PPI calculator: pixel density from resolution and diagonal, plus screen width and height, aspect ratio, dot pitch and the distance where pixels blend.
By AdminDrafted with AI writing toolsUpdated Checked examples: 5
A 27-inch 2,560 × 1,440 screen (16:9) packs 108.8 pixels per inch into a 23.5 × 13.2 in panel; beyond about 32 in (80 cm) a person with 20/20 vision can't pick out single pixels.
At this distance one pixel spans 1 arcminute, the detail 20/20 vision resolves; this is the idea behind “retina” displays.
Pixel density is the diagonal resolution in pixels divided by the diagonal size in inches: PPI = √(w² + h²) ÷ diagonal. The same ratio splits the diagonal into the physical width and height, dot pitch is 25.4 mm ÷ PPI, and the blend distance is where one pixel spans 1 arcminute, the detail that 20/20 vision resolves.
The default 27-inch 2560 × 1440 monitor has 108.79 PPI, a 16:9 panel of 23.53 × 13.24 inches, and pixels that blend beyond about 31.6 inches (80 cm). The same size at 4K, 3840 × 2160, reaches 163.18 PPI and blends beyond 21 inches.
Advertised diagonals are rounded, so results can differ slightly from a spec sheet. The blend distance assumes 20/20 vision; people with sharper eyesight can pick out pixels from further away.
Divide the screen's diagonal in pixels by its diagonal in inches: PPI = √(width² + height²) ÷ diagonal. A 27-inch 2560 × 1440 monitor has √(2560² + 1440²) = 2,937.2 pixels corner to corner, so 2,937.2 ÷ 27 = 108.79 PPI. Use the native resolution and the visible diagonal.
The same 27-inch size at 4K (3840 × 2160) has the same width and height but 163.18 PPI, with a dot pitch of 0.1557 mm.
For a 16:9 screen, the width is 0.8716 × the diagonal and the height is 0.4903 × the diagonal. A 55-inch TV is therefore about 47.9 × 27.0 inches of picture, before the bezel and stand.
Those factors come from the same triangle: width = diagonal × 16 ÷ √(16² + 9²). For any other ratio, swap in its two numbers.
A bigger screen at the same resolution has fewer pixels per inch, which is why a 55-inch 4K TV is less dense than a 24-inch 1080p monitor.
With 20/20 vision you resolve detail of about 1 arcminute, a sixtieth of a degree (AOA). Single pixels blend once one pixel spans less than that: distance = 1 ÷ (PPI × tan 1′).
The 27-inch 1440p monitor reaches that point at 31.6 inches (80 cm), and the 4K version at 21.1 inches. A 55-inch 4K TV gets there at 42.9 inches. Sharper eyesight sees pixels from further away.
This is the idea behind Apple's "Retina" name, which launched with the iPhone 4 at 326 PPI for phone viewing distances.
No single PPI works at every distance. For pixels to blend, a screen needs about 143 PPI when viewed from 24 inches but 344 PPI from 10 inches.
Divide both pixel counts by their greatest common divisor. 2560 and 1440 share 160, giving 16:9; turned to portrait, 1440 × 2560 is 9:16.
2560 × 1600 reduces to 8:5, the same shape as 16:10. Some resolutions only approximate a familiar ratio: 1366 × 768 reduces to 683:384, close to 16:9 but not equal.
| Scenario | PPI | Width, in | Height, in |
|---|---|---|---|
| Default | 108.785539 | 23.532540 | 13.237053 |
| 4K same diagonal | 163.178309 | 23.532540 | 13.237053 |
| Laptop | 226.983005 | 11.278377 | 7.048986 |
| Square | 141.421356 | 7.071068 | 7.071068 |
| Nearly widescreen | 100.454670 | 13.598173 | 7.645239 |
To resize an image or video while keeping its proportions, use the aspect ratio calculator.
Checked against: √(2560² + 1440²)/27; retina distance 1/(PPI·tan(π/10800))
Checked against: Apple MacBook Air (M1, 2020) tech specs list 227 ppi; exact decimal arithmetic gives 226.983
Checked against: 1000√2/10
Checked against: Independent calculation
Find the diagonal in pixels with Pythagoras and divide it by the diagonal in inches. A 27-inch 2560 × 1440 monitor has √(2560² + 1440²) = 2,937.2 pixels along the diagonal, so 2,937.2 ÷ 27 = 108.79 PPI. Use the visible screen diagonal, not the outside of the case.
Apple introduced the name with the iPhone 4 in 2010: a 960 × 640 screen at 326 pixels per inch, where Apple said the eye cannot make out individual pixels at a normal viewing distance. At 326 PPI one pixel spans 1 arcminute from 10.5 inches, so the threshold depends on distance: a 27-inch 4K monitor at 163 PPI passes the same test from 21 inches.
To stop seeing single pixels with 20/20 vision, sit at least about 43 inches (1.1 m) from a 55-inch 4K TV, which has 80.1 PPI, or 51 inches (1.3 m) from a 65-inch one. Beyond about 86 inches (2.2 m), a 55-inch 1080p screen blends its pixels too, so 4K adds little visible detail from that far away.
16:9: divide both numbers by their greatest common divisor, 160. TVs and most monitors are 16:9, while some laptops use 16:10, such as the 13.3-inch 2560 × 1600 MacBook Air (8:5 when reduced). A resolution such as 1366 × 768 reduces only to 683:384, which is within 0.05% of 16:9.
Advertised diagonals are rounded. The iPhone 4's 960 × 640 screen is sold as 3.5 inches, which gives 329.7 PPI, while Apple quotes 326 PPI, matching a diagonal of about 3.54 inches. Enter the diagonal to two decimal places when you know it, and check that the resolution is the panel's native one.
This calculator includes 5 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.