Touch Targets and Fitts’s Law

Ada re-derives this chapter’s own numbers step by step, at full precision

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ADA · CALCULATION AUDIT

Touch Targets and Fitts's Law

A smart thermostat ships with light gray text at a 3:1 contrast ratio on a white background and 32x32pt touch targets, and elderly users complain they can’t see the numbers or keep missing the buttons — WCAG AA requires 4.5:1 contrast and 44x44pt minimum targets. The chapter’s own numbers show a 32pt button has an area of 1024 square points against 1936 for a 44pt button, an 89% gain, and Fitts’s Law (with constants 50 and 150 and a 200pt distance) predicts that widening a button from 32pt to 48pt cuts targeting time by about 15%. This audit asks the question those figures invite: do the 89% area gain and the 15% Fitts’s-Law speedup actually check out, and does that arithmetic really justify the 44pt minimum?

Companion to the chapter Accessible Multi-Device Sync — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is touch-target side. The middle card applies this page's rule. The green card is target area. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only touch-target side, so the numeric fixture does not switch without explanation.

Walk the arrows. Widening both dimensions gives more landing area than changing only one edge.

Derive the baseline in four named moves

1
Name the input. The chapter baseline is 44 pt.
2
Name the relationship. area = side x side
3
Substitute with units. 44 pt x 44 pt = 1,936 square pt
4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change touch-target side

Try Predict the direction of area = side x side. Test another touch-target side, then compare target area.

Observe Widening both dimensions gives more landing area than changing only one edge. Reset touch-target side to 44 and compare target area.

Explain At 44 pt, widening both dimensions gives more landing area than changing only one edge.

Check yourself

What should you do before trusting a moved-control result?

Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.

What does this small model leave out?

Answer: Only touch-target side moves here. Field effects named in the technical boundary stay fixed.

Try

Compare 32 × 32 pt with 44 × 44 pt target area, then evaluate Fitts's Law at D = 200 pt for widths 32 and 48 pt using a = 50 ms and b = 150 ms.

Observe

Area rises by 89%, while predicted targeting time falls from about 479 ms to 405 ms—a reduction near 15%.

Explain

Target area grows with width squared, and Fitts's logarithmic index falls as width increases, giving the pointer more spatial tolerance at the same travel distance.

Ada: The “Putting Numbers to It” box makes two motor-accessibility claims I can check exactly: that a 44 pt target has 89% more area than a 32 pt one, and that widening a button from 32 to 48 pt cuts Fitts’s-Law targeting time by about 15%.

Target area scales with the square of the side: 32 x 32 = 1024 pt^2 versus 44 x 44 = 1936 pt^2. The ratio is 1936 / 1024 = 1.8906, i.e. +89% area - the figure holds.
Fitts’s Law with the box’s own a = 50 ms, b = 150 ms, distance D = 200 pt, width W = 32: T = 50 + 150 x log2(200/32 + 1) = 50 + 150 x log2(7.25) = 50 + 150 x 2.8580 ~= 479 ms.
For W = 48: T = 50 + 150 x log2(200/48 + 1) = 50 + 150 x log2(5.1667) = 50 + 150 x 2.3691 ~= 405 ms. The saving is (479 - 405) / 479 ~= 15%, exactly as claimed.

Both numbers are sound, and together they explain the 44 pt minimum: a larger target is quadratically easier to hit and measurably faster to reach, so the same rule that helps a user with tremor also helps everyone wearing gloves or moving in a hurry. (One note for a future edit: the contrast-ratio worked values in the same box do not follow the WCAG sRGB luminance formula and are worth re-deriving with the linked WebAIM checker - the pass and fail verdicts are correct, but the intermediate luminances are not.)

Every number above is taken from the chapter’s own material and re-derived step by step.

Technical boundaries: This one-dimensional Fitts model uses fixed fitted constants and a point target; it omits tremor profiles, touch occlusion, approach angle, device posture, visual search, reach zones, gloves, and accidental activation.

Ready: work the ledger before checking it.