Paper Size Chart

The idea behind the A series

Every A size has the same shape: the long side divided by the short side is always √2, about 1.414.

That single choice produces the property the system is built on: fold any A size in half and you get the next size down, with exactly the same proportions. Two A4 sheets side by side make A3. Two A3 make A2. Nothing is wasted and nothing is cropped.

√2 is the only ratio where this works. Halve a sheet of any other shape and the proportions change.

A0 is one square metre

The series is anchored by defining A0 as a sheet of area 1 m² with the √2 shape, which gives 841 × 1189 mm. Every other size follows by halving.

This makes paper weight trivially calculable. Paper is sold in grams per square metre, so one sheet of A0 in 80 gsm paper weighs 80 grams. A4 is one sixteenth of A0, so an A4 sheet weighs 5 g — which is how you work out postage without a scale. Five sheets and an envelope sit comfortably under 30 g.

Scaling actually works

Photocopying A4 to A3 is exactly 141 %, and A3 to A4 exactly 71 %. Those numbers are on every photocopier in Europe and they are exact rather than approximate, because the shapes match.

B and C series

• B sizes sit between consecutive A sizes, for posters and books where A is slightly wrong.
• C sizes are for envelopes, sized so an A sheet fits inside the matching C. An A4 letter goes in a C4 envelope, or folded once into a C5, or folded twice into a C6 — which is the standard business envelope.

US sizes have no system at all

Letter is 8.5 × 11 inches and Legal is 8.5 × 14. Their aspect ratios are 1.294 and 1.647, which are unrelated to each other and to anything else.

The practical result: scaling between US sizes never fits properly, and a document laid out for Letter printed on A4 (or the reverse) loses a strip at one edge or gains a margin. A4 is 6 mm narrower and 18 mm taller than Letter, which is just enough to break a layout.

The origin of 8.5 × 11 is not documented with any certainty — the most repeated explanation involves the size of a vat of paper pulp and the reach of a person's arms.

The pixel column

For print, 300 pixels per inch is the standard target. A4 at 300 dpi is 2480 × 3508 pixels, which is the canvas size to use when designing anything that will be printed. At 150 dpi it is half that, which is acceptable for large posters seen from a distance.

Common uses

• Setting up a print document at the right pixel size.
• Choosing an envelope for a folded letter.
• Working out postage weight from gsm.
• Converting a design between A4 and Letter.

Questions people ask

Why is A4 the size it is?

Because A0 is defined as one square metre with a √2 shape, and A4 is A0 halved four times. That gives 210 × 297 mm.

Why does folding A4 give A5 with the same shape?

Because the sides are in the ratio √2, the only ratio where halving preserves the proportions.

What is A4 in pixels for printing?

2480 × 3508 at 300 dpi, which is the standard target for print.

How much does a sheet of A4 weigh?

About 5 g at 80 gsm. A0 is one square metre, so it weighs the gsm figure directly, and A4 is one sixteenth of that.

Why do US Letter and A4 not match?

They have unrelated aspect ratios. A4 is 6 mm narrower and 18 mm taller, which is enough to break a layout.

Which envelope fits an A4 letter?

C4 flat, C5 folded once, or C6 folded twice — C6 being the standard business envelope.

Worked out in the page

Nothing is sent anywhere. The tables are built into the page and the arithmetic runs in your browser, so it works with no connection.