Screen size calculator
A screen's advertised size is just its diagonal. This calculator turns that one number into the things you actually need — real width and height, pixel density (PPI) and dot pitch — in inches and centimetres.
All maths runs locally in your browser. The diagonal is the viewable picture only — bezels and stands are not included, which is why a “55-inch” TV is not 55 inches wide.
The short answer
For a screen with diagonal d and aspect ratio w : h, the width is d × w ÷ √(w² + h²) and the height is d × h ÷ √(w² + h²) — Pythagoras, applied once. A 55″ 16:9 screen therefore measures 47.94 in wide × 26.96 in high (121.76 × 68.49 cm), not 55 inches across. Pixel density is the same trick in the other direction: divide the diagonal pixel count √(W² + H²) by the diagonal in inches. A 27″ 4K monitor (3840 × 2160) works out to 163.18 PPI with a dot pitch of 0.156 mm.
Why the diagonal alone misleads
Two screens can share a diagonal and have very different shapes. A 34″ ultrawide (21:9) is wider but shorter than a 32″ 16:9 monitor, and a 49″ super-ultrawide is essentially two 27″ monitors side by side with less height than a 43″ TV. That is why this calculator always asks for the ratio (or the resolution, which implies it) and always gives you width and height — the numbers that decide whether a screen fits a desk, a wall or a flight case.
Three formulas, no black box
| Question | Formula | Worked example |
|---|---|---|
| Width & height from diagonal | W = d·w÷√(w²+h²), H = d·h÷√(w²+h²) | 55″ 16:9 → 47.94″ × 26.96″ |
| Pixel density | PPI = √(W² + H²) ÷ d | 3840×2160 at 27″ → 163.18 PPI |
| Dot pitch | 25.4 ÷ PPI (mm) | 0.156 mm for the same monitor |
| Diagonal from width & height | d = √(W² + H²) | 55.00″ for a 47.94″ × 26.96″ panel |
Centimetres use the exact definition of the inch: 1 in = 2.54 cm, no rounding shortcuts. PPI assumes square pixels, which holds for effectively all modern LCD and OLED panels.
Where to go next
PPI calculator
Density only, with a preset table of well-known phones, laptops and monitors and what their PPI means in practice.
TV size calculator
TV dimensions by diagonal, plus the viewing distance most people find comfortable for each size.
Screen size chart
Every common diagonal from 5″ to 98″ as 16:9 width and height, in inches and centimetres.
Frequently asked questions
Is a 55-inch TV really 55 inches wide?
No. 55 inches is the diagonal of the viewable picture. A 16:9 55″ screen is about 47.94 inches wide and 26.96 inches high; the cabinet adds a little for the bezel.
Why does the calculator need the aspect ratio?
Because the diagonal fixes only the hypotenuse. The same 27″ diagonal gives a wide, short panel at 21:9 and a narrower, taller one at 16:10. The ratio supplies the shape; Pythagoras does the rest.
What PPI do I need?
It depends on viewing distance. Around 90–110 PPI is typical for a desktop monitor viewed at arm's length, phones sit at 400+ PPI because they are held closer, and a large TV can be under 60 PPI and still look sharp from a sofa. The PPI calculator page has reference points.
Does screen size include the bezel?
No — the rated size is the viewable area measured corner to corner. If you are cutting an alcove or checking a mount, add the manufacturer's full unit dimensions on top of the picture size you get here.