In numerical terms, the aspect is 1.414, or more precisely, the square root of two. Although this number might seem inconvenient, it was chosen so that if a sheet is cut in half parallel to the shorter edges, each of the resulting sheets also has an aspect of 1.414. Moreover, if a sheet is folded in half with the crease parallel to the shorter edges, each page thereby formed has an aspect of 1.414; this latter fact is of interest to book manufacturers. No other number has this property.
The A series contains the most popular sheet sizes. The A0 sheet has an area of one square meter, a round number which simplifies paper usage calculations for printers. An A0 when cut in half yields two A1 sheets, an A2 halved generates two A3s, half of an A3 is an A4, and so forth. The A0 sheet can also be doubled (2A0), quadrupled (4A0) et cetera.
The B series furnishes intermediate values -- each B sheet is "exponentially" halfway between two A sheets. It turns out that one edge of a B0 sheet is precisely one meter long. Much as with the A series, a B0 cut in half gives two B1s, half of a B1 is a B2, and a 2B0 is twice the size of a B0.
The C series is used primarily with envelopes whose contents are A-series sheets. For instance, a C6 envelope comfortably holds an A6 sheet unfolded, an A5 folded once, or an A4 folded twice. Each C sheet is exponentially halfway between an A sheet and the next larger B sheet.
The D series, which is rare, is suitable for envelopes containing B-series sheets. As an example, a D6 envelope suits a B7 sheet unfolded, a B6 folded once, or a B5 folded twice. Each D sheet is exponentially halfway between a B sheet and the next larger A sheet.
Scandinavian references occasionally mention the E, F and G series.
The formulas for calculating sizes appear below. Also, a long table gives explicit dimensions for a wide variety of sizes. Meanwhile, a short table gives dimensions for the ISO subset.
Here is an illustration of halving.
The following table contains size diagrams which are intended to be printed at 100% scale.
| Size of Chart | Largest Size Depicted | Smallest Size Depicted | |
| A4 | B5 | C14 | Link |
| A3 | B4 | C13 | Link |
| A2 | B3 | C12 | Link |
| A1 | B2 | C11 | Link |
| A0 | B1 | C10 | Link |
| 2A0 | B0 | C9 | Link |
| PostScript source code | |||
Although these diagrams sometimes exhibit aliasing on a computer monitor because of its limited resolution, they perform much better on a printer, which is likely to have much higher resolution than a monitor.
| Designation | Longer Side in millimeters | Shorter Side in millimeters |
|---|---|---|
| mB0 | 1000 * 2^(+4/8) * m^(1/2) | 1000 * 2^( 0/8) * m^(1/2) |
| mC0 | 1000 * 2^(+3/8) * m^(1/2) | 1000 * 2^(-1/8) * m^(1/2) |
| mA0 | 1000 * 2^(+2/8) * m^(1/2) | 1000 * 2^(-2/8) * m^(1/2) |
| mD0 | 1000 * 2^(+1/8) * m^(1/2) | 1000 * 2^(-3/8) * m^(1/2) |
m should be a power of two, such as 2, 4, 8, 16, 32 ...
| Designation | Longer Side in millimeters | Shorter Side in millimeters |
|---|---|---|
| Bn | 1000 * 2^(+4/8-n/2) | 1000 * 2^( 0/8-n/2) |
| Cn | 1000 * 2^(+3/8-n/2) | 1000 * 2^(-1/8-n/2) |
| An | 1000 * 2^(+2/8-n/2) | 1000 * 2^(-2/8-n/2) |
| Dn | 1000 * 2^(+1/8-n/2) | 1000 * 2^(-3/8-n/2) |
n should be a nonnegative integer, such as 0, 1, 2, 3, 4 ...
If we were to allow nonintegers, then for example B3, C2.75, A2.5 and D2.25 would all indicate the same size of sheet.
| 2 ^ (+4/8) = 1.414214 |
| 2 ^ (+3/8) = 1.296840 |
| 2 ^ (+2/8) = 1.189207 |
| 2 ^ (+1/8) = 1.090508 |
| 2 ^ ( 0/8) = 1.000000 |
| 2 ^ (-1/8) = 0.917004 |
| 2 ^ (-2/8) = 0.840896 |
| 2 ^ (-3/8) = 0.771105 |