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 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.

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.