The Functional Area of the Thumb on Mobile Touchscreens

















Where the thumb can reach on a touchscreen surface? The benefit of this model is that you can estimate the thumb functional area quickly and without extensive user experiments.

The model predicts the functional area of the thumb on mobile touchscreens, and can inform

  1. Designers of where to place the input elements
  2. Evaluators of the grips that cover given screen positions
  3. Adaptive interfaces of the thumb reach given current grip

The model takes 1) user hand size, 2) grip, and 3) device size as an input. Given statistics or other reference, or even an intuition as to these, the model provides the functional area of the thumb.

The paper to appear in CHI 2014, Toronto

Bergstrom-Lehtovirta, J., and Oulasvirta, A. Modeling the functional area of the thumb on mobile touchscreen surfaces. To appear in CHI '14, ACM (2014).


A challenge unique to interaction with mobile touchscreens is that not all of the surface can be reached with the thumb of the hand that holds the device. If an interaction ele­ment is beyond the thumb’s immediate reach, the user must change grip in order to reach it. Frequent grip changes can be detrimental to mobile interaction, wherein users must also devote attention to their surroundings. We believe that reaching the interactive elements is important in any one-hand use, because the costs of changing the grip can be surprisingly high, particularly when the other hand would need to be recruited for the task when it is not available. Our model can aid in designing reachable interfaces within the functional area of the thumb.

Procedure and Calculation

The models takes information about the user’s hand size, grip, and device size. You can consult statistics or otherwise estimate the input parameters.

Overview or the protocol:

  1. Obtain or estimate the finger span 's' (the distance between the extended index finger tip and thumb tip) of the target user group by measurement or by consulting anthropometric tables. In the paper the average female finger span was 184.25mm.
  2. Obtain information about the grip, via estimation, direct measurement, or consulting of statistics:
    1. Obtain the origin of the grip. This indicates the hand position on the side of the device (the red circle in the Figure above is placed 50mm from the bottom side of the device)
    2. Obtain or estimate the hand orientation against the side of the device (α in the Figure above).
    3. Measure or estimate the position of the extended index finger's tip on the back of the device (d in the Figure above is 80mm).
  3. Insert parameters in the model (Equation below), rotate according hand orientation (blue line in the Figure above illustrates α = 90◦ and red line α = 110◦), and plot the model output appropriately for the device (Lumia 900 in the example Figure above).

The model for evaluating the functional area of the thumb:

fy(x) = ay(x+h)2 +s−d(1+ak)−bk

(Note: The input parameters to this equation are s and d. You can use α and device dimensions to plot the output in relation to the device. The coefficients ay, h, ak, and bk are provided in the paper and implemented to the tool below, but you can modify those if you have collected user data.)

We also provide a simple Matlab tool for plotting the functional area of the thumb:

  1. Download Plot_Functioanl_Area.m and run in Matlab
  2. Obtain and insert the abovementioned parameters of the user hand size, grip, and device
  3. Click “calculate” to get the prediction given your input
Please note that the plotting tool doens't scale the size of the figure that it plots, so please see the axis to refer to the dimensions of your device. The tool still misses calculation of the grip coverage (see the paper), but we're working on it!

Links and contact

Email Joanna Bergstrom-Lehtovirta: joanna.bergstrom at
Antti Oulasvirta's homepage
HCI group at MPI


Last updated on 13 Mar 2014 by Joanna Bergström-Lehtovirta - Page created on 10 Mar 2014 by Joanna Bergström-Lehtovirta