A 65 inch 16:9 picture has 39.7% more area than a 55 inch picture. But the horizontal angle it occupies does not grow with the square of the diagonal. Those are different quantities, and a UI should keep them separate.

I built DisplayMath, a screen comparison calculator. Here is the geometry behind this example.

For a diagonal d and aspect ratio a:b:

function picture(d, a = 16, b = 9) {
  const k = d / Math.hypot(a, b);
  return { width: a * k, height: b * k };
}
function horizontalFov(width, distance) {
  return 2 * Math.atan(width / (2 * distance)) * 180 / Math.PI;
}

The picture function preserves the diagonal's unit. Width and distance must use the same unit in horizontalFov. These snippets illustrate the flat-screen formulas; the app's production model also handles additional inputs.

At 2.5 m, the 55, 65 and 75 inch examples span about 27.4°, 32.1° and 36.7° horizontally. The apparent-size comparison therefore needs the distance as well as the rectangle.

A few practical implementation rules:

• Derive the drawing and the measurement rows from one calculation model.
• Keep canonical units in state and convert at the boundary.
• Validate empty or incomplete inputs before deriving a screen.
• Label examples with their assumptions, including the active picture versus the whole product body.
• Preserve the selected inputs in a share URL so readers can inspect the same example.

For the visual guide, I used nominal flat 16:9 pictures and excluded bezels and stands. That is an explicit limit, not a claim about the outside dimensions of a particular television.

I am the maker of DisplayMath. Try the free comparison and change its viewing distance: https://displaymath.com/?d=4k-55_250cm,4k-65_250cm,4k-75_250cm&utm_source=hashnode&utm_medium=organic&utm_campaign=screens_to_scale_20261027#canvas

Prepared with AI assistance; the numerical examples were checked against the repository calculation model.