Screen size calculator — diagonal to width and height
Turn a screen diagonal into real width, height, viewing area and pixel density for any aspect ratio, with the Pythagoras working shown in full.
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r = 16 ÷ 9 = 1.7778
width = diagonal × r ÷ √(r² + 1)
= 27.00 × 1.7778 ÷ 2.0397
= 23.53 in
height = diagonal ÷ √(r² + 1)
= 27.00 ÷ 2.0397
= 13.24 inPPI = √(2560² + 1440²) ÷ 27.00
= 2937.2 ÷ 27.00
= 108.79 pixels per inch16:9
16:9 — HD and 4K video, most monitors and TVs
23.53 in × 13.24 in, 108.8 PPI
The diagonal is the least useful number on the box
Screens are sold by diagonal because it is one number and it sounds big. It is also the one dimension you never need: what matters is whether the panel fits the desk, the wall recess or the AV cabinet, and how tall it will be once it is on a stand. Two screens with the same diagonal can differ by ten centimetres in width and by a third in area, purely because their shapes differ.
The formula
A screen is a rectangle, so the diagonal is its hypotenuse. With r = width ÷ height:
width = diagonal × r ÷ √(r² + 1)
height = diagonal ÷ √(r² + 1)
area = width × heightFor a 27-inch 16:9 panel, r = 1.7778 and √(r² + 1) = 2.0396, giving 23.53 in wide and 13.24 in tall — 59.8 × 33.6 cm. The calculator prints those two lines with your own numbers substituted so the result is checkable rather than magic.
Common sizes worked out
| Diagonal | Ratio | Width | Height | Area |
|---|---|---|---|---|
| 24 in | 16:9 | 20.9 in / 53.1 cm | 11.8 in / 29.9 cm | 246 in² |
| 27 in | 16:9 | 23.5 in / 59.8 cm | 13.2 in / 33.6 cm | 311 in² |
| 32 in | 16:9 | 27.9 in / 70.8 cm | 15.7 in / 39.8 cm | 437 in² |
| 34 in | 64:27 | 31.4 in / 79.7 cm | 13.2 in / 33.6 cm | 414 in² |
| 55 in | 16:9 | 47.9 in / 121.7 cm | 27.0 in / 68.6 cm | 1294 in² |
| 65 in | 16:9 | 56.7 in / 143.9 cm | 31.9 in / 81.0 cm | 1806 in² |
Note the 34-inch ultrawide: it is wider than a 32-inch 16:9 monitor but shorter, and its total area is smaller. “Bigger diagonal” and “more screen” are not the same claim.
Pixel density, and what counts as sharp
PPI is the diagonal measured in pixels divided by the diagonal measured in inches:
PPI = √(w² + h²) ÷ diagonal. A 27-inch 1440p monitor is 109 PPI; the same size at
4K is 163; a 14-inch laptop at 2880 × 1800 is about 243.
| PPI | Impression at desk distance |
|---|---|
| Under 90 | Visibly pixelated; text edges look stepped |
| 90–110 | The traditional desktop norm — perfectly usable |
| 110–140 | Noticeably cleaner text |
| 140–200 | Sharp; most people stop noticing pixels |
| Over 200 | Retina-class: individual pixels are invisible at normal distance |
Sharpness depends on distance as much as density. A 65-inch 4K television is only 68 PPI, but at three metres it looks flawless — the eye resolves roughly one arcminute, so what matters is pixels per degree of vision, not pixels per inch of glass.
Buying and fitting
- Add the bezel and stand. The calculated figures are the active display area. Real products are 1–3 cm wider and considerably taller once the stand is included.
- Check the height for wall mounts. A 65-inch television is 81 cm tall — often the constraint in an alcove, not the width.
- Two 24-inch monitors ≠ one 32-inch. Two 24s give 42 in of width and 492 in² of area; a 32 gives 28 in and 437 in². The pair wins on both counts, at the cost of a bezel down the middle.
- Ultrawide versus dual. A 34-inch 21:9 is close to two 19-inch panels side by side, without the seam but also without the ability to angle them.
Phones and tablets
The same maths applies — enter the diagonal, the ratio (19.5:9 and 20:9 for modern phones, 4:3 or 3:2 for tablets) and the resolution. One caveat: manufacturers measure the diagonal as if the display were a plain rectangle, so a phone with a notch or a rounded corner has slightly less usable area than the number suggests.
Related tools
Aspect Ratio Calculator for solving pixel dimensions, CM to Inches for the unit conversion on its own, and PX to REM Converter for the CSS side of screen sizing.
Questions
How wide is a 27-inch monitor?
About 23.5 inches (59.8 cm) wide and 13.2 inches (33.6 cm) tall for a 16:9 panel — plus the bezel and stand. The diagonal alone never tells you whether a screen fits a desk or a wall recess; this page converts it into the two numbers that do.
Why are two screens with the same diagonal different sizes?
Because the shape differs. A 34-inch 21:9 ultrawide is far wider but much shorter than a 34-inch 16:9 panel would be, and a 4:3 screen of the same diagonal has noticeably more area than either. Area scales with the shape, not just the diagonal.
What is a good PPI?
Around 90–110 PPI is the traditional desktop norm (a 27-inch 1440p panel is 109). Roughly 140–180 looks noticeably crisper, and above about 200 individual pixels are invisible at normal desk distance — a 27-inch 4K panel is 163, a 14-inch laptop at 2880 × 1800 is about 243.
How is the width calculated?
With Pythagoras. If r is width ÷ height, then width = diagonal × r ÷ √(r² + 1) and height = diagonal ÷ √(r² + 1). The page prints those two lines with your numbers filled in so you can check the result by hand.
Does this work for phones and tablets?
Yes — enter the diagonal and the ratio (19.5:9 and 20:9 are common for phones; 4:3 and 3:2 for tablets) and add the resolution to get the pixel density. Note that a phone with a notch is usually measured as if the display were a full rectangle.