The relationship has three quantities for each axis: pixel count, physical length in inches, and source PPI. Knowing any two determines the third. Width and height must be calculated independently; silently deriving one side from an aspect ratio would add an assumption the user did not provide.

Divide pixels by PPI for print size

For a 3000-pixel width at 300 PPI, 3000 ÷ 300 equals exactly 10 inches. A 2000-pixel height gives 20/3 inches, a repeating decimal. DpiCalc keeps the rational value internally and displays a rounded approximation rather than converting the rounded display again.

Multiply inches by PPI for required pixels

A ten-inch target at 300 PPI requires exactly 3000 pixels along that axis. When the multiplication produces a fraction of a pixel, the minimum whole count is the ceiling. Rounding 2480.314… down to 2480 would fall slightly below the stated density, so DpiCalc returns 2481.

Convert metric length through exact inches

One inch is defined as exactly 25.4 millimetres and 2.54 centimetres. Therefore 210 mm is exactly 1050/127 inches. Multiplying that rational by 300 PPI gives 315000/127 pixels before the explicit whole-pixel ceiling. No binary floating-point approximation is needed for this linear arithmetic.

Check both axes and proportions

A pixel rectangle and a physical print rectangle can have different aspect ratios. In that case horizontal and vertical effective PPI differ. The calculator reports both and the lower limiting value; it does not decide whether to crop, add margins, stretch, or change the requested print size.