What PPI means
PPI stands for pixels per inch. It counts how many pixels sit along one inch of a screen, which makes it a measure of pixel density. Two screens with the same resolution can have a very different PPI: 1920 × 1080 pixels on a 24 inch monitor are spread over a much larger area than the same pixels on a phone, so each pixel is larger and the PPI is lower.
How to calculate pixels per inch
The resolution tells you the pixels across and down, the diagonal tells you the size. Because the width, the height and the diagonal form a right triangle, the Pythagorean theorem gives the diagonal in pixels. Divide it by the diagonal in inches and you have the PPI.
For a 24 inch screen with 1920 × 1080 pixels: √(1920² + 1080²) = 2,202.91 pixels on the diagonal, and 2,202.91 ÷ 24 = 91.79 PPI. The dot pitch, the distance from one pixel center to the next, is 25.4 ÷ 91.79 = 0.2767 mm.
If you know the diagonal in centimeters, divide it by 2.54 first. NIST lists the inch as exactly 2.54 cm in its Guide for the Use of the International System of Units (SP 811, Appendix B), so the conversion adds no rounding.
How to work out the width and height of a screen
The diagonal also gives you the physical width and height. Each side is the diagonal times its share of the diagonal in pixels:
The 24 inch 1920 × 1080 screen is 20.92 × 11.77 inches, or 53.13 × 29.89 cm. This assumes square pixels, where a pixel is as wide as it is high. ITU-R BT.709 and BT.2020, the standards for HD and UHD television, both specify square pixels.
Common resolutions and their PPI
The same resolution on a larger screen means a lower pixel density. This table shows the PPI of common resolutions at three monitor sizes.
| Name | Pixels | Aspect ratio | Megapixels | PPI at 24 in | PPI at 27 in | PPI at 32 in |
|---|---|---|---|---|---|---|
| 720p | 1280 × 720 | 16:9 | 0.92 | 61.19 | 54.39 | 45.89 |
| 1080p | 1920 × 1080 | 16:9 | 2.07 | 91.79 | 81.59 | 68.84 |
| 1440p | 2560 × 1440 | 16:9 | 3.69 | 122.38 | 108.79 | 91.79 |
| 4K | 3840 × 2160 | 16:9 | 8.29 | 183.58 | 163.18 | 137.68 |
| 5K | 5120 × 2880 | 16:9 | 14.75 | 244.77 | 217.57 | 183.58 |
| 8K | 7680 × 4320 | 16:9 | 33.18 | 367.15 | 326.36 | 275.36 |
720p is 1280 × 720 pixels in SMPTE ST 296, 1080p is 1920 × 1080 in ITU-R BT.709, and 4K and 8K UHD are 3840 × 2160 and 7680 × 4320 in ITU-R BT.2020. 1440p is named the same way, by its height in pixels. 5K is 5120 × 2880, the resolution Apple lists for its 27 inch Studio Display. All six are 16:9.
Check the result against a spec sheet
A quick way to trust a calculator is to try a screen whose maker publishes the PPI. Apple's specifications for the Studio Display list a 27 inch (diagonal) screen with 5120 by 2880 pixels at 218 pixels per inch. The formula gives √(5120² + 2880²) ÷ 27 = 217.57 PPI, which rounds to the same 218. A 27 inch 4K monitor, by comparison, has 163.18 PPI: the same size with fewer pixels.
How to compare two screens
Turn on Compare with a second screen and enter the other resolution and diagonal. The calculator shows both screens drawn to scale, a table with PPI, dot pitch, size, area and megapixels side by side, and how much higher the pixel density of one is. This helps when you choose between, for example, a larger monitor and one with more pixels.
How to use the PPI calculator
- 1Type the resolution of the screen, width × height in pixels, or pick a common one like 1080p or 4K.
- 2Type the diagonal and choose inches or cm.
- 3Read the PPI, pixels per cm, dot pitch, width, height and megapixels.
- 4To weigh up two screens, turn on Compare with a second screen. Copy the result or a link to share it.
Frequently asked questions
How do I calculate PPI?
Find the diagonal in pixels with the Pythagorean theorem, √(width² + height²), then divide it by the diagonal in inches. For a 24 inch screen with 1920 × 1080 pixels, √(1920² + 1080²) = 2,202.91 pixels, and 2,202.91 ÷ 24 = 91.79 PPI.
What does pixel density mean?
Pixel density is how many pixels fit into a given length of the screen. PPI counts them per inch, pixels per centimeter per centimeter. A higher number means smaller pixels that sit closer together, so the same image is drawn with more pixels in each inch.
How do I calculate PPI with the diagonal in cm?
Divide the diagonal by 2.54 to get inches first, since an inch is exactly 2.54 cm. A 68.58 cm diagonal is 27 inches. Or switch the calculator to cm and type the centimeters directly.
What is dot pitch?
Dot pitch, or pixel pitch, is the distance from the center of one pixel to the center of the next. The calculator gives it in millimeters. It is 25.4 ÷ PPI, because an inch is 25.4 mm. At 91.79 PPI the dot pitch is 0.2767 mm.
Why is my result a little different from the spec sheet?
A spec sheet may round the PPI to a whole number, and the diagonal you type may be rounded too. A 27 inch 5120 × 2880 screen works out to 217.57 PPI, which a spec sheet would show as 218. Type the exact diagonal if the maker lists one.
How many megapixels is a 4K screen?
4K UHD is 3840 × 2160 pixels, which is 8,294,400 pixels or 8.29 megapixels. 1080p is 2,073,600 pixels, so 4K UHD has exactly 4 times as many.
Is my data stored anywhere?
No. The calculation runs in your browser. Your numbers only end up in a link if you choose to copy one.