What this calculator does
Pixel density measures how tightly packed a screen's pixels are, expressed as pixels per inch (PPI). A phone screen and a large television can share the exact same resolution, say 1920 by 1080, and still look completely different in sharpness, because the same number of pixels is spread across a much smaller or larger physical area.
The calculation combines the two pieces of information a spec sheet gives you, resolution in pixels and diagonal size in inches, into the single figure that actually determines how sharp text and images look up close. It uses the same right-triangle logic as measuring the diagonal size itself: the pixel resolution diagonal divided by the physical diagonal.
The formula
The diagonal resolution in pixels is found with Pythagoras: the square root of the horizontal resolution squared plus the vertical resolution squared. Dividing that diagonal pixel count by the physical diagonal screen size in inches gives pixels per inch.
| Term | Meaning |
|---|---|
| PPI | Pixels per inch, the standard measure of screen pixel density. |
| Resolution | The number of pixels across the screen horizontally and vertically, such as 1920 x 1080. |
| Diagonal size | The physical screen size measured corner to corner, in inches, as sold and marketed. |
The inputs explained
| Field | What to enter |
|---|---|
| Horizontal resolution (px) | The horizontal pixel resolution, the first number in a spec like 1920 x 1080. |
| Vertical resolution (px) | The vertical pixel resolution, the second number in a spec like 1920 x 1080. |
| Diagonal screen size (in) | The screen's diagonal size in inches, as listed on the box or spec sheet. |
When to use it
Comparing a phone, monitor and TV on sharpness
Two screens with identical resolution can have very different PPI once diagonal size is accounted for, which is the actual number worth comparing when judging how crisp text and images will look.
Checking whether a resolution is "Retina-like" at a given size
Manufacturers often market a PPI threshold as the point where individual pixels become impossible to see at normal viewing distance; working out the exact PPI for a specific resolution and size checks a marketing claim directly.
Choosing between two monitor options at the same price
When a higher resolution option is also physically larger, PPI shows whether it is actually sharper or just bigger, which raw resolution numbers alone do not reveal.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How PPI changes with screen size at a fixed 1920 x 1080 resolution
The same Full HD resolution spread across a range of diagonal screen sizes.
| Diagonal size | Pixel density |
|---|---|
| 21 in | 104.9 PPI |
| 24 in | 91.8 PPI |
| 27 in | 81.6 PPI |
| 32 in | 68.8 PPI |
| 43 in | 51.2 PPI |
| 55 in | 40.1 PPI |
How PPI changes with resolution at a fixed 27-inch screen size
A fixed 27-inch screen, shown at a range of common resolutions.
| Horizontal resolution (16:9 height assumed) | Pixel density |
|---|---|
| 1920 px wide | 81.6 PPI |
| 2560 px wide | 102.9 PPI |
| 3840 px wide | 147.7 PPI |
Questions
What counts as a high PPI?
There is no fixed cutoff, but screens viewed close up, like phones, are generally considered sharp above roughly 300 PPI, while monitors viewed further away read as sharp at a lower PPI, and large televisions viewed from across a room can look fine at well under 100 PPI.
How is this different from the monitor size calculator?
The monitor size calculator works from an aspect ratio and diagonal size to find a screen's physical width and height in inches or centimetres. This calculator instead needs an actual pixel resolution, and answers a different question: how sharp the image looks, not how physically big the screen is.
Does aspect ratio matter for this calculation?
Not directly. The formula only needs the horizontal and vertical pixel counts and the diagonal size in inches; aspect ratio falls out of those two resolution numbers automatically.
Why do phone screens quote such high PPI compared with monitors?
Phone screens are held much closer to the eye than monitors or televisions, so manufacturers pack in far more pixels per inch to keep individual pixels invisible at that closer viewing distance.
To work out a screen's physical width and height from its diagonal size and aspect ratio instead, see the aspect ratio calculator.