This exercise demonstrates how to derive the constants in Fitts' Law. Given the Width, Area and Movement Time, calculate the Index of Difficulty for the given numbers to produce a table like this:
| Amplitude | Width | ID | Slope | MT |
| 8 | 8 | 1 | 254 | 254 |
| 8 | 4 | 2 | 176.5 | 353 |
| 16 | 8 | 2 | 172 | 344 |
| 8 | 2 | 3 | 160.3333333 | 481 |
| 16 | 4 | 3 | 157.3333333 | 472 |
| 32 | 8 | 3 | 167 | 501 |
| 8 | 1 | 4 | 162.25 | 649 |
| 16 | 2 | 4 | 150.75 | 603 |
| 32 | 4 | 4 | 151.25 | 605 |
| 64 | 8 | 4 | 173.5 | 694 |
| 16 | 1 | 5 | 155.6 | 778 |
| 32 | 2 | 5 | 152.6 | 763 |
| 64 | 4 | 5 | 160.8 | 804 |
| 32 | 1 | 6 | 153.5 | 921 |
| 64 | 2 | 6 | 160.5 | 963 |
| 64 | 1 | 7 | 162.4285714 | 1137 |
Then if you take the above points and plot them you can fit a line to the points and come up with an equation for Fitts' Law.
So the line that would best fit the points would be: MT=53+148ID
In extending Fitts' Law into to two dimensions, the width component of the Index of Difficulty must compensate for both width and height. There are a number of different methods for dealing with 2 dimensional targets in Fitts' Law.
| Fitts' | Fitts' | Shannon's | Shannon's | ||||
| Amplitude | Width | Height | Width | ID | MT | ID | MT |
| 2 | 4 | 2 | 4 | 0 | 230 | 1 | 396 |
| 4 | 4 | 2 | 4 | 1 | 396 | 1.584962501 | 493.1037751 |
| 6 | 4 | 2 | 4 | 1.584962501 | 493.1037751 | 2 | 562 |
| 2 | 1 | 5 | 1 | 2 | 562 | 2.321928095 | 615.4400638 |
| 4 | 1 | 5 | 1 | 3 | 728 | 3.169925001 | 756.2075502 |
| 6 | 1 | 5 | 1 | 3.584962501 | 825.1037751 | 3.700439718 | 844.2729932 |
| 2 | 3 | 4 | 3 | 0.415037499 | 298.8962249 | 1.222392421 | 432.9171419 |
| 4 | 3 | 4 | 3 | 1.415037499 | 464.8962249 | 1.874469118 | 541.1618736 |
| 6 | 3 | 4 | 3 | 2 | 562 | 2.321928095 | 615.4400638 |
| Fitts' | Fitts' | Shannon's | Shannon's | ||||
| Amplitude | Width | Height | Sum | ID | MT | ID | MT |
| 2 | 4 | 2 | 6 | -0.584962501 | 132.8962249 | 0.736965594 | 352.3362886 |
| 4 | 4 | 2 | 6 | 0.415037499 | 298.8962249 | 1.222392421 | 432.9171419 |
| 6 | 4 | 2 | 6 | 1 | 396 | 1.584962501 | 493.1037751 |
| 2 | 1 | 6 | 7 | -0.807354922 | 95.97908294 | 0.652076697 | 338.2447316 |
| 4 | 1 | 6 | 7 | 0.192645078 | 261.9790829 | 1.099535674 | 412.5229218 |
| 6 | 1 | 6 | 7 | 0.777607579 | 359.0828581 | 1.440572591 | 469.1350502 |
| 2 | 5 | 3 | 8 | -1 | 64 | 0.584962501 | 327.1037751 |
| 4 | 5 | 3 | 8 | 0 | 230 | 1 | 396 |
| 6 | 5 | 3 | 8 | 0.584962501 | 327.1037751 | 1.321928095 | 449.4400638 |
The Area Model is used by taking the product of the width and height and using it for the width in the Index of Difficulty.
| Fitts' | Fitts' | Shannon's | Shannon's | ||||
| Amplitude | Width | Height | Area | ID | MT | ID | MT |
| 2 | 4 | 2 | 8 | -1 | 64 | 0.584962501 | 327.1037751 |
| 4 | 4 | 2 | 8 | 0 | 230 | 1 | 396 |
| 6 | 4 | 2 | 8 | 0.584962501 | 327.1037751 | 1.321928095 | 449.4400638 |
| 2 | 1 | 6 | 6 | -0.584962501 | 132.8962249 | 0.736965594 | 352.3362886 |
| 4 | 1 | 6 | 6 | 0.415037499 | 298.8962249 | 1.222392421 | 432.9171419 |
| 6 | 1 | 6 | 6 | 1 | 396 | 1.584962501 | 493.1037751 |
| 2 | 5 | 3 | 15 | -1.906890596 | -86.54383887 | 0.341036918 | 286.6121284 |
| 4 | 5 | 3 | 15 | -0.906890596 | 79.45616113 | 0.61667136 | 332.3674458 |
| 6 | 5 | 3 | 15 | -0.321928095 | 176.5599362 | 0.847996907 | 370.7674865 |
Instead of always ignoring the height, you can also just pick the smaller of the height and width. Intuitively this method seems like it will produce accurate results, because the smallest dimension of the object will be the most restricting when attempting to move a cursor inside it.
| Smaller | Fitts' | Fitts' | Shannon's | Shannon's | |||
| Amplitude | Width | Height | of H&W | ID | MT | ID | MT |
| 2 | 4 | 2 | 2 | 1 | 396 | 1.584962501 | 493.1037751 |
| 4 | 4 | 2 | 2 | 2 | 562 | 2.321928095 | 615.4400638 |
| 6 | 4 | 2 | 2 | 2.584962501 | 659.1037751 | 2.807354922 | 696.0209171 |
| 2 | 1 | 6 | 1 | 2 | 562 | 2.321928095 | 615.4400638 |
| 4 | 1 | 6 | 1 | 3 | 728 | 3.169925001 | 756.2075502 |
| 6 | 1 | 6 | 1 | 3.584962501 | 825.1037751 | 3.700439718 | 844.2729932 |
| 2 | 5 | 3 | 3 | 0.415037499 | 298.8962249 | 1.222392421 | 432.9171419 |
| 4 | 5 | 3 | 3 | 1.415037499 | 464.8962249 | 1.874469118 | 541.1618736 |
| 6 | 5 | 3 | 3 | 2 | 562 | 2.321928095 | 615.4400638 |
The last model uses the length of the line between the center point of the object and the object boundary. This would be calculated along the angle of approach and would therefore be more difficult to calculate because you must know the angle between the starting point and the target object.