![Fitts Law](https://upload.wikimedia.org/wikipedia/commons/9/97/Fitts_Law.svg)
Fitts's law (often cited as Fitts' law) is a predictive model of human movement primarily used in
human–computer interaction
Human–computer interaction (HCI) is research in the design and the use of computer technology, which focuses on the interfaces between people (users) and computers. HCI researchers observe the ways humans interact with computers and design tec ...
and
ergonomics
Human factors and ergonomics (commonly referred to as human factors) is the application of psychological and physiological principles to the engineering and design of products, processes, and systems. Four primary goals of human factors learnin ...
. The
law
Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. It has been vario ...
predicts that the time required to rapidly move to a target area is a function of the ratio between the distance to the target and the width of the target.
Fitts's law is used to
model
A model is an informative representation of an object, person or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a mea ...
the act of ''pointing'', either by physically touching an object with a hand or finger, or virtually, by pointing to an object on a
computer monitor
A computer monitor is an output device that displays information in pictorial or textual form. A discrete monitor comprises a visual display, support electronics, power supply, housing, electrical connectors, and external user controls.
The di ...
using a
pointing device
A pointing device is a human interface device that allows a user to input spatial (i.e., continuous and multi-dimensional) data to a computer. CAD systems and graphical user interfaces (GUI) allow the user to control and provide data to t ...
. It was initially developed by
Paul Fitts
Paul Morris Fitts Jr. (May 6, 1912 – May 2, 1965) was a psychologist at the Ohio State University (later at the University of Michigan). He developed a model of human movement, Fitts's law, based on rapid, aimed movement, which went on to becom ...
.
Fitts's law has been shown to apply under a variety of conditions; with many different
limbs (hands, feet, the lower lip, head-mounted sights), manipulanda (input devices), physical environments (including underwater
), and user populations (young, old,
special educational needs,
and drugged participants
).
Original model formulation
The original 1954 paper by
Paul Morris Fitts proposed a metric to quantify the difficulty of a target selection task.
The metric was based on an information analogy, where the distance to the center of the target (''D'') is like a signal and the tolerance or width of the target (''W'') is like noise.
The metric is Fitts's ''index of difficulty'' (''ID'', in bits):
![Fitts Task English](https://upload.wikimedia.org/wikipedia/commons/1/16/Fitts_Task_English.jpg)
Fitts also proposed an ''index of performance'' (''IP'', in bits per second) as a measure of human performance. The metric combines a task's index of difficulty (''ID'') with the movement time (''MT'', in seconds) in selecting the target. In Fitts's words,
"The average rate of information generated by a series of movements is the average information per movement divided by the time per movement."
Thus,
Today, ''IP'' is more commonly called ''throughput'' (''TP''). It is also common to include an adjustment for accuracy in the calculation.
Researchers after Fitts began the practice of building linear regression equations and examining the correlation (''r'') for goodness of fit. The equation expresses the relationship between
''MT'' and the ''D'' and ''W'' task parameters:
where:
* ''MT'' is the average time to complete the movement.
* ''a'' and ''b'' are constants that depend on the choice of input device and are usually determined empirically by
regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
. ''a'' defines the intersection on the ''y'' axis and is often interpreted as a delay. The ''b'' parameter is a slope and describes an acceleration. Both parameters show the linear dependency in Fitts's law.
* ''ID'' is the index of difficulty.
* ''D'' is the distance from the starting point to the center of the target.
* ''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 ± of the target's center.
Since shorter movement times are desirable for a given task, the value of the ''b'' parameter can be used as a metric when comparing computer pointing devices against one another. The first
human–computer interface application of Fitts's law was by Card, English, and Burr,
who used the index of performance (''IP''), interpreted as , to compare performance of different
input device
In computing, an input device is a piece of equipment used to provide data and control signals to an information processing system, such as a computer or information appliance. Examples of input devices include keyboards, mouse, scanners, cameras ...
s, with the
mouse
A mouse ( : mice) is a small rodent. Characteristically, mice are known to have a pointed snout, small rounded ears, a body-length scaly tail, and a high breeding rate. The best known mouse species is the common house mouse (''Mus musculus' ...
coming out on top compared to the joystick or directional movement keys.
This early work, according to
Stuart Card
Stuart K. Card (born December 21, 1943), an American researcher and retired senior research fellow at Xerox PARC, is considered to be one of the pioneers of applying human factors in human–computer interaction. With Jock D. Mackinlay, George G. ...
's biography, "was a major factor leading to the mouse's commercial introduction by
Xerox
Xerox Holdings Corporation (; also known simply as Xerox) is an American corporation that sells print and electronic document, digital document products and services in more than 160 countries. Xerox is headquartered in Norwalk, Connecticut (ha ...
".
Many experiments testing Fitts's law apply the model to a dataset in which either distance or width, but not both, are varied. The model's predictive power deteriorates when both are varied over a significant range.
Notice that because the ''ID'' term depends only on the ''ratio'' of distance to width, the model implies that a target distance and width combination can be re-scaled arbitrarily without affecting movement time, which is impossible. Despite its flaws, this form of the model does possess remarkable predictive power across a range of computer interface modalities and motor tasks, and has provided many insights into user interface design principles.
Movement
A movement during a single Fitts's law task can be split into two phases:
* ''initial movement''. A fast but imprecise movement towards the target
* ''final movement''. Slower but more precise movement in order to acquire the target
The first phase is defined by the distance to the target. In this phase the distance can be closed quickly while still being imprecise. The second movement tries to perform a slow and controlled precise movement to actually hit the target.
The task duration scales linearly in regards to difficulty.
But as different tasks can have the same difficulty, it is derived that distance has a greater impact on the overall task completion time than target size.
Often it is cited that Fitts's law can be applied to
eye tracking
Eye tracking is the process of measuring either the point of gaze (where one is looking) or the motion of an eye relative to the head. An eye tracker is a device for measuring eye positions and eye movement. Eye trackers are used in research ...
. This seems to be at least a controversial topic as Drewes showed.
During fast
saccadic eye movements the user is blind. During a Fitts's law task the user consciously acquires its target and can actually see it, making these two types of interaction not comparable.
Bits per second: model innovations driven by information theory
The formulation of Fitts's index of difficulty most frequently used in the
human–computer interaction
Human–computer interaction (HCI) is research in the design and the use of computer technology, which focuses on the interfaces between people (users) and computers. HCI researchers observe the ways humans interact with computers and design tec ...
community is called the Shannon formulation:
This form was proposed by Scott MacKenzie, professor at
York University
York University (french: Université York), also known as YorkU or simply YU, is a public university, public research university in Toronto, Ontario, Canada. It is Canada's fourth-largest university, and it has approximately 55,700 students, 7,0 ...
, and named for its resemblance to the
Shannon–Hartley theorem
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy-channel coding ...
.
It describes the transmission of information using bandwidth, signal strength and noise. In Fitts's law, the distance represents signal strength, while target width is noise.
Using this form of the model, the difficulty of a pointing task was equated to a quantity of information transmitted (in units of bits) by performing the task. This was justified by the assertion that pointing reduces to an information processing task. Although no formal mathematical connection was established between Fitts's law and the Shannon-Hartley theorem it was inspired by, the Shannon form of the law has been used extensively, likely due to the appeal of quantifying motor actions using information theory. In 2002 the
ISO 9241
ISO 9241 is a multi-part standard from the International Organization for Standardization (ISO) covering ergonomics of human-computer interaction. It is managed by the ISO Technical Committee 159. It was originally titled ''Ergonomic requirement ...
was published, providing standards for human–computer interface testing, including the use of the Shannon form of Fitts's law. It has been shown that the information transmitted via serial keystrokes on a keyboard and the information implied by the ''ID'' for such a task are not consistent.
The Shannon-Entropy results in a different information value than Fitts's law. The authors note, though, that the error is negligible and only has to be accounted for in comparisons of devices with known entropy or measurements of human information processing capabilities.
Adjustment for accuracy: use of the effective target width
An important improvement to Fitts's law was proposed by Crossman in 1956 (see Welford, 1968, pp. 147–148)
and used by Fitts
in his 1964 paper with Peterson.
With the adjustment, target width (''W'') is replaced by an effective target width (''W''
e).
''W''
e is computed from the standard deviation in the selection coordinates gathered over a sequence of trials for a particular ''D-W'' condition. If the selections are logged as ''x'' coordinates along the axis of approach to the target, then
This yields
and hence
If the selection coordinates are normally distributed, ''W''
e spans 96% of the distribution. If the observed error rate was 4% in the sequence of trials, then ''W''
e = ''W''. If the error rate was greater than 4%, ''W''
e > ''W'', and if the error rate was less than 4%, ''W''
e < ''W''. By using ''W''
e, a Fitts' law model more closely reflects what users actually did, rather than what they were asked to do.
The main advantage in computing ''IP'' as above is that spatial variability, or accuracy, is included in the measurement. With the adjustment for accuracy, Fitts's law more truly encompasses the speed-accuracy tradeoff. The equations above appear in ISO 9241-9 as the recommended method of computing ''throughput''.
Welford's model: innovations driven by predictive power
Not long after the original model was proposed, a 2-factor variation was proposed under the intuition that target distance and width have separate effects on movement time. Welford's model, proposed in 1968, separated the influence of target distance and width into separate terms, and provided improved predictive power:
This model has an additional parameter, so its predictive accuracy cannot be directly compared with 1-factor forms of Fitts's law. However, a variation on Welford's model inspired by the Shannon formulation,
The additional parameter ''k'' allows the introduction of angles into the model. Now the users position can be accounted for. The influence of the angle can be weighted using the exponent. This addition was introduced by Kopper et al. in 2010.
The formula reduces to the Shannon form when ''k = 1''. Therefore, this model ''can'' be directly compared against the Shannon form of Fitts's law using the
F-test
An ''F''-test is any statistical test in which the test statistic has an ''F''-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model th ...
of nested models.
This comparison reveals that not only does the Shannon form of Welford's model better predict movement times, but it is also more robust when control-display gain (the ratio between e.g. hand movement and cursor movement) is varied. Consequently, although the Shannon model is slightly more complex and less intuitive, it is empirically the best model to use for virtual pointing tasks.
Extending the model from 1D to 2D and other nuances
Extensions to two or more dimensions
In its original form, Fitts's law is meant to apply only to one-dimensional tasks. However, the original experiments required subjects to move a stylus (in three dimensions) between two metal plates on a table, termed the reciprocal tapping task.
The target width perpendicular to the direction of movement was very wide to avoid it having a significant influence on performance. A major application for Fitts's law is 2D virtual pointing tasks on computer screens, in which targets have bounded sizes in both dimensions.
![Reciprocal Tapping Task](https://upload.wikimedia.org/wikipedia/commons/5/54/Reciprocal_Tapping_Task.jpg)
Fitts's law has been extended to two-dimensional tasks in two different ways. For navigating e.g. hierarchical pull-down menus, the user must generate a trajectory with the pointing device that is constrained by the menu geometry; for this application the
Accot-Zhai steering law The steering law in human–computer interaction and ergonomics is a predictive model of human movement that describes the time required to navigate, or ''steer'', through a 2-dimensional tunnel. The tunnel can be thought of as a path or trajectory ...
was derived.
For simply pointing to targets in a two-dimensional space, the model generally holds as-is but requires adjustments to capture target geometry and quantify targeting errors in a logically consistent way.
Multiple Methods can be used to determine the target size :
* status Quo: horizontal width of the target
* sum model: ''W'' equals height + width
* area model: ''W'' equals height * width
* smaller of model: ''W'' smaller value of height and width
* W-model: ''W'' is the effective width in the direction of the movement
Overall the ''W''-model represents the state-of-the-art measurement.
Characterizing performance
Since the ''a'' and ''b'' parameters should capture movement times over a potentially wide range of task geometries, they can serve as a performance metric for a given interface. In doing so, it is necessary to separate variation between users from variation between interfaces.
The ''a'' parameter is typically positive and close to zero, and sometimes ignored in characterizing average performance, as in Fitts' original experiment.
Multiple methods exist for identifying parameters from experimental data, and the choice of method is the subject of heated debate, since method variation can result in parameter differences that overwhelm underlying performance differences.
An additional issue in characterizing performance is incorporating success rate: an aggressive user can achieve shorter movement times at the cost of experimental trials in which the target is missed. If the latter are not incorporated into the model, then average movement times can be artificially decreased.
Temporal targets
Fitts's law deals only with targets defined in space. However, a target can be defined purely on the time axis, which is called a temporal target. A blinking target or a target moving toward a selection area are examples of temporal targets. Similar to space, the distance to the target (i.e., temporal distance ''D''
t) and the width of the target (i.e., temporal width ''W''
t) can be defined for temporal targets as well. The temporal distance is the amount of time a person must wait for a target to appear. The temporal width is a short duration from the moment the target appears until it disappears. For example, for a blinking target, ''D''
t can be thought of as the period of blinking and ''W''
t as the duration of the blinking. As with targets in space, the larger the ''D''
t or the smaller the ''W''
t, the more difficult it becomes to select the target.
The task of selecting the temporal target is called ''temporal pointing''. The model for temporal pointing was first presented to the
human–computer interaction
Human–computer interaction (HCI) is research in the design and the use of computer technology, which focuses on the interfaces between people (users) and computers. HCI researchers observe the ways humans interact with computers and design tec ...
field in 2016.
The model predicts the error rate, the human performance in temporal pointing, as a function of temporal index of difficulty (''ID''
t):
Implications for UI design
![Radial Menu English](https://upload.wikimedia.org/wikipedia/commons/f/f6/Radial_Menu_English.jpg)
Multiple design guidelines for
GUI
The GUI ( "UI" by itself is still usually pronounced . or ), graphical user interface, is a form of user interface that allows users to interact with electronic devices through graphical icons and audio indicator such as primary notation, inste ...
s can be derived from the implications of Fitts's law. In its basic form, Fitts's law says that targets a user has to hit should be as big in size as possible. This derived from the ''W'' parameter. More specifically, the effective size of the button should be as big as possible, meaning that their form has to be optimized for the movement direction of the user onto the target.
Layouts should also group functions that are used commonly with each other close. Optimizing for the ''D'' parameter in this way allows for smaller travel times.
Placing layout elements on the four edges of the screen allows for infinitely large targets in one dimension and therefore present ideal scenarios. As the user's pointer will always stop at the edge, they can move the mouse with the greatest possible speed and still hit the target. The target area is effectively infinitely long along the movement axis. Therefore, this guideline is called “Rule of the infinite edges”. The use of this rule can be seen for example in
MacOS
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lapt ...
, which places the menu bar always on the top left edge of the screen instead of the current program's windowframe.
This effect can be exaggerated at the four corners of a screen. At these points two edges collide and form a theoretically infinitely big button.
Microsoft Windows
Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...
(prior to
Windows 11
Windows 11 is the latest major release of Microsoft's Windows NT operating system, released in October 2021. It is a free upgrade to its predecessor, Windows 10 (2015), and is available for any Windows 10 devices that meet the new Windows 11 ...
) places its "Start" button in the lower left corner and
Microsoft Office
Microsoft Office, or simply Office, is the former name of a family of client software, server software, and services developed by Microsoft. It was first announced by Bill Gates on August 1, 1988, at COMDEX in Las Vegas. Initially a marketin ...
2007 uses the upper left corner for its "Office" menu. These four spots get called the "magic corners".
MacOS
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lapt ...
places the close button on the upper left side of the program window and the menu bar fills out the magic corner with another button.
A UI that allows for pop-up menus rather than fixed drop-down menus reduces travel times for the ''D'' parameter. The user can continue interaction right from their mouse position and don't have to move to a different preset area. Many operating systems use this when displaying right-click context menus. As the menu starts right on the pixel which the user clicked on, this pixel is referred to as the "magic" or "prime pixel".
James Boritz et al. (1991)
compared
radial menu
In user interface design, a pie menu or radial menu is a circular context menu where selection depends on direction. It is a graphical control element. A pie menu is made of several "pie slices" around an inactive center and works best with styl ...
designs. In a radial menu all items have the same distance from the prime pixel. The research suggests that in practical implementations the direction in which a user has to move their mouse has also to be accounted for. For right-handed users selecting the left most menu item was significantly more difficult than the right-sided one. No differences were found for transitions from upper to lower functions and vice versa.
See also
*
Accot–Zhai steering law
*
Hick's law
*
Point-and-click
Point and click are the actions of a computer user moving a pointer to a certain location on a screen (''pointing'') and then pressing a button on a mouse, usually the left button (''click''), or other pointing device. An example of point and cli ...
*
Crossing-based interface {{short description, Type of graphical user interface
Crossing-based interfaces are graphical user interfaces that use crossing gestures instead of, or in complement to, pointing. Where a pointing task involves moving a cursor inside a graphical o ...
References
Bibliography
*
*
*
*
External links
An Interactive Visualisation of Fitts's Law with JavaScript and D3by Simon Wallner
Fitts' Lawat CS Dept. NSF-Supported Education Infrastructure Project
compiled by I. Scott MacKenzie
Fitts' Law Software – Free Downloadby I. Scott MacKenzie
{{DEFAULTSORT:Fitts's Law
Human–computer interaction
Motor control