. K., Kornblum, S., Abrams, R. A., & Wright, C. E. (1990). Speed-accuracy tradeoffs in aimed movements: Toward a theory of rapid voluntary action. In M. Jeannerod (Ed.), Attention and performance XIII (pp. 173-226). Hillsdale, NJ: Lawrence Erlbaum. http://www.umich.edu/~bcalab/Meyer_Bibliography.html
  • A. T. Welford (1968). Fundamentals of Skill. Methuen, 1968.
• Regarding two conventions on the definition of index of performance IP
  • Shumin Zhai (2002). On the Validity of Throughput as a Characteristic of Computer Input, IBM Research Report RJ 10253, 2002, Almaden Research Center, San Jose, California. http://www.almaden.ibm.com/u/zhai/papers/ZhaiIBMReporRJ10253.pdf

Human–computer interaction (HCI) or, alternatively, computer–human interaction (symbolized as Χ χ Chi, the 22nd letter of the Greek alphabet) is the study of interaction between people (users) and computers. ... The Association for Computing Machinery, or ACM, was founded in 1947 as the worlds first scientific and educational computing society. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Allen Newell (March 19, 1927 - July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND corporation and at Carnegie-Mellon’s School of Computer Science. ...

See also

• Point and click — A basic interaction technique of graphical user interfaces, one of the main applications of Fitt's Law.
• Accot-Zhai steering law — An extension of Fitt's law to steering tasks.
• Hick's law — Another human-computer interaction model, which is similar in form to Fitts' law, describes the time it takes for a user to make a decision as a function of the possible choices he or she has.
• Crossing Based Interfaces — Another interaction technique of graphical user interfaces based on the steering law.

Point and click describes the simple action of a computer user moving a cursor to a certain location on a screen (point) and then clicking a mouse button, usually the left one (click), or other pointing device. ... The Accot-Zhai steering law, also known as Accots law (Accot is pronounced ah-caught in English and ah-koh in French) or the steering law, is a model of human movement. ... Hicks law, or the Hick-Hyman law, is a human-computer interaction model that describes the time it takes for a user to make a decision as a function of the possible choices he or she has. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

External links

• Fittsbits, a game used to investigate Fitts' Law by Willem Vervuurt and Laura Cuijpers
• First Principles of Interaction Design by Bruce Tognazzini
• A Quiz Designed to Give You Fitts by Bruce Tognazzini
• Fitts' Law
• Fitts’ Law: Modeling Movement Time in HCI
• Bibliography of Fitts' Law Research compiled by I. Scott MacKenzie
• Fun interactive demonstration
• Fitts' Law in Microsoft Office User Interface by Jensen Harris