How this calculator works
Pixel density links the digital image to a physical print: the print width is the pixel width divided by the chosen density, and the height follows the same way, so the print keeps the image ratio. Density is a choice, not a property of the file. A gallery print is usually made at 300 ppi for close viewing, a poster at 150 ppi because it is seen from further away, and a billboard can be far below 50 ppi. If you instead know the print width you want, dividing the pixel width by that width in inches gives the density the file supports. Upscaling software can add pixels but cannot recover detail that was never recorded.
Formula
print width (in) = image width in pixels / PPI. print height (in) = image height in pixels / PPI. print diagonal = sqrt(width^2 + height^2). To reverse: PPI = image width in pixels / print width in inches.
Worked example
A 3000 by 2000 pixel photograph printed at 300 ppi is 10 inches wide and 6.667 inches high, with a diagonal of about 12.02 inches. It holds 6 megapixels. Printed at 150 ppi the same file is 20 by 13.333 inches, and at 100 ppi it is 30 by 20 inches, though the detail per inch falls. If you want a 10 inch wide print, the file supports 3000 / 10 = 300 ppi.
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Frequently asked questions
What is the best PPI for printing photos?
Around 300 ppi is the usual target for prints viewed in the hand, which is why labs ask for it. Large prints viewed from a metre or more can look excellent at 100 to 150 ppi, and the eye cannot resolve finer detail at that distance anyway.
Can I print larger than the calculated size?
Yes, but the density falls. Below about 100 ppi on a small print, individual pixels and interpolation softness become visible. Better printing software, or a viewing distance that increases with size, can make low density acceptable.
Does this calculator account for cropping?
No. It assumes the whole file is printed. If you crop to a different ratio, use the cropped pixel width and height, otherwise the print size on one axis will not match what you ordered.
Why do labs quote DPI when they mean PPI?
The terms are widely mixed up. For printing image files, the useful figure is pixels per inch. DPI properly describes how finely a printer places ink dots, which is usually higher than the pixel density.