Paper Size Calculator: A4, A3, Letter in mm and Inches

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How to use this tool

Pick a size. You get millimetres, inches, typographic points and the pixel dimensions at whatever DPI you set, which is what you actually need when setting up a document for print. The compare box puts any two sizes side by side and says how far apart they are.

The square root of two, and why it matters

Every sheet in the A series has the same shape: the long side divided by the short side is the square root of two, about 1.4142. That is not a design preference, it is the only ratio with a particular property.

Cut a sheet in half across its long side and the two halves have the same ratio as the original. Only the square root of two does this. Any other shape changes proportion when you halve it, which is why A4 folded is exactly A5, and two A4 sheets side by side make exactly A3, with nothing trimmed and nothing left over.

This is where the photocopier buttons come from. The 141 percent button is the square root of two, moving you up one size. The 71 percent button is its reciprocal, moving you down one. Those two numbers are on machines all over the world and almost nobody knows why.

The series is anchored by area rather than length. A0 is defined as one square metre, then each size halves it. A4 is one sixteenth of a square metre, which is 624 square centimetres. In practice A0 is 841 by 1189 mm and that comes to 0.999949 square metres rather than exactly one, because the dimensions are rounded to whole millimetres.

A4 against US Letter

They are close enough to look interchangeable and different enough to cause trouble. A4 is 210 by 297 mm. Letter is 215.9 by 279.4 mm, which is 8.5 by 11 inches exactly.

Letter is 5.9 mm wider and 17.6 mm shorter. Neither fits inside the other, so there is no scaling that maps one onto the other without either cropping an edge or leaving a band. A4 has about 3.4 percent more area. Letter also has a ratio of 1.2941, nowhere near the square root of two, so the whole halving property is absent and North American paper sizes have no clean sequence at all.

A worked check you can repeat on paper

Start at A0, which is 841 by 1189 mm. Halve the long side: 1189 divided by 2 is 594.5, rounded down to 594. Now A1 is 594 by 841, the old width becoming the new height.

Repeat. 841 halves to 420, giving A2 as 420 by 594. Again gives A3 as 297 by 420. Again gives A4 as 210 by 297. Four halvings from A0 and every intermediate size is a whole number of millimetres, which is the reason for the rounding at each step.

Check the ratio at the end: 297 divided by 210 is 1.414286, against a true square root of two of 1.414214. The tiny difference is that millimetre rounding, and it is far too small to matter on any printer.

Mistakes that catch people out

Printing A4 artwork on Letter without checking. The page is shorter, so the bottom of an A4 layout gets cropped or scaled down. Set the paper size before designing, not after.

Confusing the B and C series. C sizes are envelopes, sized so the matching A sheet slides in. A C4 envelope takes an unfolded A4 sheet, C5 takes A4 folded once, C6 takes it folded twice.

Forgetting bleed and margins. The sizes here are the finished trimmed sheet. Anything printing to the edge needs artwork extending past it, usually by 3 mm.

Assuming pixels are fixed. A4 at 300 DPI is 2480 by 3508 pixels, at 150 DPI it is half that in each direction and a quarter of the total. A pixel dimension is meaningless without the DPI attached.

Paper sizes in millimetres and inches

The sizes people look up most. Each opens the calculator on that size with its own address.

How this was checked

The A series was generated from A0 by repeated halving with rounding down at each step, exactly as ISO 216 specifies, then checked against the published dimensions. A3 came out as 297 by 420, A4 as 210 by 297, A5 as 148 by 210 and A6 as 105 by 148, all matching. B4 gave 250 by 353 and C4 gave 229 by 324, again matching, which confirms the same generation rule works for all three series from their own starting sheets.

The A0 area came out at 0.999949 square metres rather than exactly one, which is the expected consequence of rounding to whole millimetres rather than an error. A4 in inches came to 8.268 by 11.693, and and the area comparison came out at 3.39 percent, meaning A4 is that much larger than Letter, or equivalently Letter is 3.28 percent smaller than A4. Both figures describe the same gap from opposite ends.

Related Calculators and Reference

• Aspect Ratio Calculator for shapes measured by ratio rather than by standard size.
• Length Converter for taking any of these dimensions into other units.
• Area of 2D Shapes Calculator for areas beyond rectangles.
• Area Converter for converting these areas into other units.
• ISO 216 is the standard that defines the A, B and C series.