DPI calculator
Give it any two of pixels, print size and DPI and it works out the third, and shows the sum. It opens on the commonest question: how many pixels an 8 × 10 inch print needs at 300 DPI.
Free, no account. The sums are done in your browser: nothing you type is sent anywhere.
2,400 × 3,000 pixels
7.2 megapixels
8 in × 300 DPI = 2,400 pixels across, and 10 in gives 3,000 down.
Sharp at reading distance: this is print quality.
Your own numbers
How to use the calculator
- Choose what you want to work out: the pixels a print needs, how large a picture prints, the DPI of a print, or the PPI of a screen.
- Press a size, a picture or a resolution to use a common one, or type your own numbers in the boxes underneath.
- Read the answer at the top. The line under it shows the sum, so you can check it or do the next one in your head.
The one sum behind all of it
Pixels, size and resolution are tied together by a single relation: pixels = inches × DPI. An 8 inch side at 300 DPI needs 8 × 300 = 2,400 pixels. Turned round, a side of 2,400 pixels printed at 300 DPI is 2,400 ÷ 300 = 8 inches, and 2,400 pixels spread over 8 inches is 2,400 ÷ 8 = 300 DPI.
For centimetres or millimetres, convert to inches first: one inch is exactly 2.54 cm, or 25.4 mm. An A4 sheet is 210 × 297 mm, which is 8.27 × 11.69 inches, so at 300 DPI it is 2,480 × 3,508 pixels.
A picture has no fixed DPI of its own. The same 4,000 × 3,000 pixel photo is 13.3 × 10 inches at 300 DPI and 26.7 × 20 inches at 150 DPI. The number stored in the file is only a note of the size someone intended.
Which DPI to aim for
- 300 DPI is the usual figure asked for by printers of books, photos and anything held in the hand.
- 150 DPI is enough for a poster looked at from a step or more away, and halves the pixels needed each way.
- 600 DPI and above is for line art and text supplied as pictures, where edges are hard black against white.
- Screens are a different matter: a picture on a screen is shown pixel for pixel, and the 72 or 96 DPI written in a file changes nothing about how it looks there.
Screen PPI
A screen’s pixel density comes from its pixel size and its diagonal. The diagonal in pixels is the square root of width² + height² (Pythagoras), and dividing that by the diagonal in inches gives pixels per inch. A 27 inch monitor of 3,840 × 2,160 pixels has a diagonal of 4,406 pixels, so 4,406 ÷ 27 = 163 PPI.
For screens the correct term is PPI, pixels per inch. DPI, dots per inch, belongs to printers. In everyday use the two words are swapped freely, and for these sums the number is the same.
Questions
How do I calculate DPI?
Divide the pixels along a side by the length of that side in inches. A picture 3,000 pixels wide printed 10 inches wide is 3,000 ÷ 10 = 300 DPI.
How many pixels is 300 DPI?
300 pixels for every inch of the print. A 4 × 6 inch print is 1,200 × 1,800 pixels, a 5 × 7 is 1,500 × 2,100 and an 8 × 10 is 2,400 × 3,000.
Does changing the DPI change the quality?
Not by itself. Changing only the number stored in a file changes the size it prints at, not its pixels. Quality changes only when pixels are added or thrown away, which is called resampling.
What if the picture is a different shape from the print?
The calculator gives the DPI across and the DPI down, and uses the lower of the two. To fill the print without stretching, the picture has to be cropped to the print’s shape first.
Is this the DPI of a mouse?
No. Mouse DPI is how far the pointer moves for an inch of hand movement. This calculator is about pictures, prints and screens.