Angular size is the design variable, not physical size

What it is

A two-metre panel at four metres and a one-metre panel at two metres throw roughly the same image on the retina. People read angular size, not metres. Specifying width in centimetres and placement as “put it at 1.5 m” splits two quantities that move together. Step closer and centimetres stay, the visual angle grows; step back and type shrinks on the retina. Degrees are the design variable; metres are the dependent quantity backed out of degrees.

Why it happens

Retinal size is ≈ 2 arctan(s / 2d). Readability, hit-target size, how many columns fit in a glance — all follow that angle, not s or d alone. A fixed physical size plus a chosen stand-off only holds if the person never leaves that point. Walk, and d changes, the angle follows, and the layout scales on the retina. That is not the same event as dragging a desktop window nearer, because the desktop has no walk-driven scaling. Conversely, lock the angle and let physical size scale with distance: the page on the retina stays put; walking only changes vergence demand and reach, not “is this still that page”. Type that scales with distance is one special case of angular thinking; column width, line count, and button hit-angle of the whole panel should be specified in degrees as well.

Studying it

The same reading or selection task, comparing a panel locked in metres with a panel locked in degrees, completed from several standing positions.

Independent variables: size-lock mode (metres / degrees), standing distance, task type (reading / pointing). Dependent variables: reading speed, click errors, a rating of “still the same board”, forward–back movement made to hunt a comfortable angle.

Snellen / ETDRS already calibrate acuity in angle; MNREAD print size is angular. In XR, do not describe the stimulus as “how many centimetres wide”; report degrees.

Where it stops holding

Content that must register to a real object (a label on a door, a 1:1 part) has its size set by the object; angle should change with walking and must not be locked. Operations that measure width with the hands (estimating a piece of cloth) run on body scale, not retinal scale. On optical see-through, real objects have angles set by true distance; a virtual panel that locks angle will lose relative size next to a real doorframe. Low vision needs a higher angular floor, not more centimetres.

Applying it

• Specify the panel as horizontal degrees × vertical degrees. When distance changes, change physical size to keep that angle.
• Do not world-scale a reading UI in fixed centimetres; walking should change near/far, not the page.
• Expose a “lock angle / lock metres” switch: lock metres when registering to a physical object, lock angle when reading.
• How to check: stand at near, mid, and far and compare the retinal page (or ask whether type and columns still feel the same size). Angle-locked should be nearly the same. If near becomes a wall and far a postage stamp, the spec is still in centimetres.

Related

• Same group: N3.09.2 Very few depth layers remain usable · N3.09.3 Letting people set distance is more reliable than one universal preset · N3.09.4 Comfort viewing distance narrows toward mid-range as the session lengthens
• Nearby: N3.02 Interface Distance · N3.04 Text Readability in 3D Space
• Search terms: angular size · visual angle · size-distance scaling