PPI Calculator

How PPI Is Calculated

PPI (pixels per inch) measures pixel density: how tightly packed a screen's pixels are relative to its physical diagonal size. It's found by first calculating the diagonal resolution in pixels — using the Pythagorean theorem on the width and height in pixels — then dividing that by the diagonal size in inches.

$$\text{PPI} = \frac{\sqrt{W^2 + H^2}}{D}$$

Worked Example

A 24-inch monitor at 1920×1080 resolution: diagonal pixels = square root of (1920 squared plus 1080 squared) = square root of 4,852,800 ≈ 2,202.9 pixels. Dividing by the 24-inch diagonal gives about 91.8 PPI — a fairly typical density for a mid-size desktop monitor, noticeably lower than a modern phone screen, which packs far more pixels into a much smaller diagonal.

Why PPI Matters Beyond the Raw Resolution Number

Two screens can share the exact same resolution — say, 1920×1080 — yet look completely different in sharpness depending on their physical size. A 55-inch 1080p TV has a much lower PPI (and visibly larger, softer-looking pixels up close) than a 24-inch 1080p monitor, because the same pixel count is stretched across far more physical area. This is why "resolution" alone is an incomplete way to judge how sharp a display will actually look — PPI (or its close cousin, PPD — pixels per degree, which also factors in viewing distance) is the more complete picture.

PPI vs. DPI

PPI and DPI are often used interchangeably but technically describe different things: PPI (pixels per inch) describes a digital display's pixel density, while DPI (dots per inch) technically refers to a printer's physical ink dot density. In everyday conversation the terms get mixed constantly, but on a calculator specifically about screens, PPI is the technically correct term.

A Brief History of Pixels Per Inch

The dots-per-inch idea predates digital screens by decades. Print shops and typesetters used DPI to describe how finely a printing press or dot-matrix printer could lay down ink, since a printed image is built from a dense grid of physical dots rather than continuous tone — a higher DPI meant finer, less visible dots and a sharper-looking print. Early inkjet and laser printer marketing carried that same DPI figure directly over into consumer computing.

When digital displays needed a comparable measure of sharpness, the print-world term got adapted rather than reinvented, even though a pixel and a printed ink dot are physically different things, hence the PPI versus DPI distinction covered below. The term became a mainstream marketing focus mainly once Apple introduced "Retina" displays in 2010, packaging PPI into a single number ordinary buyers could compare between devices, well after PPI had already been a real, if less publicly discussed, spec for years.

Common PPI Calculation Mistakes

Using the screen's width or height alone instead of the true diagonal resolution is the most common error — PPI is defined against the diagonal, not a single dimension, because diagonal size (the number manufacturers advertise) is measured corner to corner. Confusing a device's marketed resolution with its actual rendering resolution is another — some displays render at a lower native resolution and upscale, which this calculator can't detect from specs alone.

Display Terms You Should Know

Pixel Density — how many pixels are packed into a given area of a screen, most commonly expressed as PPI.

Retina Display — Apple's marketing term for a PPI high enough that individual pixels aren't distinguishable at that device's typical viewing distance.

PPD (Pixels Per Degree) — a more complete sharpness measure than PPI alone, factoring in viewing distance as well as pixel density.