PPI Calculator — pixel density of a screen

How it works

PPI (pixels per inch), also called pixel density, tells you how tightly packed a display's pixels are — the higher the number, the sharper the image. It combines the resolution with the physical screen size:

PPI = √(width² + height²) ÷ diagonal

The top part, √(width² + height²), is the diagonal resolution in pixels. Since a screen's width and height are the two legs of a right triangle, the diagonal is the hypotenuse — the Pythagorean theorem. Dividing that diagonal pixel count by the screen's diagonal size in inches gives pixels per inch.

Two screens with the same resolution have different sharpness if their sizes differ: the smaller one packs the same pixels into less space, so it has a higher PPI. Above roughly 300 PPI at normal viewing distance, individual pixels become hard to see — what marketing calls a "retina" display.

Worked example

A 1920×1080 panel on a 24-inch monitor has a diagonal resolution of √(1920² + 1080²) = √4 852 800 ≈ 2203 pixels, so its density is 2203 ÷ 24 ≈ 91.8 PPI. The same 24-inch size at 4K (3840×2160) doubles the linear resolution to about 183 PPI, and a 6.1-inch phone at 1170×2532 reaches about 457 PPI — far sharper because those pixels are squeezed into a tiny screen.

Frequently asked questions

What is PPI?

PPI stands for pixels per inch — the number of pixels packed into each inch of a display. It measures pixel density, or sharpness: a higher PPI means smaller, more tightly packed pixels and a crisper image.

How is PPI calculated?

Take the diagonal resolution in pixels, √(width² + height²), and divide by the diagonal screen size in inches. The square root comes from the Pythagorean theorem, since the screen's width and height are the legs of a right triangle whose hypotenuse is the diagonal.

What is the difference between PPI and DPI?

PPI (pixels per inch) describes screens; DPI (dots per inch) describes printers. They are often used interchangeably, but strictly PPI is about the pixel grid of a display while DPI is about the ink dots a printer lays down. This calculator computes PPI.

What PPI counts as "retina" or high-density?

Apple's original "Retina" threshold was about 300 PPI for a phone held around 10–12 inches away, where the eye can no longer resolve individual pixels. Larger screens viewed from farther away need less — a TV across a room looks sharp at well under 100 PPI. It depends on viewing distance.

Does a higher resolution always mean higher PPI?

No — PPI depends on resolution *and* size. A 4K TV at 65 inches has a lower PPI than a 1080p phone, because the TV spreads far more pixels over a much larger screen. To compare sharpness you must account for both, which is exactly what PPI does.

Why does the calculator ask for the diagonal in inches?

Screen sizes are quoted by their diagonal (a "24-inch monitor"), and PPI is defined per inch, so the diagonal in inches is the natural denominator. Enter the diagonal your display is advertised as, and the resolution in pixels, to get its density.