# A Paper Size Scale & Magnification Factors

 Size Size Decimal Percentage A0   A1   A2   A3   A4   A5   A6   A7   A8   A9   A10 to A0   A1   A2   A3   A4   A5   A6   A7   A8   A9   A10 is 0.7071 or 71%

Select the paper sizes from the two 'Size' selector boxes and the magnification factor will appear in the two factor boxes as a decimal and as a percentage (useful for photocopying).

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)√0.50.707171%
B(n) -> A(n)√(√0.5)0.840984%
A(n-1) -> B(n)√(√0.5)0.840984%
A(n) -> B(n)√(√2)1.1892119%
B(n) -> A(n-1)√(√2)1.1892119%
A(n) -> A(n-1)√21.4142141%

## 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 A2 A3 A4 A5 A6 A7 A8 A9 A10 A1 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).

SizeB0B1B2B3B4B5B6B7B8B9B10
A0119%84%59%42%30%21%14.8%10.5%7.4%5.2%3.7%
A1168%119%84%59%42%30%21%14.8%10.5%7.4%5.2%
A2238%168%119%84%59%42%30%21%14.8%10.5%7.4%
A3336%238%168%119%84%59%42%30%21%14.8%10.5%
A4476%336%238%168%119%84%59%42%30%21%14.8%
A5673%476%336%238%168%119%84%59%42%30%21%
A6955%673%476%336%238%168%119%84%59%42%30%
A71347%955%673%476%336%238%168%119%84%59%42%
A81911%1347%955%673%476%336%238%168%119%84%59%
A92719%1911%1347%955%673%476%336%238%168%119%84%
A103822%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).

SizeA0A1A2A3A4A5A6A7A8A9A10
B084%59%42%30%21%14.8%10.5%7.4%5.2%3.7%2.6%
B1119%84%59%42%30%21%14.8%10.5%7.4%5.2%3.7%
B2168%119%84%59%42%30%21%14.8%10.5%7.4%5.2%
B3238%168%119%84%59%42%30%21%14.8%10.5%7.4%
B4336%238%168%119%84%59%42%30%21%14.8%10.5%
B5476%336%238%168%119%84%59%42%30%21%14.8%
B6673%476%336%238%168%119%84%59%42%30%21%
B7955%673%476%336%238%168%119%84%59%42%30%
B81347%955%673%476%336%238%168%119%84%59%42%
B91911%1347%955%673%476%336%238%168%119%84%59%
B102719%1911%1347%955%673%476%336%238%168%119%84%