Screen diagonal:
from width and height to inches, and back
Screen sizes are sold by the diagonal, which hides the actual width and height. Here is how to move between them for any aspect ratio.
Calcylator Editorial Team
Updated · 4 min read
Why screens are sold by a single number
A television is advertised as 55 inches, a monitor as 27 and a phone as 6.7. None of those figures is the width, the height or the area. Each is the length of the line from one corner of the visible picture to the opposite corner. The habit goes back to round cathode-ray tubes, whose size was easiest to describe by a single measurement across.
The diagonal is a convenient label, but it is a poor guide to whether a screen will fit on a desk, in a TV unit or in a pocket. For that you need the width and the height, and getting them takes two pieces of information: the diagonal and the aspect ratio.
Going the other way, from a measured width and height to the diagonal, is a straight application of the Pythagorean theorem, because the diagonal of a rectangle is the hypotenuse of a right triangle whose legs are the two sides.
Diagonal from width and height
- d:
- diagonal, in the same unit as w and h
- w:
- visible width
- h:
- visible height
Width
59.8 cm
Height
33.6 cm
w² + h²
3576.04 + 1128.96 = 4705.00
Diagonal
68.6 cm = 27.0 in
√4705.00 = 68.59 cm, and 68.59 ÷ 2.54 = 27.01, so this is a 27-inch panel.
Measure only the visible picture. The bezel and the stand are not part of the screen size, and including them will push the number up by a centimetre or two.
Width and height from a diagonal
For the reverse, you need the aspect ratio, written as width : height. A 16:9 screen is 16 units wide for every 9 units high. Its diagonal in those units is √(16² + 9²) = √337, about 18.36 units, and you scale to the real diagonal.
- d:
- advertised diagonal
- a : b:
- aspect ratio, for example 16 : 9
Diagonal
55 in
Aspect ratio
16 : 9
√(16² + 9²)
18.358
Width × height
47.9 in × 27.0 in
That is 122 cm by 68 cm. Check: √(47.94² + 26.96²) = 55.0 in.
The same sums work for a phone. A 6.7-inch screen at 9 : 20 comes to about 2.7 in wide by 6.1 in tall, since phones are held upright.
Some products list a viewable diagonal that is smaller than the nominal one, mostly older CRT sets and some projectors with a masked image. Flat panels are normally labelled by the actual visible diagonal, so a quick measurement with a tape from one inner corner of the picture to the opposite one is a good check against the label.
Reference sizes for a 16:9 screen
Most monitors and televisions today use a 16:9 shape, so one table covers the usual sizes. The metric figures are for the visible area.
| Diagonal | Diagonal in cm | Width × height (in) | Width × height (cm) |
|---|---|---|---|
| 24 in | 61.0 cm | 20.9 × 11.8 in | 53 × 30 cm |
| 27 in | 68.6 cm | 23.5 × 13.2 in | 60 × 34 cm |
| 32 in | 81.3 cm | 27.9 × 15.7 in | 71 × 40 cm |
| 43 in | 109.2 cm | 37.5 × 21.1 in | 95 × 54 cm |
| 55 in | 139.7 cm | 47.9 × 27.0 in | 122 × 68 cm |
| 65 in | 165.1 cm | 56.7 × 31.9 in | 144 × 81 cm |
Round the figures up a little when you plan furniture. Bezels are thin on modern panels, but a stand or a wall bracket adds several centimetres on each side, and a soundbar below the screen needs its own clearance.
Same diagonal, different amount of screen
A 27-inch label does not guarantee the same surface in every shape. A squarer panel packs more area into the same diagonal, and a very wide one gives up height. The table shows a 27-inch diagonal in four common ratios.
| Aspect ratio | Width | Height | Area |
|---|---|---|---|
| 4:3 | 21.6 in | 16.2 in | 350 sq in |
| 16:10 | 22.9 in | 14.3 in | 328 sq in |
| 16:9 | 23.5 in | 13.2 in | 312 sq in |
| 21:9 | 24.8 in | 10.6 in | 264 sq in |
The 21:9 ultrawide is the widest, but it has the least area, so a 27-inch ultrawide shows less than a 27-inch 16:9 and noticeably less than a 4:3. It makes up for this with a long horizontal field. A wide screen at the same diagonal also looks smaller to the eye, because its height is lower.
Will it fit? Checks before you buy
A final point about labels: advertised diagonals are rounded to a convenient number. A panel sold as 27 inches may measure 26.9 or 27.0, and a 55-inch TV may be 54.6. The difference is small, but you should use a measured value when the fit is tight.
- Measure the opening or the desk with the width of the screen, not its diagonal. A 55-inch 16:9 TV is about 48 inches wide, plus the frame.
- Add the stand footprint. Many TVs have feet that are nearly as wide as the screen, and some are placed at the far corners.
- Check the viewing distance. A common rule is a distance of roughly 1.2 to 1.6 times the diagonal for a 4K TV, closer for a monitor.
- Convert units on the spec sheet. Some brands list centimetres, some inches, and both can appear in the same catalogue.
- Look at the resolution next to the size. A bigger panel with the same pixel count has coarser pixels.
Common questions
How do I calculate the diagonal of a screen?
Square the width, square the height, add them and take the square root. A screen 59.8 cm wide and 33.6 cm tall gives √(3576 + 1129) = 68.6 cm, which is 27.0 inches when divided by 2.54.
How do I find the width and height of a 55-inch TV?
For a 16:9 screen, multiply 55 by 16 and divide by √(16² + 9²) = 18.36 to get the width, about 47.9 inches. Multiply 55 by 9 and divide by 18.36 for the height, about 27.0 inches.
Is screen size measured diagonally?
Yes. Televisions, monitors, laptops and phones are all labelled by the diagonal of the visible picture area, usually in inches. The frame around it is not counted, so the outer dimensions of the product are larger than the screen suggests.
How many cm is a 32-inch screen diagonally?
Multiply inches by 2.54. A 32-inch screen has a diagonal of 81.3 cm. If the aspect ratio is 16:9, it is about 70.8 cm wide and 39.8 cm tall.
Does aspect ratio change screen area at the same size?
Yes. At the same diagonal, a squarer ratio has more area. A 27-inch 4:3 panel has about 350 square inches, a 16:9 about 312, and a 21:9 about 264. So two screens with the same inches label can give different amounts of picture.
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