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PPI Calculator

See how sharp a screen is (its pixels per inch), plus its real width, height and pixel size, from its resolution and diagonal.

Level: Grades 8–9

  • Common Core standard 8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Printable worksheet

PPI Calculator

Know the answer you need? Pick an input to work backward.

Inputs

Measured corner to corner across the visible picture, as screens are advertised.

Result

Pixel density

91.79 PPI

A 1,920 × 1,080 screen measuring 24 in diagonally has about 91.79 pixels per inch.

Pixels per centimeter
36.14 px/cm
Screen width
20.92 in
Screen height
11.77 in
Screen width (metric)
53.13 cm
Screen height (metric)
29.89 cm
Screen area
246.12 in²
Dot pitch (pixel size)
0.2767 mm
Diagonal in pixels
2,202.91 px
Total pixels
2.07 megapixels

See the step-by-step solution ↓

Step-by-step solution

  1. Find how many pixels fit along the diagonal, using the right-triangle rule (the Pythagorean theorem)

    d=1,9202+1,0802=2,202.90717 px

  2. Divide the pixels on the diagonal by the real diagonal in inches. That gives the pixels per inch

    PPI=2,202.90717 px24 in=91.787799

  3. Divide each side's pixel count by the density to get its real length in inches

    1,92091.787799=20.917813 in,1,08091.787799=11.76627 in

  4. Find the width of one pixel (the dot pitch): one inch, 25.4 mm, divided by the density

    25.491.787799=0.276725 mm

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how sharp a screen will look, and how big it really is. Pixels are the tiny dots that make up the picture. Pixel density, measured in pixels per inch (PPI), tells you how tightly a screen packs them. Two monitors can both have a 2560 × 1440 resolution (pixel count). But the 27-inch one spreads those pixels over a larger area than a 24-inch one. So text and edges look slightly rougher up close. Density, not resolution alone, decides how sharp a screen looks from a given distance.

Enter the resolution and the advertised diagonal size. You get the pixel density, the screen's actual width and height, and its area. You also get the dot pitch, the size of a single pixel. The width and height come from the resolution's shape. So this also answers a common question: how wide is a screen of a given diagonal, really?

Where it's used

Why this math matters outside the classroom:

  • Phone screens. A 6.1 inch phone at 2532 × 1170 has a diagonal of about 2,789 pixels, so roughly 457 PPI.
  • Monitors. A 27 inch monitor at 2560 × 1440 has a diagonal of about 2,937 pixels, which works out to about 109 PPI.
  • Printing. Designers check that an image has enough pixels for its print size, often aiming for about 300 per inch.
  • Comparing screens. Shoppers compare screens of different sizes by pixel density rather than by resolution alone.

Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics 8.G.B.7. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Enter the horizontal and vertical resolution in pixels, for example 1920 and 1080.
  2. Enter the diagonal size and choose inches or centimeters.
  3. Read the pixel density. The screen width, height, area and dot pitch are below it.

What the inputs mean

Horizontal resolution
The number of pixels across. Use the screen's built-in (native) resolution, not a scaled desktop setting.
Vertical resolution
The number of pixels from top to bottom.
Diagonal screen size
The visible screen, measured corner to corner. Screens are sold by this diagonal size, not by their width.

Formula and method

diagonal in pixels = √(width px² + height px²)
PPI = diagonal in pixels ÷ diagonal in inches
screen width = width px ÷ PPI,  screen height = height px ÷ PPI
dot pitch (mm) = 25.4 ÷ PPI

Here "width px" and "height px" are the pixel counts across and down. PPI is pixels per inch. The pixels form a grid, so the Pythagorean theorem (the right-triangle rule) gives the number of pixels along the diagonal. Divide that by the real diagonal in inches to get the pixels per inch. When pixels are square, that's the same in every direction.

Once you know the density, each side's length in inches is its pixel count divided by the density. Dot pitch is 1 divided by the density, turned into millimeters. It uses the exact 25.4 mm per inch.

Worked example

A 24-inch monitor has a resolution of 1920 × 1080.

  1. Diagonal in pixels: √(1920² + 1080²) = √4,852,800 = 2202.91 px.
  2. Pixel density: 2202.91 ÷ 24 = 91.79 PPI.
  3. Width: 1920 ÷ 91.79 = 20.92 in. Height: 1080 ÷ 91.79 = 11.77 in.
  4. Dot pitch: 25.4 ÷ 91.79 = 0.2767 mm.

Result: The monitor has about 91.79 pixels per inch, and it measures roughly 20.92 × 11.77 inches. Each pixel is about 0.2767 mm wide.

Understanding the result

Higher density means finer detail at the same distance. Whether you can see the difference depends on how far away you sit. A TV watched from across a room can have far lower density than a phone held at reading distance. It can still look just as sharp.

Dot pitch is the same information turned around. A smaller pitch means smaller pixels. It's handy when comparing displays listed in millimeters, such as LED video walls.

Assumptions and limitations

  • Pixels are square, so density is the same across and down.
  • The diagonal covers the visible picture only. The border around the screen (the bezel) and the frame aren't included.
  • One inch is exactly 2.54 cm.
  • Advertised diagonals are often rounded. A "27-inch" screen may be 27.0 or 26.9 inches, which shifts the result slightly.
  • Screens with rounded corners, notches or other non-rectangle shapes have a slightly smaller usable area than the rectangle worked out here.
  • Display scaling in your computer's settings changes how large things look. It doesn't change the real pixel density.

Frequently asked questions

Is PPI the same as DPI?

People often use them to mean the same thing for screens. Strictly, though, PPI counts pixels on a display. DPI (dots per inch) counts the ink dots a printer places per inch. A printer may use several dots to make one image pixel. So for printing, the two numbers can't be compared directly.

How wide is a 55-inch 16:9 television?

Enter any 16:9 resolution, such as 3840 × 2160, and a 55-inch diagonal. The width is about 47.94 inches and the height about 26.96 inches. Here the resolution only sets the shape. Any 16:9 resolution gives the same size.

Why do two screens with the same resolution look different?

If one is physically larger, its pixels are bigger and its density is lower. From the same distance, the smaller screen looks sharper. The larger one shows the same content at a bigger size.

Can I enter the size in centimeters?

Yes. Choose cm next to the diagonal. The calculator converts using 2.54 cm per inch and also reports pixels per centimeter.

How this calculator is checked

Method: Pythagorean theorem on the pixel grid; definition of pixel density; 1 in = 25.4 mm exactly. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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