PPI Calculator – Pixels per Inch
This calculator works out the pixel density (PPI) of a screen from its resolution and diagonal, and converts between pixels and print size at any DPI. Enter width, height and diagonal to get PPI, dot pitch, physical dimensions and viewing distance.
Calculate Screen Pixel Density, Viewing Distance and Print Sizes
PPI Formula
Where:
- \(w\) — resolution width in pixels
- \(h\) — resolution height in pixels
- \(d\) — physical screen diagonal in inches
The first formula divides the diagonal measured in pixels by the diagonal measured in inches, giving pixels per inch. The companion formulas derive the pixel size in millimetres, the distance at which individual pixels become indistinguishable to 20/20 vision, and the size a digital image will print at a given DPI.
PPI – Calculation Example
Example: a 24-inch monitor with a Full HD resolution of 1920 × 1080 pixels (the calculator's default values).
\[ \sqrt{1920^2 + 1080^2} = \sqrt{4{,}852{,}800} \approx 2202.91 \text{ px} \]
\[ PPI = \frac{2202.91}{24} \approx 91.79 \]
Result: about 91.79 PPI. The dot pitch is 25.4 ÷ 91.79 ≈ 0.2767 mm, the screen measures roughly 20.92 × 11.77 in (53.1 × 29.9 cm), the total resolution is 2.07 megapixels, and pixels become indistinguishable from about 37.5 in (95 cm) away.
How to use the calculator
- Open the Mode dropdown and choose Screen pixel density (PPI) or Print resolution (PPI / DPI).
- In screen mode, pick a Resolution preset (e.g. 1920 × 1080) or select Custom and type your own Resolution width and Resolution height in pixels.
- Enter the Diagonal size of the display and set the Unit to inches or centimetres. Use the advertised diagonal, bezel excluded.
- Read the results: pixel density, dot pitch, physical screen width and height, aspect ratio, total megapixels and the 20/20-vision viewing distance. Calculation details shows every step.
- In print mode, set the Print resolution in DPI and the Conversion direction: Pixels → print size uses the same resolution fields, while Print size → required pixels asks for Print width and Print height in inches or centimetres.
What is PPI and why does it matter?
Pixels per inch (PPI) is the pixel density of a display: how many pixels fit into one linear inch of screen. Higher density means finer detail, smoother edges and crisper text. Two monitors can share the same 1920 × 1080 resolution yet look completely different — a 24-inch model spreads those pixels at about 92 PPI, while the same resolution on a 6-inch phone screen exceeds 360 PPI, which is why small screens look so sharp.
The key insight behind the formula is that a resolution such as 1920 × 1080 is itself a right triangle. By the Pythagorean theorem, \(\sqrt{1920^2 + 1080^2} \approx 2202.91\) pixels sit along the diagonal, so dividing by the physical diagonal in inches yields density directly. This works only because pixels are square and evenly spaced, which holds for virtually all modern LCD and OLED panels.
Interpreting the result depends on viewing distance. The companion figure in the results, viewing distance, is the distance at which one pixel subtends 1 arcminute — the resolution limit of 20/20 vision. Viewed from that distance or farther, individual pixels merge and the image appears perfectly smooth. This is why a 55-inch 4K TV at 80 PPI looks fine from a sofa, while a phone held 30 cm from the eye needs 400 PPI or more.
PPI is a property of hardware; DPI (dots per inch) belongs to printers and scanners. In everyday use the two terms are used interchangeably for print, even though an inkjet printer typically lays down several dots to render a single image pixel. The print mode of this calculator converts an image's pixel dimensions to a physical print size, or tells you how many pixels you need for a given print size — for example, an 8 × 10 in photo at 300 DPI requires 2400 × 3000 pixels, about 7.2 megapixels.
Assumptions, limitations and tips
- Square pixels are assumed. CRT-era and a few exotic displays used non-square pixels; the result would be misleading for them.
- Use the real diagonal, not the bezel measurement. Include only the active display area, otherwise the PPI comes out too low.
- PPI is not the same as perceived sharpness. Sharpness at a given pixel density shrinks with distance — always pair the PPI figure with the viewing-distance result.
- For print, 300 DPI is a safe standard for photo-quality output at reading distance; 150 DPI is usually acceptable for posters viewed from a metre or more, and 600 DPI suits ultra-fine art reproductions.
- Scaling matters in practice. High-PPI screens typically run at 150–200% interface scaling, which affects readability of UI elements but not the underlying density.
- Upsampling cannot add detail. Enlarging an image to meet a DPI target increases pixel count, not real detail; for genuine print quality you can also check colour values with the Color Converter or inspect image data with the Hex Converter.
Typical pixel densities
| Device | Resolution | Diagonal | Approx. PPI |
|---|---|---|---|
| 24″ Full HD monitor | 1920 × 1080 | 24 in | 92 |
| 27″ 4K monitor | 3840 × 2160 | 27 in | 163 |
| 13″ QHD+ laptop | 2560 × 1600 | 13.3 in | 227 |
| 55″ 4K TV | 3840 × 2160 | 55 in | 80 |
| Modern smartphone | 1080 × 2400 | 6.5 in | 400 |
Densities above roughly 300 PPI are marketed as “Retina”-class — beyond that, pixels are invisible at normal viewing distances, and further increases mainly benefit VR headsets viewed through lenses.
Frequently Asked Questions
How do I calculate the PPI of a screen by hand?
Multiply the width in pixels by itself, then the height by itself, add the two results, and take the square root — this is the diagonal in pixels. Then divide by the screen’s diagonal in inches. For a 1920 × 1080 panel on a 27″ display: \(\sqrt{1920^2 + 1080^2} \approx 2202.91\), and \(2202.91 \div 27 \approx 81.59\) PPI. No other measurements are needed because the resolution already forms the diagonal’s right triangle.
What is a good or normal PPI value?
It depends on the device and viewing distance. Desktop monitors at 90–110 PPI are standard and comfortable; 150+ PPI looks noticeably sharper. Laptops typically range from 130 to 220 PPI, and modern phones sit at 400–500 PPI. Anything above roughly 300 PPI is “Retina”-class — pixels are invisible at normal viewing distances, so further gains matter mostly for VR headsets. A large TV can look great at just 80 PPI because you sit several metres away.
Can I calculate PPI using centimetres for the diagonal?
Yes. First convert the diagonal to inches by dividing by 2.54, then divide the pixel diagonal by that figure. For example, a 60 cm diagonal equals \(60 \div 2.54 \approx 23.62\) inches. The calculator also accepts centimetres directly via the unit dropdown next to the diagonal field, so no manual conversion is necessary.
Why is my calculated PPI lower than the manufacturer’s claim?
The most common cause is using the wrong diagonal. The PPI formula requires the active display area only — the bezel and any glass border must be excluded, so take the diagonal from the official specifications, not a ruler across the whole panel front. Also double-check that the resolution you entered matches the panel’s native resolution, not the scaled or reduced setting the operating system is currently using.
What is the difference between PPI and DPI?
PPI describes how many pixels a screen fits per linear inch and is a fixed hardware property. DPI counts the ink dots a printer places per inch and is a printing parameter. In casual print talk the terms get mixed, but an inkjet printer usually lays down several physical dots to reproduce a single image pixel, so a printer’s DPI setting is typically higher than the image’s effective PPI. For choosing image resolution before printing, the two are used interchangeably.
How do I convert PPI to dot pitch in millimetres?
Divide 25.4 (the number of millimetres in an inch) by the PPI. A 300 PPI screen gives \(25.4 \div 300 \approx 0.0847\) mm, while 92 PPI gives about 0.277 mm. Dot pitch is the centre-to-centre distance between neighbouring pixels — the smaller it is, the finer the image. If you know the dot pitch instead, invert the calculation: \(PPI = 25.4 \div \text{dot pitch in mm}\).
How many pixels do I need for a specific print size at 300 DPI?
Multiply each dimension in inches by the DPI setting. An 8 × 10 in print at 300 DPI needs \(8 \times 300 = 2400\) pixels wide and \(10 \times 300 = 3000\) pixels tall — about 7.2 megapixels. An A4 (8.27 × 11.69 in) print needs roughly 2480 × 3507 pixels. Upsampling a smaller image to hit these targets adds pixels but not real detail, so start with a photo large enough for your intended print size.