Type size must scale with distance

What it is

A heading that is just readable at one metre, moved unchanged to three metres, is still a few centimetres tall and about a third as large on the retina. Type size scaling with distance means the physical height is multiplied by the same factor as the distance, so the visual angle on the retina is kept. It is about whether the letters remain readable after a move, not about declaring which metre the panel should sit at, and not about promoting visual angle to the only design unit.

Why it happens

Pinhole geometry is similar triangles: tan θ ≈ h / d. Triple d and hold h, and θ falls to about a third, so strokes occupy proportionally fewer pixels. Screen UI can write type as “16 px” because viewing distance is almost constant. In space, d is a free variable, and the same centimetres are not the same reading condition at every depth.

Proportional means a linear factor, not “a bit larger when farther.” Move from 1.2 m to 2.4 m and the height must double for that line to stay the same size on the retina. Adding twenty percent looks like an adaptation and still drops the angle sharply. The other direction is the same rule: pull the large letters from three metres in to one metre unchanged, and they become a sign in the face.

Studying it

Prepare two versions of the same passage: physical height locked, and height scaled in proportion to distance. Take two or three depths, and measure reading rate, errors, and subjective effort. The scaled set should hold similar reading performance across depths; the locked set should worsen with distance.

Independent variables: distance, scaling rule (locked physical height / proportional to distance), typeface. Dependent variables: reading rate, misidentification rate, subjective effort, pixels per letter (recovered from headset PPD and visual angle).

A flat screenshot in place of the headset misses stereo and head motion and produces a false negative of “it looks the same size on the monitor.” Present at real depth in the headset. If people are allowed to walk up to read at the far distance, the scaling rule has not been tested — they have already rewritten d with their feet.

Where it stops holding

When headset resolution is the floor, further proportional enlargement still hits too few pixels per degree at range — that is a device limit, not a missed multiply. At extreme nearness, shrinking type in proportion does not make an too-near panel comfortable; the vergence conflict remains. Dense Chinese strokes and a small Latin x-height do not share a readable threshold at the same angle; a factor copied from Latin will not carry to 汉字. A billboard that wants to be recognised from far away spends angle on attention; that is not the rule for body text.

Applying it

• Give each text role a visual angle to keep (one for a heading line, one for body). When distance changes, retarget physical height in proportion to d; do not stop at “looks about the same.”
• Do not move a panel farther and keep the centimetres. Farther means larger.
• Check that Chinese counters (口, 日, 目) still separate at the target distance; do not inspect only Latin x-height.
• How to check: the same passage at 1.2 m and 2.4 m, height h near and 2h far. Reading rate and errors should be close. If the far setting is still clearly slower, either the ratio is wrong or resolution has already been hit. Add a control that keeps h at the far distance; that is the group that should drop.

Related

• Same group: N3.02.1 Too near causes vergence conflict and a sense of pressure · N3.02.2 Too far lowers readability and pointing precision
• Nearby: N3.09 Interface Distance and Comfort Viewing Distance · N1.04 Vergence–Accommodation Conflict
• Search terms: distance-scaled type · size-distance scaling · visual angle of type