Paper Size Scale and Magnification Factors.pdf

8/12/2019 Paper Size Scale and Magnification Factors.pdf

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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 significantlydifferent 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

calculate 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. and 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 Formulae 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%


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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).

Size4A

02A0 A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10

4A0100%

71% 50% 35% 25% 18%12.5%

8.8%

6.3%

4.4%

3.1%

2.2%

1.6%

2A0141%

100%

71% 50% 35% 25% 18%12.5%

8.8%

6.3%

4.4%

3.1%

2.2%

A0200

%

141

%

100

%71% 50% 35% 25% 18%

12.5

%

8.8

%

6.3

%

4.4

%

3.1

%

A1283%

200%

141%

100%

71% 50% 35% 25% 18%12.5%

8.8%

6.3%

4.4%

A2400%

283%

200%

141%

100%

71% 50% 35% 25% 18%12.5%

8.8%

6.3%

A3566%

400%

283%

200%

141%

100%

71% 50% 35% 25% 18%12.5%

8.8%

A4800%

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%

A61600%

1132%

800%

566%

400%

283%

200%

141%

100%

71% 50% 35% 25%

A72265%

1600%

1132%

800%

566%

400%

283%

200%

141%

100%

71% 50% 35%

A83200%

2265%

1600%

1132%

800%

566%

400%

283%

200%

141%

100%

71% 50%

A94573%

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%


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Magnification Scale Factors Table for A Paper Sizes to BPaper 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%

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%


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Magnification Scale Factors Table for B Paper Sizes to APaper 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%

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%

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Paper Size Scale and Magnification Factors.pdf