DPI Calculator
This calculator converts a screen's pixel resolution and diagonal size into the numbers people actually compare: pixel density in pixels per inch (PPI), the simplified aspect ratio, total megapixels, and the physical width and height of the screen in centimetres. Use it when comparing phone and monitor sharpness, checking whether an image will look pixel-dense or blocky on a display, or designing interfaces against a device's real physical size. This page does not measure your actual display, does not change any settings, and does not judge whether a screen looks good.
Method and formula
A display with W pixels across and H pixels down has a diagonal resolution of √(W² + H²) pixels. Dividing by the diagonal length in inches gives pixel density:
PPI = √(width² + height²) ÷ diagonal (inches)
The remaining outputs follow from the same triangle and the pixel count:
aspect ratio = width : height, reduced by the largest common divisor
total megapixels = width × height ÷ 1,000,000
screen width (cm) = width ÷ PPI × 2.54
screen height (cm) = height ÷ PPI × 2.54
Despite the tool's common name, the number it computes is strictly PPI (pixels per inch). DPI (dots per inch) is a printing term for ink dots, and PPI and DPI are equal only when one display pixel corresponds to one device dot.
Worked example
For a 1920 × 1080 monitor with a 24-inch diagonal:
- Diagonal resolution: √(1920² + 1080²) ≈ 2203 pixels
- PPI: 2203 ÷ 24 ≈ 91.79 PPI
- Aspect ratio: 1920 : 1080 = 16:9
- Total megapixels: 1920 × 1080 ÷ 1,000,000 ≈ 2.07 MP
- Screen size: 1920 ÷ 91.79 × 2.54 ≈ 53.1 cm wide, 29.9 cm high
As a second example, a 6.1-inch 2532 × 1170 phone display works out to about 457 PPI, which is why the same interface looks crisper on the phone than on a 24-inch monitor of the previous example.
What the result means
PPI is a density: higher values mean finer detail at the same viewing distance. Comparing PPI is only meaningful between devices held at similar distances — a 90 PPI desk monitor looks sharp at arm's length, while a 90 PPI phone would look coarse. The centimetre outputs describe the viewable rectangle implied by the diagonal and aspect ratio; the actual monitor bezel is larger, and laptop or phone specifications quote the panel, not the casing.
The aspect ratio is reduced by the largest common divisor, so 3840 × 2160 shows as 16:9 and 2880 × 1800 shows as 8:5. Odd resolutions can reduce to ratios like 683:384, which are correct but not marketing-friendly labels.
Accuracy and limitations
- Inputs must be positive numbers. The diagonal must be the panel's diagonal in inches; entering centimetres or a wrong diagonal shifts every output.
- The calculation assumes square pixels. Some panels use non-square pixel geometry, and some projectors shift pixels; results for such devices are approximations.
- The tool does not account for overscan, rounded corners, notches, or the difference between physical and logical resolution introduced by operating-system scaling (for example, a "2x" Retina setting).
- Comparing PPI across devices does not by itself predict perceived sharpness, which also depends on viewing distance, panel technology, and subpixel layout.
Sources
- NIST Special Publication 811, Guide for the Use of the International System of Units — the exact inch-to-centimetre conversion factor (1 in = 2.54 cm) used in the physical size outputs.
- International Telecommunication Union — Recommendation BT.2020: Parameter values for ultra-high definition television — standard UHD resolutions and 16:9 aspect-ratio conventions referenced for the examples.
Editorial record
- Author: SoupCalc Editorial Team
- Method review: SoupCalc Engineering Review
- Last reviewed: September 2, 2026
- Review scope: PPI and aspect-ratio mathematics, unit conversion, examples, source links, and claims about the tool's actual functions