How this calculator works
Viewing distance and screen width form a triangle with the viewer at the apex. For a chosen horizontal viewing angle, the distance is half the screen width divided by the tangent of half the angle. THX recommends a 40 degree angle for an immersive cinema-like view, and SMPTE treats 30 degrees as the minimum comfortable angle, which gives a longer distance and a smaller apparent screen. Inverting the relation turns a seating distance into the screen size range that produces those angles. A separate check uses visual acuity: once each pixel subtends less than about one arc minute, the eye cannot resolve it, so sitting farther than that distance means the extra resolution is wasted.
Formula
distance = (screen width / 2) / tan(viewing angle / 2). For 16:9, screen width = 0.8716 x diagonal and screen height = 0.4903 x diagonal. pixel-free distance = (screen height / vertical pixels) / tan(1 arc minute).
Worked example
At 2.5 metres, the THX 40 degree view calls for a diagonal of 2.5 / 1.1973 = 2.088 metres, or 82.2 inches, and the SMPTE 30 degree view calls for 2.5 / 1.6264 = 1.537 metres, or 60.5 inches. For a 65 inch screen, the THX distance is 1.651 x 1.1973 = 1.977 metres and the SMPTE distance is 2.685 metres. With a 1080p panel the screen height is 0.809 metres, each of the 1080 rows is 0.749 mm tall, and pixels stop being visible at 0.749 / tan(1 minute) = 2.576 metres.
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Frequently asked questions
Which distance should I choose?
Sit at the THX distance for an immersive film experience and at the SMPTE distance for a more relaxed view where the whole screen can be taken in at once. Between the two is comfortable for mixed television, sport and film.
Does resolution change the recommended size?
It changes the distance at which pixels become visible, not the ideal angle. If you sit closer than the pixel-free distance, a higher resolution panel shows more detail; farther away, 1080p and 4K look much the same.
Is a bigger screen always better?
No. A screen that is too large for the room forces you to move your eyes constantly and can make lower quality sources look soft. Match the size to the seating distance and the resolution of your usual content.
How does this compare with the mounting height page?
This page finds the size and distance, and the mounting height page finds the height on the wall for a chosen screen and seat. Use both together when planning a room.