PPI Calculator: Pixels Per Inch from Diagonal

The PPI Calculator derives pixels per inch from a display's pixel width, pixel height and diagonal size in inches. It also reports pixels per centimetre, PPI squared, diagonal length in pixels and dot pitch in millimetres. A comparison mode ranks two screens by density. PPI alone does not decide perceived sharpness; viewing distance still matters, and the page states that limit next to every result.

All calculation runs in your browser. Nothing you enter is sent to a server.

Calculate pixels per inch from resolution and screen size

PPI is pixel density along the diagonal: how many pixels sit in one inch of screen. Enter the resolution as width × height in pixels and the diagonal in inches as printed on the device spec. The calculator returns PPI to two decimal places by default, with secondary fields for related measures.

Higher PPI means finer detail at the same physical size. A phone at 400 PPI and a television at 80 PPI can share a 3840×2160 signal; the phone packs those pixels into a few inches while the television spreads them across a wall. Density, not resolution alone, is what this tool measures.

Find the diagonal in pixels with Pythagoras

The pixel diagonal is the hypotenuse of the resolution rectangle. Square the width in pixels, square the height, add the two squares, and take the square root. That length is still measured in pixel units, not inches, until it is divided by the physical diagonal from the product sheet to produce PPI.

diagonal_pixels = √(width² + height²)

For 1920×1080:

√(1920² + 1080²) = √(3,686,400 + 1,166,400) = √4,852,800 ≈ 2202.91 pixels

That figure is not a physical length until it is paired with the inch diagonal. It is the number of pixel steps from one corner of the framebuffer to the opposite corner, counting in pixel units rather than inches.

Apply the PPI formula

Divide the pixel diagonal by the physical diagonal in inches to obtain PPI. The same pair of quantities also yields dot pitch when the inch spacing is converted to millimetres with the factor 25.4. Both results describe density along the diagonal for ordinary rectangular pixel grids with square pixels, which covers the displays this calculator targets.

PPI = diagonal_pixels ÷ diagonal_inches

The same relationship rearranges to solve for a missing diagonal when PPI and resolution are known, but the primary mode on this page takes resolution and inches as inputs. Dot pitch, the centre-to-centre spacing of pixels, is the reciprocal relationship expressed in millimetres:

dot_pitch_mm = (diagonal_inches ÷ diagonal_pixels) × 25.4

Because there are 25.4 millimetres in an inch, converting the inch pitch to millimetres is a fixed scale factor. Smaller dot pitch means pixels sit closer together.

Calculate PPI for a 1920x1080 10-inch screen

The fixture uses Full HD resolution on a 10-inch diagonal, a tablet-class size that makes density easy to read. The pixel diagonal is about 2202.91 pixels, and dividing by 10 inches produces 220.29 PPI. Secondary fields report PPI squared near 48,528 and a dot pitch near 0.1153 mm for the same inputs.

1. Pixel diagonal. √(1920² + 1080²) ≈ 2202.91 px

2. Divide by inches. 2202.91 ÷ 10 = 220.29 PPI

3. Related values. PPI² ≈ 48,528 Dot pitch ≈ 0.1153 mm Pixels per cm ≈ 86.73 Aspect ratio reported alongside: 16:9 (reduction explained on the Aspect Ratio Calculator)

A 10-inch 1080p tablet-class panel at about 220 PPI is much denser than a 24-inch 1080p monitor at roughly 92 PPI, even though both light the same number of pixels. The calculator's primary result for this case is 220.29, matching the engine test.

Calculate pixels per square inch

PPI measures linear density along the diagonal. Squaring that value estimates how many pixels fall in one square inch of screen area, which helps when comparing detail per unit area rather than along a single line. For 220.29 PPI the square is about 48,528, assuming a uniform square pixel grid on both axes.

pixels_per_square_inch ≈ PPI²

For 220.29 PPI, PPI² ≈ 48,528. That number assumes a square pixel grid and uniform pitch along width and height, which is true for the ordinary displays this tool targets. It is not a separate sensor measurement; it is derived from the same diagonal PPI.

Calculate dot pitch in millimetres

Dot pitch is the physical centre-to-centre spacing of pixels, usually quoted in millimetres on older datasheets. It is the reciprocal of PPI after converting inches to millimetres with 25.4. For the 10-inch 1080p example the pitch is about 0.1153 mm, so denser panels show a smaller pitch number for the same resolution formula.

dot_pitch_mm = (10 ÷ 2202.91) × 25.4 ≈ 0.1153 mm

Datasheets sometimes quote dot pitch instead of PPI. Converting either way uses the same reciprocal pair. Older CRT literature used stripe pitch with slightly different definitions; for modern LCD and OLED panels, the diagonal method above matches how PPI is commonly derived from published resolution and size.

Compare the sharpness of two screens

Comparison mode accepts two sets of width, height and diagonal, computes both PPI values, and reports which is denser and by how many PPI. Percentage difference follows from the two densities when a relative gap is more useful than an absolute one.

Example pairing:

Screen	Resolution	Diagonal	PPI (approx.)
A	1920×1080	24 in	91.79
B	3840×2160	27 in	163.18

Screen B is sharper by about 71 PPI in this pairing. Whether that gap is visible still depends on how far the viewer sits; the next section covers distance.

Understand why viewing distance matters

Perceived sharpness is an angular question: how large each pixel appears to the eye. A billboard at 60 PPI looks continuous from across a street because each pixel subtends a tiny angle at that distance. The same 60 PPI on a phone held 12 inches away looks blocky.

Apple's "Retina" marketing threshold is often summarised near 300 PPI for phone-distance viewing, but that number is not a universal law. Print work commonly targets about 300 DPI at arm's length for magazines. Living-room televisions sit far enough that 80 PPI can look excellent. The calculator warns that PPI alone does not determine perceived sharpness; distance belongs in the decision.

Understand PPI versus DPI

PPI counts pixels on a display. DPI counts ink dots in a printed image or the addressability of a printer. The terms are swapped casually in forums and even in some software dialogs, but a print shop asking for 300 DPI is not asking for a screen measurement.

Term	Domain	Measures
PPI	Display	Pixel density on a screen
DPI	Print	Dot density of ink or printer output

Exporting a 72 PPI web image to a magazine usually needs more pixels (higher resolution at the print size), not a renamed unit. The PPI Calculator is a display tool; treat print DPI as a separate workflow even when the numbers look similar.

Frequently asked questions

Summary

The PPI Calculator divides the pixel diagonal by the inch diagonal to produce pixels per inch, with PPI², dot pitch and a two-screen comparison available beside the primary result. A 1920×1080 display at 10 inches measures 220.29 PPI, with a pixel diagonal of about 2202.91 and a dot pitch near 0.1153 mm.

Viewing distance still governs perceived sharpness, and DPI remains a print term rather than a synonym for screen PPI.