98-inch QHD (2560×1440) — 404.8 cm recommended

One arcminute decides where pixels show

Normal 20/20 vision is defined as resolving one arcminute, a sixtieth of a degree. A pixel smaller than that blends into its neighbour. Working out the distance at which one pixel spans an arcminute gives the line where the grid starts to show: 109 cm for 4K on a 55-inch screen, 218 cm for FHD. Twice the pixel density halves the line.

So when does 4K actually earn its keep

For extra resolution to reach your eye, you have to sit close enough to resolve the pixels of the resolution one step below. Farther than that, the lower resolution already looks smooth and nothing changes. This turns up something neat: at the SMPTE distance, FHD pixels sit exactly on the threshold — the recommended distance is only 4 % beyond the pixel limit. The ratio holds for every screen size, because both quantities scale with screen width.

Nearby sizes

Same size, other resolutions

Same resolution, other sizes

Living rooms are usually farther than that

A sofa two and a half to three metres from the screen is common. The pixel limit for 4K on a 55-inch set is 109 cm, so from that seat 4K and the resolution below it look the same. There are two ways out: sit closer, or keep the distance and go bigger — a larger screen has larger pixels, which pushes the limit farther out.

How to read this

• Width = diagonal × 0.8716, height = diagonal × 0.4903 (16:9).
• Recommended distance = screen width ÷ 2 ÷ tan(angle/2). SMPTE 30°, THX 40°.
• Pixels become visible at pixel size ÷ tan(one arcminute).
• For this resolution to matter, sit inside the pixel limit of the step below.