I have been studying this law all the week but I still don’t understand how it works or in other words, I have an example but I don’t know how to apply the law to it.


  • MT = a + b log2 2·A/W
  • ID = log2 2·A/W

I’m going to use it in the 2-dimensional space (x-y axes).

See [3*] for quick review of the definition of this theorem.


According to this paper [1*] and the video [A1] they give an example where W (width of the target) and A (amplitude or distance from initial position to target position) are changed every time they use it. This because they seems to say that “hey, guys this theorem works fine” so they take many different examples, but now my problem is when I want to apply this theorem to the same value of W and A; how can I get value of a and b? and how it works? Does it work by taking a group of people and calculate the time they take or what?

Why would I take the same value of W and A? this because I have an example where a user move the mouse from top-left to bottom-right so A = 800 pixels and W = 10 pixels. Now, can you tell me how to get the value of a and b? or can you tell me what kind of experiment that I can do in order to get these two values a and b?

Note: The question might be not clear, so I will edit the question as possible to be clear, as if there is something no clear, point out and I'll try to explain it.


  • [1*] “Extending Fitts' Law to Two-Dimensional Tasks” by S. MacKenzie and W. Buxton.

  • [2*] “Movement Time Prediction in Human-Computer Interfaces” by S. MacKenzie

  • [3*] “Fitts Law: Modeling Movement Time in HCI” by H. Zhao

some video resources are:

  • 2
    a and b are model variables and to be empirically determined: interaction-design.org/literature/book/… – locationunknown Nov 16 '15 at 9:48
  • @locationunknown That's right, but how to get these values using the experiment when ID is constant? – user777 Nov 16 '15 at 9:56
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    You can run the test even though ID is constant. a is never 0 because no-one can click the target fast enough and b is 0 because ID is constant. So MT becomes a, which should be somewhere around the average of click times. – locationunknown Nov 16 '15 at 10:22

ID must vary

You cannot get the values of a and b if ID is constant. In fitting parameters to a model, you need at least as many conditions as parameters to estimate. You have two parameters (a and b), so you need at least two values of ID. I don't think it makes sense to make any assumptions about the values of one parameter (e.g., that b is 0).

So your experiment must vary ID by varying A, W, or both. Choose values of A and W to include the range of values you want your derived equation to apply to. Generally, you’ll include the extremes that are physically plausible, such moving from one button to another when (1) the buttons are right next to each other, and (2) when the buttons are on opposites side of the control panel or screen(s) (for physical or virtual buttons respectively). At a minimum your experiment needs two values of ID, but I suggest also including in-between values, just to make sure Fitt's law is "working" in your case.

Draw a line to determine a and b

As a result of the experiment you have a bunch of different MT values paired with ID values. Plot these pairs of values as dots on graph paper with MT on the Y-axis. Draw a single straight line that runs closest to the dots (despite it being Fitt’s “Law” the dots won’t perfectly line up due to “noise” including person-to-person variation). The slope of the line is b and the Y-intercept is a. If the dots do not distribute evenly around a single straight line (i.e., the cloud of dots curves up and/or down), then Fitt's Law does not apply in your case, for some reason.

Actually, you’d make a scatter plot of the MT and ID in Excel, add a linear trend line with “Display Equation on chart” checked, then read a and b from the equation. That provides you a linear regression best-fit straight line, which is conceptually the same as above, but more accurate than eye-balling the line. You should still visually inspect the scatter plot to be sure Fitt's Law is applying.

Using the resulting equation

Once you have a and b from the experiment, you can use your Fitt's equation to predict average times of the single particular value of ID you're interested in, although there is not much point in using Fitt's for a single value of ID. If you want to know how long it takes to slew from the top left to bottom right, forget about Fitt's and run an experiment where users slew from the top left to the lower right and take the average.

Fitt's is useful for when you have various IDs, especially when the IDs are not necessarily all equal to the values you used experimentally (although for accuracy they should be within the range of values you used experimentally). For example, you could use your equation to see the impact of moving the target to other places in the window than the bottom right (including places you didn't think of when you did the experiment). You can use Fitts to determine the position (or target size) that corresponds to a minimally acceptable MT. Fitt's can be used for a series of IDs. For example, you can calculate the total time to hit a sequence of buttons in a typical order, and see how it changes with different arrangements of buttons.

You can use Fitts to compare input devices, such as mouse versus an alternative to a mouse, by deriving separate Fitt’s equations for each. Of course, you can and should simply compare average MTs for the two devices over a representative mix of As and Ws. However, comparing a’s and b’s from the two Fitt’s equations can provide additional insight. Forlines et al. (2007), for example, found lower average MTs for a touchscreen. Consistent with this, the b for the touchscreen was smaller than the b for the mouse. However, the a for the touchscreen was bigger than the a for the mouse, implying that for lower IDs, (small distances or large targets), the mouse is faster. To be exact, Forlines et al.'s equations suggest the mouse is faster for ID < 1.636. Using their definition of ID (a little different than yours) a mouse is predicted to be faster for a 20-pixel target if it’s closer than 42 pixels from the current position.

The equation should not be used outside of the sort of experimental conditions you used to determine a and b. For example, as Forlines et al shows, you shouldn’t use an equation from an experiment with a mouse to predict the MTs of a touchscreen. It’s risky to extrapolate the equation beyond the range of As and Ws that were in the experiment (which is precisely what I did in suggesting the mouse is better for smaller IDs –I don’t think Forlines et al actually tested smaller IDs to be sure Fitts still applies on such scales).

Using Fitt's conceptually

Fitt's law can also be useful conceptually, without actually deriving parameters experimentally. For example, it's obvious that bigger separation distances mean longer MTs, so we should arrange our menu, window, and page layouts to minimize mouse slewing.

Less obvious is that the larger the target (W) the lower the MT, suggesting that commonly used controls should be bigger than rarely used controls. Also, if you have put a button far from the mouse pointer's likely current location, then you can compensate by increasing the button's size. According to Fitt's, a button twice the normal size will be as fast to click as a normal one half the distance away.

Fitt's Law posits a log relation between ID and MT. This implies that, in a pulldown menu, there is a bigger difference in MT between the first and second menu items than between the seventh and eighth menu items, so ordering menu items by frequency of use is more important for the first few menu items than the later ones.

Fitt's law implies that controls on the border of a screen in a desktop application tend to be the fastest to get to. Although A is generally large, W is basically infinite. Because the pointer won't go beyond the screen border, user can (and will) slew the mouse quickly as if to over-shoot the border for a much larger target.

You can use Fitt’s to determine the upper bound of relative improvement of different places for a control (the percent of time Location 1 takes to move to versus Location 2). The ratio of MTs of two locations is maximized when a is zero. In that case, b cancels out, and the ratio of MTs is:

Rextreme = Log(2 A1 / W) / Log(2 A2 / W)

With this, you can show that putting your 10 pixel target in the upper left (say A1 = 10 pixels), rather than the lower right (A2 = 800 pixels) will improve MT by as much as 86% (Rextreme = 0.14). On the other hand, moving the mouse from a checkbox at the bottom of a dialog box to a 70-pixel-wide OK button in the Window’s position (say, 300 pixels away) versus the Mac-position (about 380 pixels) is at most only 11% faster for Windows.

  • Wonderful answer, I just know see how Fitt's law is used, Thank you for your effort and time to explain this amazing answer. one simple question regarding the last example, for A1 = 800 px, and A2= 10, what is the value of W? Suppose W = 10, then I got the R<extreme> = 0.14, this imply that I have around (100 - 14 = 86% to improve MT to be minimized) Is that right? – user777 Nov 17 '15 at 2:24
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    @user777. Your numbers are correct, and I've corrected mine to match. When I tracked down the scrap paper I used, I see I set A(1) = 20 pixels. I must've changed my mind when I turned to write up the example, but didn't update the numbers. – Michael Zuschlag Nov 17 '15 at 14:45

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