Quick answer
PPI = √(width² + height²) ÷ diagonal size. A 1920 × 1080 display at 24 inches has √(1920² + 1080²) = 2,202.9 pixels along the diagonal and 91.79 PPI.
Enter the horizontal and vertical pixels and the diagonal size in inches. The calculator returns pixel density.
Related tools: Decimal to Hex Converter: Convert integers between binary, octal, decimal and hexadecimal.
How to use the Pixels Per Inch (PPI) Calculator
- Enter horizontal pixels (a whole number, 1 or more).
- Enter vertical pixels (a whole number, 1 or more).
- Enter diagonal size (inches) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Horizontal pixels | A whole number | ≥ 1 |
| Vertical pixels | A whole number | ≥ 1 |
| Diagonal size | A number, in inches | > 0 |
Formula and method
Formula
PPI = √(w² + h²) ÷ diagonal
IEEE-754 double precision; shown to at most 6 decimal places.
Diagonal pixel count over diagonal length.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Horizontal pixels = 1920; Vertical pixels = 1080; Diagonal size = 24.
| Result | Value |
|---|---|
| Pixel density | 91.79 ppi |
Example 2
Inputs: Horizontal pixels = 3840; Vertical pixels = 2160; Diagonal size = 27.
| Result | Value |
|---|---|
| Pixel density | 163.18 ppi |
The first line is the headline result (pixel density). IEEE-754 double precision; shown to at most 6 decimal places.
What PPI means
Higher PPI packs pixels more tightly and makes text look sharper at the same viewing distance. Common values are about 92 for a 24-inch 1080p monitor, 163 for a 27-inch 4K monitor and 326 or more for phones.
PPI versus DPI
PPI is for screens, DPI for printers. Viewing distance matters: phones are held closer and need a higher PPI to look sharp.
How the result changes with horizontal pixels
Holding every other input at the first worked example, this table changes only horizontal pixels. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Horizontal pixels | Pixel density |
|---|---|
| 960 | 60.21 ppi |
| 1920 | 91.79 ppi |
| 3840 | 166.21 ppi |
| 7680 | 323.15 ppi |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Diagonal size: entering "0" shows "Diagonal size must be greater than 0." beside that field and no result.
Choosing between the Pixels Per Inch (PPI) Calculator and similar calculators
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Assumptions and limitations
- Diagonal in inches
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for diagonal size to confirm this.
Frequently asked questions
What PPI is retina?
Around 220 or more at desktop distances, depending on viewing distance.
Does aspect ratio matter?
Yes, through the width and height.
Is 91.79 PPI good?
It is standard for 24-inch 1080p.
What does the Pixels Per Inch (PPI) Calculator calculate?
Pixel density of a display. It returns Pixel density.
What formula does the Pixels Per Inch (PPI) Calculator use?
PPI = √(w² + h²) ÷ diagonal. Diagonal pixel count over diagonal length.
What do I need to enter in the pixels Per Inch (PPI) Calculator?
You enter Horizontal pixels, Vertical pixels and Diagonal size (inches).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Diagonal in inches.
What is an example of a pixels Per Inch (PPI) result?
With horizontal pixels 1920, vertical pixels 1080 and diagonal size 24, the pixel density is 91.79 ppi.
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Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.