What a TV’s size really tells you
TVs and monitors are sold by their diagonal in inches, measured corner to corner across the visible picture. That single number hides the dimensions that matter when you plan a wall or a TV stand: the width and the height. It also says nothing about how far away you should sit. This calculator works out all of them from the diagonal and the aspect ratio.
The formulas
For a screen with diagonal D and aspect ratio r (width ÷ height, such as 16 ÷ 9 = 1.778):
- Height = D ÷ √(1 + r²).
- Width = height × r.
- Viewing distance for a given field of view θ = width ÷ (2 × tan(θ ÷ 2)).
- Pixel density (ppi) = horizontal pixels ÷ width in inches.
The closest distance uses a 40-degree field of view, close to what home theater guidelines recommend for a cinema-like picture. The farthest uses 30 degrees, a widely used minimum for a comfortable, immersive image.
Worked example: a 55-inch 4K TV
- Height: 55 ÷ √(1 + 1.778²) = 27.0 inches.
- Width: 27.0 × 1.778 = 47.9 inches.
- Closest distance: 47.9 ÷ (2 × tan 20°) = 65.9 in = 5.5 feet.
- Farthest distance: 47.9 ÷ (2 × tan 15°) = 89.4 in = 7.5 feet.
- Pixel density: 3,840 ÷ 47.9 = 80 ppi. The screen area is 1,293 square inches.
Size and seating distance for 16:9 screens
| Diagonal | Width | Height | Closest | Farthest |
|---|---|---|---|---|
| 43 in | 37.5 in | 21.1 in | 4.3 ft | 5.8 ft |
| 50 in | 43.6 in | 24.5 in | 5.0 ft | 6.8 ft |
| 55 in | 47.9 in | 27.0 in | 5.5 ft | 7.5 ft |
| 65 in | 56.7 in | 31.9 in | 6.5 ft | 8.8 ft |
| 75 in | 65.4 in | 36.8 in | 7.5 ft | 10.2 ft |
| 85 in | 74.1 in | 41.7 in | 8.5 ft | 11.5 ft |
Choosing the right size for your room
Work backward from your couch. Measure the distance from your eyes to the wall where the TV will go, then pick the largest size whose range includes that distance. If you sit 8 feet away, a 65-inch screen lands near the farthest distance and a 75-inch near the close end of its range. Many buyers who follow the old advice of sitting very far away end up wishing they had chosen a bigger screen.
Resolution and distance
With 4K, the pixel grid is invisible at the closest recommended distance for most viewers, so you can sit near the 40-degree mark. With a 1080p screen of the same size, sitting closer than about 1.6 times the diagonal can reveal pixel structure, so the far end of the range works better. 8K gives a visible benefit only on very large screens viewed from close up.
Other aspect ratios
Ultrawide 21:9 monitors are wider and shorter than a 16:9 screen with the same diagonal: a 34-inch ultrawide is about as tall as a 27-inch 16:9 monitor. When comparing screens of different shapes, compare their widths and heights, not their diagonals.
Before you mount it
Add the bezel, usually a fraction of an inch to an inch on each side, and check the stand’s footprint or the VESA mounting pattern. For wall mounting, place the center of the screen at roughly seated eye level, about 40 to 45 inches above the floor, to avoid neck strain.