PPI Calculator

PPI = √(width² + height²) ÷ diagonal

width

Horizontal resolution, in pixels (px)

height

Vertical resolution, in pixels (px)

diagonal

Screen diagonal, the size the panel is sold by (in)

PPI

Pixel density, in pixels per inch (ppi)

The numerator is the number of pixels along the diagonal — the Pythagorean sum of the two resolution figures, not either one of them. Two consequences follow, and both are visible in the table below. Doubling both sides of a resolution multiplies the pixel count by four and the density by two, so 4K is twice as dense as 1080p and not four times. Spreading the same resolution over a larger diagonal divides the density down, which is why a large television can be less dense than a small laptop. The same triangle gives the dot pitch, the distance between pixel centres, as 25.4 ÷ PPI millimetres — so 81.59 ppi is a 0.31 mm pitch.

1. A 27-inch 1440p monitor

   1. Known: resolution 2560×1440, diagonal 27 inches.
   2. Pixels along the diagonal: √(2560² + 1440²) = √(6 553 600 + 2 073 600) = √8 627 200 = 2937.2.
   3. Divide by the diagonal: 2937.2 ÷ 27 = 108.79 ppi.
   4. Dot pitch: 25.4 ÷ 108.79 = 0.2335 mm between pixel centres.
   5. Total pixels: 2560 × 1440 = 3 686 400, that is 3.69 megapixels.
   6. The panel itself, at 16:9, measures 59.77 × 33.62 cm.

   The diagonal a monitor is sold by is the hypotenuse of the panel, not its width — which is why this is a triangle problem rather than one division by the width.

2. A 55-inch 4K television

   1. Known: 3840×2160, 55 inches.
   2. √(3840² + 2160²) = √(14 745 600 + 4 665 600) = √19 411 200 = 4405.8 pixels along the diagonal.
   3. 4405.8 ÷ 55 = 80.11 ppi.
   4. Dot pitch: 25.4 ÷ 80.11 = 0.3171 mm.
   5. 8 294 400 pixels, or 8.29 megapixels.
   6. At 16:9 the picture measures 121.76 × 68.49 cm.

   Four times the pixels of a 1440p monitor, and the density lands 26% lower: the pixel count grew by 2.25 and the diagonal by 2.04, and 1.5 ÷ 2.04 is the ratio between the two densities.

3. A 13.3-inch laptop at 1080p

   1. Known: 1920×1080, 13.3 inches.
   2. √(1920² + 1080²) = 2202.9 pixels along the diagonal.
   3. 2202.9 ÷ 13.3 = 165.63 ppi.
   4. Dot pitch: 25.4 ÷ 165.63 = 0.1534 mm, about half the pitch of a 24-inch monitor.
   5. 2 073 600 pixels, or 2.07 megapixels — the same pixel count as any other 1080p panel.
   6. The panel measures 29.44 × 16.56 cm.

   Exactly the same 1920×1080 as a 24-inch monitor at 91.79 ppi. Nothing about the resolution changed — only the area it had to cover.

This is the panel's geometry, not a verdict on how sharp it looks, and two qualifications matter. First, viewing distance is not an input, and it is what decides whether a given density is enough: the eye resolves detail by angle, so what counts is how many pixels fall into a degree of vision rather than how many fit in an inch. Second, pixels per inch counts whole pixels, while what the eye sees is the subpixel structure — a panel with a non-standard subpixel layout can look softer than its PPI suggests, and a signal that does not match the native mode is scaled up, which is never as crisp as the panel's own resolution. The diagonal used here is also the quoted size of the panel, measured corner to corner across the glass, so the lit image inside the bezel is a little smaller than the numbers imply.

How do I calculate PPI from a resolution and a screen size?

Divide the number of pixels along the diagonal by the diagonal itself. That pixel count is √(width² + height²), so a 2560×1440 panel has √(2560² + 1440²) = 2937 pixels corner to corner, and on a 27-inch screen that is 2937 ÷ 27 = 108.79 ppi. The same panel at 24 inches across would be 122.38 ppi, because the same pixels are packed into less glass.

Why does the same resolution give different pixel densities on different screens?

Because density is a ratio of two things and the resolution is only one of them. A 1920×1080 panel holds 2.07 megapixels whether it is 13.3 inches or 24 inches across, and those pixels cover very different areas: 165.63 ppi on the laptop against 91.79 ppi on the monitor. The rule of thumb is that density scales with the square root of the pixel count and inversely with the diagonal, so four times the pixels is twice the density at an unchanged size.

Is a higher PPI always better?

No, and that is why this page gives no verdict. Sharpness is judged at a viewing distance: the eye resolves detail by angle, so what matters is how many pixels fall into a degree of vision, not how many fit in an inch. A 55-inch 4K television at 80 ppi watched from three metres and a 27-inch 4K monitor at 163 ppi at arm's length look about equally sharp. Higher density also costs more power and more money, so for a screen you sit far away from, a larger and less dense panel is often the better buy.

What is dot pitch, and how does it relate to PPI?

Dot pitch is the distance between the centres of two neighbouring pixels, and it is 25.4 ÷ PPI millimetres, because an inch is 25.4 mm. A 27-inch 1440p monitor at 108.79 ppi has a pitch of 0.2335 mm; the 55-inch 4K television at 80.11 ppi has 0.3171 mm. The two figures carry the same information in opposite directions — a smaller pitch is a denser screen — but pitch is the one that appears on panel datasheets, which is why it is reported here alongside the density.

What is the difference between PPI and DPI?

PPI counts pixels, the individually addressable elements of a screen. DPI counts dots, and it is a printing term for how many ink droplets a printer puts down in an inch. On a monitor the two get used interchangeably in casual speech, but a 300 DPI printer has nothing resembling a 300 PPI screen: the printer's dots are not addressable one by one, and several of them go into a single pixel. When a phone or camera specification quotes DPI, it usually means the PPI of the display.

Why does the calculator also give the width and height in centimetres?

Because the physical size is the other half of the question, and it falls out of the same triangle at no extra cost. A 27-inch 16:9 screen is 59.77 × 33.62 cm and a 55-inch one is 121.76 × 68.49 cm — the numbers you need when measuring a desk, a wall or a camera bag. To turn either of them into inches, divide by 2.54, which makes the 55-inch panel 47.94 inches wide.

• Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — NIST
• Recommendation ITU-R BT.2020: Parameter values for ultra-high definition television systems — ITU-R