Fitts's law

Fitts had people tap alternately between two metal plates, varying the width of the plates and the distance between them, defined an index of difficulty as log2(2A/W) bits, and found the rate of movement roughly constant across conditions: the claim was never that bigger is better, but that the price of precision is logarithmic. He also noted performance falling off “at the largest amplitudes and tolerances.” MacKenzie's review calls the model “one of the most robust, highly cited, and widely adopted models to emerge from experimental psychology,” replicated for wrist, finger, foot and head movement, under a microscope and underwater, in children and older adults, in Parkinson's disease, and in monkeys; the form HCI now uses is his Shannon version, MT = a + b·log2(A/W + 1). What it covers is narrow, though: Fitts and Peterson ran the task as a discrete response to a stimulus light and reported their rate only after factoring reaction time out. Size and distance govern the reach to a target the user has already chosen, and finding it is a separate, roughly linear cost.

Because difficulty is a logarithm of the distance-to-width ratio, each doubling of a target's width removes less difficulty than the last: from a target an eighth of the distance away, successive doublings take the index from 3.17 bits to 2.32, then 1.58, then 1.00 — savings of 0.85, then 0.74, then 0.58 bits. Parhi and colleagues found the ceiling empirically on a touchscreen: their pilots showed performance “leveled off for target sizes greater than 11.5 mm,” and in the study proper tap speed still improved from 9.6 mm to 11.5 mm while the error rate did not differ between those two sizes at all. Past roughly a finger pad you are paying pixels for nothing, so spend them on the next control. The constants do not travel either: across 24 published mouse models, Soukoreff and MacKenzie found reported throughput for ordinary pointing spread from 2.55 to 12.5 bits/s, tenfold for the same device and task, so no published slope is a time budget for your screen. The model also assumes roughly 4% of taps miss, and a control people miss a third of the time is not being described by it at all.

For finger input the law holds only with a term for the finger itself. Bi, Li and Zhai modelled endpoint spread as two independent normal distributions, one from the speed–accuracy trade-off and one the absolute imprecision of the finger, and their error rates are the numbers to size against: on 2.4 mm circular targets participants missed 65–66% of the time; at 4.8 mm, 25–27%; at 7.2 mm, 7%. Time degrades gently as targets shrink; accuracy falls off a cliff. How best to estimate the finger term is still argued over — Ko and colleagues fit it better as a free parameter than as a pre-measured constant — but the direction is not in dispute. Part of that floor is a systematic offset rather than noise, and it is in the hardware. Holz and Baudisch found users aligning features on the top of the finger with the target while capacitive hardware senses the contact area underneath, and their projected-centre model cut error offsets to 1.6 mm from 4 mm. Henze, Rukzio and Boll instrumented an Android game, found touch positions systematically skewed across over 120 million taps, and shipped a compensation function that reduced the error rate by 7.79%. You cannot style your way out of a sensor that reads low.

The platform minimums everyone quotes are convention that happens to agree with that work, not conclusions drawn from it. WCAG 2.2 adds Success Criterion 2.5.8 Target Size (Minimum) at Level AA — “The size of the target for pointer inputs is at least 24 by 24 CSS pixels” — with five exceptions: spacing, an equivalent control elsewhere on the page, inline targets in a sentence, user-agent-determined sizes, and presentations that are essential or legally required. Success Criterion 2.5.5 Target Size (Enhanced), at Level AAA, asks for “at least 44 by 44 CSS pixels” with four. Android's guidance states that “A touch target of 48x48dp results in a physical size of about 9mm” and that “The recommended target size for touchscreen objects is 7-10mm,” recommends 8dp of separation, and cites nothing on the page. That 9 mm sits almost exactly on the 9.2 mm for discrete tasks and 9.6 mm for serial tasks that Parhi, Karlson and Bederson recommended, so the number is defensible, just not derived in the document that publishes it.

Thumb-reach maps are the weakest link in the chain. The grip figures everyone redraws come from Hoober's observation of 1,333 people in public, 780 of them touching the screen: 49% one-handed, 36% cradled, 15% two-handed. It is a field survey rather than an experiment, the article says the reach zones “are only approximate and vary for different individuals,” and Hoober later told readers to ignore the touch-location drawings in it. Bergstrom-Lehtovirta and Oulasvirta derived the thumb's functional area from the kinematics of the gripping hand, with surface size, hand size and index-finger position as inputs, which is to say there is no single map. Where region has been tested directly the result is modest: on a 3.5-inch device Parhi found a main effect of target size on both time and errors but none of screen location on either, with only comfort ratings moving, while Trudeau and colleagues found right-handed thumb tapping on an iPhone best at the top right and worst at the bottom right. Design the thumb arc, but do not trust a coloured overlay copied from a blog post.

Screen edges invert between pointer and finger, which makes the desktop heuristic actively wrong on a phone. With a mouse the edge stops the cursor, making the target effectively unbounded and overshoot impossible, and a recent modelling paper surveying that literature puts the gain at as much as 44% over regular pointing, citing Appert, Chapuis and Beaudouin-Lafon. With a finger there is nothing to stop: Avrahami and Usuba, Yamanaka and Sato both found that smaller target-to-edge gaps increase movement time, Usuba's crowdsourced replication found error rate rising too, the standing guideline from these studies is a gap of at least 4 mm, and Henze's taps likewise showed edge targets to be less accurate. Kasahara's 2026 preprint complicates even that, reporting success rates improving when a target actually touches the edge, apparently because people tap the target and the bezel together — unreviewed, and on current phones the edges are given over to system gestures anyway. What reliably buys size is a hit area larger than the graphic. McGuffin and Balakrishnan found that “users benefit from target expansion even if the target only begins expanding after 90% of the distance to the target has been travelled,” with performance governed by the final size rather than the initial one. Their own caveat is the one to design around: with several adjacent expanding widgets the expansions collide, which is exactly what happens when overlapping touch padding is bolted onto a dense row of icons.

So the core claim is as strong as anything in this library, and almost everything built on top of it is weaker. The millimetre minimums are vendor convention, the thumb maps rest on one partly retracted field survey plus kinematic models of twenty hands, the edge rule reverses on touch, and none of it says anything about whether the target can be found. Use the law to decide what gets the big target and how far the hand must travel to it, then check the error rate, because that is the measure that moves first when a control is too small.