The question Is there any difference in element minimal sizes on 10 and 24 inch touch screens? made me wonder; has Fitts' Law been successfully converted to Touch related events? There's 3D movement in touch events and certain types of rapid movement are easier in Touch from my experience, so I definitely think it's not directly compatible with the original Fitts' Law as it's designed for 2D movement.

Has any approximation (however rough) been made for Touch? I've found the question Fitts' Law, applying it to touch screens but there's really only info on why Fitts' law doesn't fit, not any alternate algorithms/etc.

Note: I know there are assorted guidelines related to the size of elements for Touch, but I'm talking specifically about an analog or adaptation of Fitts' law relating to ease of pointing as a function of size and distance, not just minimum size suggestions etc.

  • 8
    Fitt's law originated with physical controls. Touchscreens are proto-physical so it applies the same way.
    – dnbrv
    Commented Jun 21, 2012 at 14:46
  • 5
    Touch screens have been adapted to Fitts' law :) Commented Jun 21, 2012 at 17:53
  • What if you have fat fingers, does it still apply? - I mean it, I reckon this could be a question by itself...
    – edgarator
    Commented Jun 22, 2012 at 7:42
  • This might be of interest to you: Bi, X., Li, Y., & Zhai, S. (2013, April). FFitts law: Modeling finger touch with Fitts' law. In Proceedings of the 2013 ACM annual conference on Human factors in computing systems (pp. 1363-1372). ACM. ISO 690 dl.acm.org/citation.cfm?id=2466180 Commented Apr 11, 2014 at 13:30

7 Answers 7


Warning. This turned out to be more of a rant than an answer. Feel free to downvote it, I'm just glad to (finally) get it off my chest :-P

I usually get both eager and upset everytime I stuble upon advanced UX topics, like Fitts' law.

Eager because I find the basic research very interesting, and upset because there are so many misinterpretations of these.

I actually have my own version Fitts' law:

Don't use Fitts' law as a formula, use it as a guideline.

So, what is the simple guideline we can use from Fitts' law?

The size of the target and the distance to the target matters. Period. Don't calculate how large the button should be, and don't calculate where it should be. Don't calculate how much time it will take to hit an advertisement or a menu item. Just bear in mind that size and position matters.

Heck, low level estimation methods like GOMS+KLM doesn't even bother to calculate Fitts' law. They did it a couple of times and concluded that every mouse movement takes approximately 1.1 second (excluding click).

Besides, some of the components in Fitts' law are based on empirical data. Yes, you have to perform some empirical investigation to get a reliable result. :-) Well, that's what we call a deal-breaker, isn't it? You have to perform some empirical testing to find the constants you need to perform a reliable calculation of a movement time. Well...

So, what is Fitts' law, really?

Fitts' law is just model of human movement. A model. A formula that was originally proposed by Paul Fitts in 1954. A formula that has been revised several times.

In plain English, the model describes that a movement consists of several controlled micro-movements. The time it takes to perform a micro-movement is equal to the "feecback-loop"/"reaction time". Take a look at MHP for more information about this. The "feecback-loop"/"reaction time" includes observation with perceptual (visual) processor, evaluation of position (cognitive processing), and then performing a (new) movement as a response to the evaluation.

There are several ways to calculate the reaction time. You can for instance do it with an online test.

According to MHP, the average response time is 240 ms (Perceptual processor cycle time = 100 ms, Cognitive processor cycle time = 70 ms and Motor processor cycle time = 100). One should also know that MHP operates with the terms "Slow-Man" and "Fast-Man" to emphasize that there are documented variation from person to person. (Did you notice that the empirical data on the online test were 215 ms, btw? Quite accurate these "old" theories about the human brain...)

So, each micro-movement takes about 240 ms, and during the first 70-80% of total movement you can move pretty fast. During the last 20-30% you need to slow down to be able to hit the target accurately.

Fitts did a lot of one dimensional tests and proposed a formula to represent the math behind this movement.

enter image description here

  • MT is the average time taken to acquire the target.
  • a and b are empirical constants determined through linear regression.
  • A 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.
  • c is a constant which is either 0, 0.5, or 1, depending on the specific environment.

OK. You probably just skimmed over this list, but look at it again. Read and understand every piece of the formula. I'll help:

  1. MT = average time. This is pretty simple. The average time it takes to do perform a single scenario (startposition, target, target size etc...)

  2. a and b are empirical constants. Note: empirical constants. You need to get these constants somewhere. I'll explain more about these below.

  3. A is the distance to the target. Just measure a strait line from starting position to center of target. Pretty simple. I just one small note I would like to say about this. The immediate response from most people who hear about Fitts' law for the first time is "yay, let me find a ruler and start measuring". Well, you don't need a ruler. Since all the measurements are in the A/W part of the formula, you can use whatever you want. The ratio will be the same. Use pixels, inches, thumbs, feet or toothpicks. It doesn't matter...

  4. W is the distance from the center of the target to the point of the target where the line you drew in the 3rd point meets the target. Or, you can just measure the plain width and height of the target and use the smallest value divided by 2. I've elaborated a little about this below.

  5. c is yet another constant you need to get somewhere. It is context based. Take a look at point 8 and 9 below.

  6. The last part of this formula log2(2A/W) is what Fitts defined as the Index of Difficulty (ID). This is the part of the formula that says size and distance matters. The ID is defined by a metric he called "bits". As explained in point 3, you can measure the distance and the target size with whatever you want. The A/W ratio (and thus the ID) will always result in the same "bits" measurement. (I believe that "bits" were chosen because he used the 2 as the base for this logarithm.)

  7. Note that the logarithmic function implies that a small increase in size is much more effective for small targets than large targets. A small justification on large objects won't make that much of a difference. Likewise for the distance.

  8. Both Welford and Shannon have suggested some modifications to Fitts formula to better suit small ID's. Welfords data (1960) showed that Fitts' formula were wrong for easy tasks (ID < 3 bits), and suggested a new ID formula to correct this: ID = log2(A/W + 0.5). Shannon argued that these formulas would give a negative ID for situations where the distance to the target were less than half the target size (A < W/2). Hence the formula ID = log2(A/W + 1.0) was suggested to avoid a negative ID.

  9. These justifications are captured in c in the general formula. So when the formula tells you to use 0, 0.5 or 1. It's actually a matter of who's formula you wish to use, or rather a specification of the distance and target size situation.

  10. So, what´s the 2A/W vs A/W all about? Using 2A or just A is actually a matter of "Using the whole width of the target" or "distance from edge to center" of target. (2*A)/W is the same as A/(W/2). There have been various suggestions to whether one should use distance from the edge to the center along the line of movement, or simply the smallest of the width and height, or half the smallest width. At the end of the day, this is not very important, because the justification constants (a+b) will adjust this. The important part is the choice of c.

  11. So, now that we have a basic calculation of the ID, we just need to adjust the formula to match empirical data. :-) Fitts' law only describes how the human brain works during a movement, and how size and distance affect the task difficulty (ID). Fitts' law doesn't take into account the actual user group's capabilities (slow-man vs fast-man, under water vs outer space etc) nor the characteristics of the pointing device (mouse, finger, foot, trackball, joystick etc). That's why we need to determine a and b in the formula.

  12. First we add b to the formula to adjust the slope of the line. I.e. How much harder is is to hit targets that are far away.

    MT = b * ID

  13. Then we add ato the formula to avoid that the graph starts in the origin. I.e. what is the shortest MT you can have for the easiest task. 0 ms is not realistic even if we're talking about "the fastest pixel" - the pixel right under the cursor. We usually use a constant time factor depending on the task to be performed. Due to learnability, ' a ' will probably change over time.

    MT = a + (b * ID)

  14. enter image description here


I had a couple of additional points I wanted to add...

First. I should put all the information above into a conclusion that actually answers your question. When iPhone was introduced, Apple had a guideline that suggested 44 pixels to be the smallest size of a button. The resolution back then was 320x480. So if you put two 44x44 buttons in each corner diagonally, then you get the most difficult task. By using Shannon's formula, we get an Index of Difficulcy equal to 1.38. That is very easy! When Fitts experimentet he used ID=16 as the most difficult task...


download bmml source – Wireframes created with Balsamiq Mockups

Second. For the fun of it, I created a small tool to calculate ´a´ and ´b´ for you. You can run in you browser or you can run it on your phone. The chart obviously needs some work, but the result you get is correct. Chase the button 20 times and get your result.

Goto http://smartmobilestudio.com/smartdemo/Fitts/
or scan the QR code below to get started.
enter image description here

enter image description here

  • +1 but your demo requires 21 clicks(after clicking start), not 20 (:
    – user16280
    Commented Jul 10, 2012 at 16:19
  • 1
    @DorinDuminica Ah. You're right! How could I miss that!? :-P Classical off-by-one error in the human brain... Commented Jul 10, 2012 at 16:21
  • This is what I call overkill answer but still a good one. :D +1 Commented Dec 14, 2014 at 15:30

In Designing Gestural Interfaces, Dan Saffer touches (!) the subject of Fitts' Law in relation to touchscreens (specifically pp. 40-2.) Saffer argues that the law holds true for gestural interfaces; minimize reaching across the interface and making sure that targets are appropriately sized to accommodate the "cursor" (i.e., the finger.)

However, he also notes that touchscreens are seldom subject to the benefit of the "inifinite edge":

One corollary to Fitts' Law isn't as true for gestural interfaces. With traditional input devices such as a mouse or trackball, it makes good sense to place targets such as menu items on the edges of the screens so that the hit target becomes huge because the user cannot overshoot the target; the cursor stops at the edge of the screen. With gestural interfiaces, this is rarely true. With touchscreens, users are seldom dragging their fingers across the screen as they do with a cursor—instead, they will likely lift their fingers and place them on the new target. And with free-standing gestural interfaces. there is seldom an "edge" to bump into, unless it is a physical wall!
(Saffer 2008, p. 42)


Saffer, D. (2008). Designing Gestural Interfaces: Touchscreens and Interactive Devices. Sebastopol, CA: O'Reilly Media, Inc.

  • 3
    Good stuff. In fact touchscreens have sort of the opposite of infinite edge; small controls close to the edge can be very hard to press on some screens; especially Android where the bottom of the screen is very close to the soft buttons
    – Zelda
    Commented Jun 22, 2012 at 13:45

As you can see on its wikipedia page, Fitts Law goes well beyond 2D movement (and HCI in general).

What's known as Fitts Law originates from a (military) memorandum written by P.M Fitts in 1947 (warning: pdf link) that deals with ergonomics of WW2 airplane cockpits, and how the layout of instruments, their scales and the directions of their indicators may confuse the pilot thus yielding "pilot error" (between quotes also in the original document).

Later (in 1954) a paper by Fitts studied not only the perception issue, but the interactions as well. (again warning: pdf link) In this paper one can find many examples, as for instance:

In the first experiment two closely related reciprocal tapping tasks were studied. The 5s were asked to tap two rectangular metal plates alternately with a stylus. Movement tolerance and amplitude were controlled by fixing the width of the plates and the distance between them. The task was accomplished primarily by movements of the lower arm

  • 1
    Can you elaborate on this? Currently this is more of a link to another site than an answer in its own right.
    – JonW
    Commented Jun 21, 2012 at 22:00
  • I'll try as soon as I have some time. I prefer citation since english is not my first language hence I could introduce errors/misunderstanding.
    – Daniele
    Commented Jun 22, 2012 at 7:23

Yes, the Fitts' paradigm has been converted to touch related events.

Bi, Li & Zhai (2013) proposed a new version of the Fitts' paradigm's Index of Difficulty. However, I have not found reports stating experiences from others with this model.

Basic Fitts' law describes correlation between motion time MT and the Index of Difficulty of the pointing task:

$$MT = 2 $$

The 'a' and 'b' are experimentally found regression coefficients.

The adaptation of Index of Difficulty (ID) by Bi et al. (2013) is:

The first distribution measure (expressed as sigma squared) reflects the common speed-accuracy tradeoff in the human motor system. The second distribution measure (expressed as sigma_a squared) reflects the absolute precision on pointing tasks.

For a more detailed technical description, see the following article.

Bi, X., Li, Y., & Zhai, S. (2013, April). FFitts law: Modeling finger touch with Fitts' law. In Proceedings of the 2013 ACM annual conference on Human factors in computing systems (pp. 1363-1372). ACM. ISO 690


Disclaimer : This response is based upon my own analysis

I cant find any research studies but the place where Fitts law is applicable in case of touch screens is when the pointing device (in most cases the finger) is required to be dragged across the screen to fulfill a task (for example dragging a app or icon to an trash can).

However if we were just going to look at directly selecting an item on a screen from a discontinuous perspective taking into consideration 3D movement, multiple factors come into the picture such as relative distance to the target, the size of the target, the angle of the target with regards to the finger (or stylus) and relative positioning of the target with regards to the focus of the user.There could be an argument made that the the angle of the target and the relative positioning could be the constants A and B used in Fitts law

  • I share your thoughts. I was hoping that somebody have already done the job of calculating those A-s and B-s for such screens. Commented Jun 25, 2012 at 11:35

These extensions of Fitts' Law fit better to touch screens that the original 1D point'n'click task:

  • Law of Crossing: Crossing a target of width W at distance D with your pen or finger to trigger an action follows the same rule as the original setup of Fitts. [Accot & Zhai, More than dotting the i's - foundations for crossing-based interfaces, CHI'2002]

  • Law of Steering: The difficulty of following a curved tunnel or road can be derived from Fitts by building the integral form over infinitesimal small D. Originally described in [Accot & Zhai, Beyond Fitts’ Law: Models for Trajectory-Based HCI Tasks, CHI'1997] now part of [ISO 9241-9].


Fitt's Law gives you guidance on how to size and position elements to make them easy clickable. In my opinion we should not try to just adapt this to touch screens, but go one step back an ask: How should elements be positioned and sized to be easily touchable.

This depends on the target device. On a larger tablet the reachability of elements in the center of the screen is not the same as on a smart phone.

Microsofts Windows 8 Touch guidance gives some hints for tablets: Microsofts Windows 8 Touch guidance


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