A screen's advertised size is its diagonal. To get the width and height, treat the aspect ratio as a right triangle: for 16:9 the diagonal of the ratio is √162 + 92 = √337 ≈ 18.36, so a 65-inch TV is 65 × 16 ÷ 18.36 ≈ 56.65 in wide and 65 × 9 ÷ 18.36 ≈ 31.87 in tall.
How to use the screen size calculator
- Enter the diagonal in inches or centimeters. TVs and monitors are almost always sold by the diagonal in inches.
- Choose the aspect ratio, the shape of the screen written as width : height. If your exact shape is not listed, pick Match resolution to use the pixel counts, or Custom to type your own, such as 19.5 : 9 for many phones.
- Add the resolution (optional), such as 3840 × 2160 for 4K, to get the pixel density in pixels per inch (PPI). If the resolution's shape differs from the ratio you picked by more than 2%, the calculator points it out.
- Add a second screen (optional) to see both drawn to the same scale, with the area of screen B as a percentage of screen A.
The results update as you type, and the page address changes with them, so you can bookmark a comparison or send it to someone.
How diagonal screen size works
Width, height and diagonal form a right triangle, with the diagonal as the hypotenuse. The aspect ratio tells you the shape of that triangle but not its size. A 16:9 screen is 16 units wide and 9 units tall for some unit, and the Pythagorean theorem gives the diagonal in the same units. Dividing the real diagonal by that number tells you how big one unit is. Since 337 is not a perfect square, √337 is an irrational number (see square roots), so screen dimensions are almost never whole numbers.
Two practical details. First, the diagonal measures the picture area, from one corner of the lit image to the opposite corner, not the frame around it. Second, many TVs are sold by size "class": a "65-inch class" set may measure slightly less, such as 64.5 in, on the diagonal. The spec sheet lists the exact viewable size, and that is the number to type in.
Screen size formulas
For a screen with diagonal d and aspect ratio w : h, first find the diagonal of the ratio, √w2 + h2, then scale:
width= d · w over √w2 + h2height= d · h over √w2 + h2The area is width times height. For 16:9 screens this simplifies to area = 144 d2 ÷ 337 ≈ 0.427 d2, so a 65-inch TV has about 0.427 × 652 ≈ 1,805 square inches of picture. To go backward from a width you have room for, solve the first formula for the diagonal: d = width · √w2 + h2 ÷ w. One shape is special: a 4:3 screen is a 3-4-5 triangle, so its diagonal of the ratio is exactly 5 and a 20-inch 4:3 screen measures exactly 16 × 12 in.
Pixel density uses the same theorem on the pixel grid. A screen with pw by ph pixels has √pw2 + ph2 pixels along its diagonal, so
PPI = √pw2 + ph2 over d (in inches)This works whatever the aspect ratio, because it compares the diagonal in pixels with the diagonal in inches. The same idea, measuring a straight line across a grid, is the distance formula, and computers use it constantly; see the Pythagorean theorem in computer science.
Worked examples
Example 1: how big is a 55-inch TV?
A 55-inch TV has a 16:9 screen.
k= 55 ÷ √337 ≈ 2.9960width= 16k ≈ 47.94 inheight= 9k ≈ 26.96 inThe picture is about 47.9 in wide and 27.0 in tall (121.8 × 68.5 cm).
Example 2: what fits a 40-inch-wide space?
A cabinet opening is 40 in wide. What is the largest 16:9 screen whose picture fits?
d = 40 × √337 over 16 ≈ 45.89 inA screen with a diagonal up to about 45.9 in. A 43-inch TV (picture 37.5 in wide) fits with room for its frame; a 50-inch TV (43.6 in wide) does not.
Example 3: pixel density of a 27-inch monitor
A 27-inch monitor shows 2560 × 1440 pixels.
diagonal= √25602 + 14402≈ 2937.2 pixelsPPI≈ 2937.2 ÷ 27 ≈ 108.8About 109 PPI. The same size at 4K (3840 × 2160) gives about 163 PPI, so text and images look noticeably sharper.
Example 4: ultrawide versus standard
Compare a 34-inch 21:9 ultrawide with a 27-inch 16:9 monitor.
The ultrawide works out to 31.25 × 13.39 in and the 27-inch to 23.53 × 13.24 in. They are almost the same height, so the ultrawide is like a 27-inch monitor with about 7.7 in of extra width. A 34-inch ultrawide with 3440 × 1440 pixels is really 43:18 (about 2.39 : 1) rather than 21:9 (2.33 : 1); choosing Match resolution gives 31.36 × 13.13 in.
Same diagonal, different shapes
The diagonal alone does not tell you how much screen you get. Every rectangle with a 32-inch diagonal has its four corners on the same circle, because the diagonal is a diameter of that circle. Wide, thin shapes have less area than squarer ones.
For any other rectangle, such as a room, a frame or a sheet of plywood, the rectangle diagonal calculator works the same way from the length and the width. Area also grows with the square of the diagonal. For two screens of the same shape, the area ratio is (d2 ÷ d1)2. A 65-inch TV is only 18% longer on the diagonal than a 55-inch one, but (65 ÷ 55)2 ≈ 1.40, so it has about 40% more picture.
Common screen sizes
| Diagonal | Width × height (in) | Width × height (cm) | Area (in²) |
|---|---|---|---|
| 32″ | 27.89 × 15.69 | 70.8 × 39.8 | 438 |
| 43″ | 37.48 × 21.08 | 95.2 × 53.5 | 790 |
| 50″ | 43.58 × 24.51 | 110.7 × 62.3 | 1,068 |
| 55″ | 47.94 × 26.96 | 121.8 × 68.5 | 1,293 |
| 65″ | 56.65 × 31.87 | 143.9 × 80.9 | 1,805 |
| 75″ | 65.37 × 36.77 | 166.0 × 93.4 | 2,404 |
| 85″ | 74.08 × 41.67 | 188.2 × 105.8 | 3,087 |
| Screen | Width × height (in) | Resolution | PPI |
|---|---|---|---|
| 24″ 16:9 | 20.92 × 11.77 | 1920 × 1080 | 91.8 |
| 27″ 16:9 | 23.53 × 13.24 | 2560 × 1440 | 108.8 |
| 27″ 16:9 (4K) | 23.53 × 13.24 | 3840 × 2160 | 163.2 |
| 32″ 16:9 (4K) | 27.89 × 15.69 | 3840 × 2160 | 137.7 |
| 34″ ultrawide | 31.36 × 13.13 | 3440 × 1440 | 109.7 |
| 49″ 32:9 | 47.17 × 13.27 | 5120 × 1440 | 108.5 |
| 13.3″ 16:10 laptop | 11.28 × 7.05 | 2560 × 1600 | 227.0 |
A higher PPI means smaller pixels, but how sharp a screen looks also depends on how far away you sit. A 65-inch 4K TV has only about 68 PPI, yet it looks sharp from the sofa because you sit several feet farther away than you would from a monitor. TV and monitor sizes are a favorite type of Pythagorean theorem word problem, and one of many everyday uses of the theorem.
Frequently asked questions
How is a TV screen measured?
Diagonally, from one corner of the picture area to the opposite corner. The frame around the picture is not included, so the TV itself is wider and taller than the screen dimensions this calculator gives. For the outside size, check the manufacturer's dimensions.
How wide is a 65-inch TV?
A 65-inch 16:9 TV has a picture about 56.65 in wide and 31.87 in tall (143.9 × 80.9 cm). The frame adds to that; the manufacturer's spec sheet lists the outside width of the set.
How do I calculate PPI?
Use the theorem on the pixel counts: PPI = √pw2 + ph2 ÷ d. A 24-inch 1920 × 1080 monitor has √19202 + 10802 ≈ 2202.9 pixels on its diagonal, so about 91.8 PPI.
Is a 75-inch TV much bigger than a 65-inch TV?
Bigger than the numbers suggest. Area grows with the square of the diagonal, so a 75-inch set has (75 ÷ 65)2 ≈ 1.33 times the picture area, about 33% more. A 75-inch is also about 8.7 in wider (65.37 versus 56.65 in).
Why doesn't my 21:9 monitor match the 21:9 result exactly?
"21:9" is a marketing name. A 3440 × 1440 monitor is really 43:18 (2.39 : 1) and a 2560 × 1080 monitor is 64:27 (2.37 : 1), while true 21:9 is 2.33 : 1. Enter the resolution and pick Match resolution for exact dimensions.
Does it work for phones and tablets?
Yes. Choose Custom and enter the ratio, such as 19.5 : 9, or enter the resolution and choose Match resolution. Phones with rounded corners are usually measured as if the corners were square, so the real viewable area is slightly smaller.
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