# Areas Of A Series Paper Sizes

The area of each of the A paper sizes are set by the A paper size definitions (see below). A0 is defined as having an area of 1 square metre, however the A paper size standard also specifies that each size is rounded to the nearest millimetre. Thus A0 is 841mm x 1189mm giving an area of 0.999949 square metres.

Theoretically the area of a sheet of paper of size An can be calculated as 1/2^{n} m^{2}.

The following table gives theoretical areas compared with actual areas for each of the A paper sizes from 4A0 to A10.

## Table of Theoretical and Actual Areas of A Paper Sizes

Size | Theoretical Area (sq m) | Actual Area (sq m) | Difference (sq m) | Difference (%) |
---|---|---|---|---|

4A0 | 4 | 3.999796 | 0.000204 | 0.0051% |

2A0 | 2 | 1.999898 | 0.000102 | 0.0051% |

A0 | 1 | 0.999949 | 0.000051 | 0.0051% |

A1 | 0.5 | 0.499554 | 0.000446 | 0.0892% |

A2 | 0.25 | 0.24948 | 0.00052 | 0.208% |

A3 | 0.125 | 0.12474 | 0.00026 | 0.208% |

A4 | 0.0625 | 0.06237 | 0.00013 | 0.208% |

A5 | 0.03125 | 0.03108 | 0.00017 | 0.544% |

A6 | 0.015625 | 0.01554 | 0.000085 | 0.544% |

A7 | 0.0078125 | 0.00777 | 0.0000425 | 0.544% |

A8 | 0.00390625 | 0.003848 | 0.00005825 | 1.4912% |

A9 | 0.001953125 | 0.001924 | 0.000029125 | 1.4912% |

A10 | 0.0009765625 | 0.000962 | 0.0000145625 | 1.4912% |

At the smaller sizes (A8, A9 & A10) the discrepancy between the theoretical area of the sheet and the actual area is about 1.5%. Larger sizes have significantly lower differences between the theoretical area and the actual area.

## A Series Paper Sizes Defined

The A series paper sizes are defined in ISO 216 by the following requirements:

- The length divided by the width is 1.4142
- The A0 size has an area of 1 square metre.
- Each subsequent size A(n) is defined as A(n-1) cut in half parallel to its shorter sides.
- The standard length and width of each size is rounded to the nearest millimetre.

Note: For reference the last item is there because the root 2 aspect ratio doesn't always give a whole number.