PPI calculator

How is PPI calculated?

Find the diagonal in pixels with the Pythagorean theorem, √(width² + height²), and divide by the diagonal in inches. A 24-inch 1920 × 1080 monitor has √(1920² + 1080²) ÷ 24 = 91.79 PPI.

What is dot pitch?

The distance between pixels: 25.4 mm ÷ PPI. At 91.79 PPI it is 0.2767 mm.

Is PPI the same as DPI?

They are often used interchangeably, but PPI describes pixels on a screen and DPI describes ink dots from a printer.

How big is the screen itself?

From the diagonal and the ratio of the resolution: a 24-inch 16:9 screen is about 20.92 × 11.77 inches.

Does a higher PPI always look sharper?

Only up to a point — how sharp a screen looks also depends on how far away you sit.

Worked example: three screens

For a 27-inch 3840 × 2160 monitor the pixel diagonal is √(3840² + 2160²) = 4406, and dividing by 27 inches gives 163.2 PPI. The dot pitch is 25.4 ÷ 163.2 = 0.156 mm. A 16:9 screen of that diagonal measures 23.5 × 13.2 inches. The 24-inch 1920 × 1080 monitor above has 91.8 PPI, so the 27-inch screen packs about 1.8 times as many pixels along each inch. A 6.1-inch display with 2532 × 1170 pixels reaches 457 PPI.

At what distance can I no longer see individual pixels?

A common rule uses visual acuity. Standard 20/20 vision corresponds to a minimum angle of resolution of one minute of arc (one sixtieth of a degree), so detail smaller than that cannot be told apart. A pixel subtends one arcminute at a distance of 1 ÷ (PPI × tan(1/60°)) inches, which is about 3,438 ÷ PPI. That is about 37 inches for the 91.79 PPI monitor, 21 inches for the 163 PPI one and 7.5 inches for the phone-sized display. Closer than that, a person with 20/20 vision may begin to see pixels; farther away, extra PPI would be invisible to a 20/20 eye. Real eyes vary, so treat the figure as a guide.

Common mistakes with PPI

Using the wrong diagonal: PPI is very sensitive to it, and entering 28 instead of 27 inches for the 4K monitor changes the answer from 163.2 to 157.4. Swapping width and height does not change the result (91.79 either way), but entering the wrong resolution does. Treating a marketing name such as “4K” as the pixel count; use the actual width and height. Confusing the screen’s PPI with the PPI of an image file: an image has pixels and no inch size until it is printed or scaled. And assuming that software scaling changes PPI: it changes how large things appear, not how many pixels the panel has.

PPI of common screens

The same formula applied to familiar combinations of resolution and diagonal:

• 24-inch monitor, 1920 × 1080: 91.8 PPI, dot pitch 0.277 mm
• 24-inch monitor, 2560 × 1440: 122.4 PPI, dot pitch 0.208 mm
• 27-inch monitor, 2560 × 1440: 108.8 PPI, dot pitch 0.233 mm
• 27-inch monitor, 3840 × 2160: 163.2 PPI, dot pitch 0.156 mm
• 32-inch monitor, 3840 × 2160: 137.7 PPI, dot pitch 0.184 mm
• 13.3-inch laptop, 1920 × 1080: 165.6 PPI, dot pitch 0.153 mm
• 15.6-inch laptop, 3840 × 2160: 282.4 PPI, dot pitch 0.090 mm
• 55-inch TV, 3840 × 2160: 80.1 PPI, dot pitch 0.317 mm

Two things stand out. Raising the resolution on the same diagonal raises the density in proportion to the pixel count along the diagonal, so the 24-inch screen goes from 91.8 to 122.4 PPI when moving from 1080p to 1440p. And the same 4K resolution gives very different densities on different sizes: the 55-inch TV is far below the 15.6-inch laptop because the pixels are spread over a much larger area, which is why TVs are viewed from a couch rather than from arm's length.

PPI, scaling and printing

PPI is a property of the panel, set by its resolution and physical size. Operating-system scaling (125%, 150%, 200%) changes how large text and icons are drawn, not the density, and a scaled setting still uses every pixel. For print, an image file has no inch size of its own: divide its pixel width by the print width to see the PPI it will have on paper. Target PPI for prints is a quality choice, so use the print size calculator for that, and remember that a screen viewed from 20 inches and a poster viewed from 6 feet need very different densities.

Sources and related calculators

Sources: the Pythagorean theorem and unit definition (1 inch = 25.4 mm exactly); M. Kalloniatis and C. Luu, “Visual Acuity,” Webvision, for the one-arcminute definition of 20/20 acuity; American Academy of Ophthalmology EyeWiki, “Visual Acuity Testing in Adults.” Related: aspect ratio calculator, TV size calculator, print size calculator and Pythagorean theorem calculator.