Calculator

PPI and pixels-per-degree calculator

Enter a diagonal, a resolution and your viewing distance. The calculator gives the density of the panel and, more usefully, what it means from where you sit.

Diagonal ″ Width px Height px Viewing distance cm

Common formats:

Pixel density: 108.8 PPIpixels per inch of panel
Pixel pitch: 0.233 mmcenter to center of two pixels
Angular density: 48.6 PPDpixels per degree at your distance; 60 is the limit of 20/20 vision
Pixels vanish from: 31.6 indistance at which the density reaches 60 pixels per degree
Width × height: 23.5 in × 13.2 invisible surface, bezels excluded
Viewing angle: 49.4°horizontal, from your distance
Suggested scaling: 100%keeps interface text at its usual size
Pixels to drive: 3.69 Mpxload on the graphics card grows with this figure

The formulas

All results derive from four inputs: the diagonal D in inches, the width w and height h in pixels, and the viewing distance d.

PPI = √(w² + h²) ÷ D
pixel pitch (mm) = 25.4 ÷ PPI
width = D × w ÷ √(w² + h²)
PPD = PPI × d (in inches) × 2 · tan(0.5°)
viewing angle = 2 · atan(width ÷ 2d)

The distance from which pixels vanish is the one where the density reaches 60 pixels per degree, that is one pixel per arcminute, the detail separated by 20/20 vision: d = 3438 ÷ PPI, in inches.

Reading the results

Pixel density (PPI) describes the panel alone. Around 90 PPI is the density of a 24-inch 1080p monitor, 110 PPI that of a 27-inch 1440p, 160 PPI that of a 27-inch 4K, 220 PPI that of the 5K and 6K displays designed for macOS.

Angular density (PPD) is the figure to judge sharpness, since it includes your distance. Under 40, pixels are visible in text. Around 50, text is clean. From 60, the grid is below what the eye separates. The chapter on pixel density explains these thresholds.

The viewing angle tells whether the screen fits your field of view. A 16:9 monitor is comfortable between 40 and 53 degrees, an ultrawide between 44 and 60: see viewing distance.

Suggested scaling is the interface setting that keeps text at its usual physical size on this density, in steps of 25%. Dividing the resolution by it gives the real workspace, as explained in resolution and scaling.

The calculator works for any screen: laptop, tablet, television. For a phone held at 12 in (30 cm) or a television watched from 10 ft (3 m), the same thresholds apply; only the distance changes. To let these quantities choose a monitor for you, use the selector.

Frequently asked questions

How do I calculate the PPI of a monitor?

Divide the diagonal resolution in pixels by the diagonal in inches: PPI = √(width² + height²) ÷ diagonal. For a 27-inch screen of 2560 × 1440 pixels: √(2560² + 1440²) = 2937, and 2937 ÷ 27 = 109 PPI.

What is the difference between PPI and PPD?

PPI (pixels per inch) is the density of the panel. PPD (pixels per degree) is the number of pixels inside one degree of your vision at your viewing distance. PPD is what determines perceived sharpness: the same panel has a higher PPD when you sit farther away.

At what distance does a screen become “Retina”?

At the distance where it reaches 60 pixels per degree: 3438 divided by its PPI, in inches. That is 31.5 in (80 cm) for a 27-inch 1440p screen, 21 in (54 cm) for a 27-inch 4K screen and 16 in (40 cm) for a 27-inch 5K screen.