# A Paper Size Scale & Magnification Factors

The ISO 216 paper sizes have some great properties when it comes to enlarging and reducing documents, because they all have the same aspect ratio. If an A4 page is enlarged to A3 the margins around the page don't vary such that the top and side margins are of significantly different proportions and you don't get the text lost at the top, bottom or sides.

The scale factor for each reduction or enlargement is the same, so reducing from A3 -> A4 (71%) is the same scaling as from A4 -> A5 and from A5 -> A6. Note that the reduction between each size is not 50% even though the smaller size has half the area. The scale factor for reduction is calculated by dividing the longer edge of the smaller size by the longer edge of the larger size (or the shorter edge of the smaller size by the shorter edge of the larger size).

## Magnification Scale Factors Background

For the mathematically minded the scaling factor between A4 and A3 is the square root of 2 (√2) expressed as a percentage.
The scaling factor between A4 and A2 is (√2)^{2} (i.e. 2) expressed as a percentage. The table below gives
generic formulae for conversions between different sizes of the same series and conversions between series for A and B paper
sizes.

Conversion | Formula | Decimal | Percentage |
---|---|---|---|

A(n-1) -> A(n) | √0.5 | 0.7071 | 71% |

B(n) -> A(n) | √(√0.5) | 0.8409 | 84% |

A(n-1) -> B(n) | √(√0.5) | 0.8409 | 84% |

A(n) -> B(n) | √(√2) | 1.1892 | 119% |

B(n) -> A(n-1) | √(√2) | 1.1892 | 119% |

A(n) -> A(n-1) | √2 | 1.4142 | 141% |

## Magnification Scale Factors Table for A Paper Sizes

The table below gives scale factors for enlarging or reducing documents between all of the A series paper sizes expressed as percentages (as this is how they are most commonly displayed on photocopiers and in print software). To get conversion factors from the table select the row for the size you are converting from (blue) and the column for the size you are converting to (red).

Size | 4A0 | 2A0 | A0 | A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

4A0 | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.3% | 4.4% | 3.1% | 2.2% | 1.6% |

2A0 | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.3% | 4.4% | 3.1% | 2.2% |

A0 | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.3% | 4.4% | 3.1% |

A1 | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.3% | 4.4% |

A2 | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.3% |

A3 | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% |

A4 | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% |

A5 | 1132% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% |

A6 | 1600% | 1132% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% |

A7 | 2265% | 1600% | 1132% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% |

A8 | 3200% | 2265% | 1600% | 1132% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% |

A9 | 4573% | 3200% | 2265% | 1600% | 1132% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% |

A10 | 6400% | 4573% | 3200% | 2265% | 1600% | 1132% | 800% | 566% | 400% | 283% | 200% | 141% | 100% |

## Magnification Scale Factors Table for A Paper Sizes to B Paper Sizes

The table below gives scale factors for enlarging or reducing documents between A paper sizes and B series paper sizes expressed as percentages (as this is how they are most commonly displayed on photocopiers and in print software). To get conversion factors from the table select the row for the size you are converting from (blue) and the column for the size you are converting to (red).

Size | B0 | B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 | B10 |
---|---|---|---|---|---|---|---|---|---|---|---|

A0 | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% | 5.2% | 3.7% |

A1 | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% | 5.2% |

A2 | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% |

A3 | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% |

A4 | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% |

A5 | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% |

A6 | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% |

A7 | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% |

A8 | 1911% | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% |

A9 | 2719% | 1911% | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% |

A10 | 3822% | 2719% | 1911% | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% |

## Magnification Scale Factors Table for B Paper Sizes to A Paper Sizes

The table below gives scale factors for enlarging or reducing documents between B paper sizes and A series paper sizes expressed as percentages (as this is how they are most commonly displayed on photocopiers and in print software). To get conversion factors from the table select the row for the size you are converting from (blue) and the column for the size you are converting to (red).

Size | A0 | A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
---|---|---|---|---|---|---|---|---|---|---|---|

B0 | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% | 5.2% | 3.7% | 2.6% |

B1 | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% | 5.2% | 3.7% |

B2 | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% | 5.2% |

B3 | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% | 7.4% |

B4 | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% | 10.5% |

B5 | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% | 14.8% |

B6 | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% | 21% |

B7 | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% | 30% |

B8 | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% | 42% |

B9 | 1911% | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% | 59% |

B10 | 2719% | 1911% | 1347% | 955% | 673% | 476% | 336% | 238% | 168% | 119% | 84% |