The short answer

PPI is pixels per inch: how many image pixels occupy one inch, whether on a display or when an image is printed. DPI is dots per inch: how many ink dots a printer physically places on paper in one inch.

If you are talking about a screen, or about how large an image will print, the accurate term is PPI. DPI belongs to the printer.

Why the confusion exists

Desktop publishing software has labelled its resolution field “DPI” for decades, so the habit is deeply set. Search for a “DPI calculator” and what you almost always want is a PPI calculation. Ratio & Rule answers that intent — the PPI Calculator is the tool people usually mean — while using the accurate term for what it computes.

What PPI describes

On a display, PPI is fixed by the hardware: divide the diagonal in pixels by the diagonal in inches. A 27-inch screen at 2560 × 1440 works out at about 108.8 PPI.

pixelDiagonalequals√(pixelWidth² + pixelHeight²)

PPIequalspixelDiagonal ÷ diagonalInches

For a printed image, PPI is a choice rather than a property. The same file printed at 300 PPI covers a quarter of the area it covers at 150 PPI. Nothing about the file changes; only the size you asked for does.

What DPI describes

An inkjet printer builds each image pixel from many tiny ink dots, because a single dot can only be one colour. That is why printers advertise figures such as 1440 or 2880 DPI while the images they print are prepared at around 300 PPI. The two numbers count different things and are not interchangeable.

A note on pixel density and quality

Density is a measurement, not a verdict. What you actually perceive depends on how large a pixel appears from where you are sitting, which involves viewing distance as much as density. A television at three metres does not need the density of a phone at arm's length. For that reason Ratio & Rule reports density figures without labels such as “excellent” or “retina”.

Which tool do you need?