Throughout our day we use or interact with things that are made of paper. One of the most common usages of paper is for writing or printing on it. From an official application form to greetings card to large posters, everything uses paper of one or the other kind.

Paper item comes in different size and shapes. A greetings card is smaller than an application form while a poster is usually larger than both. Another thing to notice is how all applications have similar sizes, all magazines have similar sizes, etc. It’s like the sizes for each of these items are well defined and followed by all. Well, that’s because it is kind of true. While there is no standard for the sizes of each and everything that’s made of paper, there are standards that define sizes of paper and we use different sized papers for different purposes.

So, when you hear someone refer to A4, A3, Letter, etc., they are actually referring to paper sizes. So, that brings us to the next point which is, who decides the sizes?

The paper size standard used most widely in the world today is known as the ISO 216 standard and it is defined by the International Organization for Standardization or ISO in short. ISO 216 standard for paper sizes is the most widely used standard with almost all the countries in the world using it with the exception of North America and a few Latin American countries. The standard defines a set of sizes for papers ranging from a very large sheet of paper to very small-sized ones, in order to address every kind of use case. The beauty of the sizes defined by ISO standard is in its aspect ratio, which makes it easily scalable. Let’s see how the aspect ratio does its magic.

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## The Magic Aspect Ratio

The ISO paper sizes are defined using an aspect ratio of 1:√2, or 1: 1.4142 which is also known as the Lichtenberg Ratio. The magic lies in the fact that if you cut a sheet of paper having the aspect ratio of 1:√2 in half, midway along its longer side, both the resulting sheets of paper will retain the same aspect ratio. Repeat the process and the aspect ratio stays the same for the new sheets of paper.

This unique property of this aspect ratio was used by the German DIN paper sizes standard in the 1920s and later on used by the ISO 216, which is based on the DIN system to a large extent. This unique property of the ratio however is not a new fact. The earliest recorded mention of this ratio was in a letter that German scientist Georg Christoph Lichtenberg wrote to Johann Beckmann in 1786, where he mentioned.

The short side of the rectangle must relate to the large one like 1 : √2, or like the side of a square to its diagonal

## ISO 216

The ISO 216 standard defines two different series of paper sizes. Series A and B. Later on, Series C was defined in the ISO 269 which is actually meant to standardize envelope sizes. The ISO 269 standard was later withdrawn but no replacement was defined for it. However, to keep things simple we’ll discuss all the three series A, B, and C in this post.

Before we get started with each series, let’s look at how they are named. Each size name is defined as the letter of its series and then a number. The number starts with 0 being the largest size in the series and then incremented by 1 for a size smaller. So, we have sizes like A0, A1, A2, etc, where A0 is the largest, A1 is smaller than A0, A2 is smaller than A1, and so on. The sizes in all the series are based on the aspect ratio of 1:√2. Now, let’s take a closer look at each of the series.

## A Series Paper Sizes

Series A starts with the size A0, which is the largest size in the A series with a dimension of 841 × 1189 mm or 33.1 × 46.8 inches. This means that an A0 size paper has an area of 1 square meter (rounding up). This makes it quite a large sheet of paper suitable only for specific usage like in technical drawing.

If we cut an A0 paper in half, midway along its longer sides, we will get two sheets of paper of the size A1. A1 sized paper has a dimension of 594 × 841 mm or 23.4 × 33.1 in. This is also quite a large sheet of paper and is used mainly for technical drawing, maps, posters etc.

If we cut an A1 paper in similar fashion, we will get two sheets of paper of the size A2, which has a dimension of 420 × 594 mm or 16.5 × 23.4 in. A2 papers are primarily used for drawing, printing photos or posters etc.

Cutting a paper of size A2 in half, we get two sheets of A3 size papers, each with a dimension of 297 × 420 mm or 11.7 × 16.5 in. A3 papers are used for drawings, photos, magazines, posters, certificates etc.

If we cut an A3 sized paper in half, we will have two sheets of A4 paper. The dimension of an A4 size paper is 210 × 297 mm or 8.3 × 11.7 in. It is perhaps the most well-known and widely used size of paper globally. It is used for various purposes including standard documents such as letters or forms, magazines, school notepads etc.

Cutting an A4 sized paper in half, we get two sheets of A5 sized paper. A5 paper has a dimension of 148 × 210 mm or 5.8 × 8.3 in. A5 is also a popular format and is mainly used for notebooks, printing books, leaflets etc.

If we cut an A5 sheet into two, we get two sheets of A6 sized paper. An A6 paper has a dimension of 105 × 148 mm or 4.1 × 5.8 in. A6 paper format mainly finds use in postcards, greetings card, leaflets, pocket diaries etc.

Cutting an A6 sheet into two halves, we get two sheets of A7 sized paper, each having a dimension of 74 × 105 mm or 2.9 × 4.1 in. It is mainly used to make flyers or greetings cards.

Now, let’s cut an A7 sheet into two halves, which will give us two sheets of A8 sized papers, each with a dimension of 52 × 74 mm or 2.0 × 2.9 in. This is almost similar to the size of a business card.

Cutting an A8 sheet into two gives us two A9 sized papers each of which has a dimension of 37 × 52 mm or 1.5 × 2.0 in.

Going one step further, if we cut a sheet of A9 paper in two halves, we’ll get two A10 sized papers. A10 sized paper has a dimension of 26 × 37 mm or 1.0 × 1.5 in.

Size | Dimension in mm | Dimension in inch |
---|---|---|

A0 | 841 × 1189 | 33.1 × 46.8 |

A1 | 594 × 841 | 23.4 × 33.1 |

A2 | 420 × 594 | 16.5 × 23.4 |

A3 | 297 × 420 | 11.7 × 16.5 |

A4 | 210 × 297 | 8.3 × 11.7 |

A5 | 148 × 210 | 5.8 × 8.3 |

A6 | 105 × 148 | 4.1 × 5.8 |

A7 | 74 × 105 | 2.9 × 4.1 |

A8 | 52 × 74 | 2.0 × 2.9 |

A9 | 37 × 52 | 1.5 × 2.0 |

A10 | 26 × 37 | 1.0 × 1.5 |

## B Series Paper Sizes

The size of B series paper sheets is the geometric mean of the successive A series sheets. What it simply means is that the sizes of B series papers fall between A series sizes. For example, B1 is between A0 and A1 in size, B2 is between A1 and A2 and so on.

Similar to A series, the B series sizes are also based on an aspect ratio of 1: √2. Although B series sizes are not as widely used as the A series, it standardizes paper sizes that were not included in the A series.

The series starts with its largest size, the B0. It has a dimension of 1000 × 1414 mm or 39.4 × 55.7 in. Due its large size it finds use in printing of enlarged photos or posters.

Similar to what we did with the series A sizes, here also we can fold or cut the paper in half, midway along its longer side, and keep arriving at the next size defined in the series. So, cutting the B0 paper in this way we get two B1 sized papers each with a dimension of 707 × 1000 mm or 27.8 × 39.4 in. B1 is smaller than A0 and larger than A1 and is mainly used for posters and signs.

Cutting or folding the B1 sheet in half we get B2 size paper which has a dimension of 500 × 707 mm or 19.7 × 27.8 in. B2 is smaller than A1 and larger than A2 and is used for printing posters.

Next up is the B3 size which, we can get by cutting the B2 sheet in half. It has a dimension of 353 × 500 mm or 13.9 × 19.7 in. B3 is smaller than A2 and larger than A3 and is mostly used for smaller posters and paintings.

Cutting a B3 paper in half, we get the B4 size, which has a dimension of 250 × 353 mm or 9.8 × 13.9 in. B4 is smaller than A3 and larger than A4 and used mainly for smaller posters and notebooks.

By cutting a B4 paper in half, we get the B5 sized paper which has a dimension of 176 × 250 mm or 6.9 × 9.8 in. B5 is smaller than A4 and larger than A5 and is used for making menus, flyers and magazines.

Now, let’s cut a B5 sheet in half, which will give us two sheets of B6 sized paper, each with a dimension of 125 × 176 mm or 4.9 × 6.9 in. B6 is smaller than A5 and larger than A6 and is mainly used for flyers.

Cutting a B6 sized paper in half, we will get two sheets of B7 sized paper, which has a dimension of 88 × 125 mm or 3.5 × 4.9 in. B7 is smaller than A6 and larger than A7 and is used mostly for flyers and small notebooks.

Let’s now cut this sheet of B7 in half, which will give us 2 sheets of B8 sized paper, each with dimension of 62 × 88 mm or 2.4 × 3.5 in. B8 is smaller than A7 and larger than A8 and finds use in flyers or business cards.

Similarly, cutting the B8 sized paper in half, we get two B9 sized paper which has a dimension of 44 × 62 mm or 1.7 × 2.4 in. B9 is smaller than A8 and larger than A9 and their small size is ideal for labels.

Cutting a B9 sized paper in half, we get two B10 sized papers, each with a dimension of 31 × 44 mm or 1.2 × 1.7 in. B10 is smaller than A9 and larger than A10. This small size can be used for small vouchers or similar things.

Size | Dimension in mm | Dimension in inch |
---|---|---|

B0 | 1000 × 1414 | 39.4 × 55.7 |

B1 | 707 × 1000 | 27.8 × 39.4 |

B2 | 500 × 707 | 19.7 × 27.8 |

B3 | 353 × 500 | 13.9 × 19.7 |

B4 | 250 × 353 | 9.8 × 13.9 |

B5 | 176 × 250 | 6.9 × 9.8 |

B6 | 125 × 176 | 4.9 × 6.9 |

B7 | 88 × 125 | 3.5 × 4.9 |

B8 | 62 × 88 | 2.4 × 3.5 |

B9 | 44 × 62 | 1.7 × 2.4 |

B10 | 31 × 44 | 1.2 × 1.7 |

## C Series Envelope Sizes

Even though all the three series i.e., A, B and C are often clubbed together and are related, it is good to know that the Series C envelope sizes were not defined in the ISO 216 standards, rather, it was defined as part of ISO 269. The ISO 269 were withdrawn later without any replacement being specified. However, it is still used in the national standards of many countries and often thrown together with series A & B while discussing ISO paper sizes, and this post is no exception.

Unlike the series A and B, the series C sizes are mostly used for envelopes. The C series sizes also maintains an aspect ratio of 1:√2. Other than being meant to be used as envelopes the basic principles of the series C are the same as series A & B. So, for this series also, we can arrive at the next size in the series by cutting or folding the current size in half, midway along its longer side. The series starts with the largest size C0 which has a dimension of 917 × 1297 mm or 36.1 × 51.1 in which is larger than A0 but smaller than B0.

Next, we have C1 which has a dimension of 648 × 917 mm or 25.5 × 36.1 in. C1 is larger than A1 but smaller than B1. Let’s refer to the table below for series C sizes.

Size | Dimension in mm | Dimension in inch |
---|---|---|

C0 | 917 × 1297 | 36.1 × 51.1 |

C1 | 648 × 917 | 25.5 × 36.1 |

C2 | 458 × 648 | 18.0 × 25.5 |

C3 | 324 × 458 | 12.8 × 18.0 |

C4 | 229 × 324 | 9.0 × 12.8 |

C5 | 162 × 229 | 6.4 × 9.0 |

C6 | 114 × 162 | 4.5 × 6.4 |

C7 | 81 × 114 | 3.2 × 4.5 |

C8 | 57 × 81 | 2.2 × 3.2 |

C9 | 40 × 57 | 1.6 × 2.2 |

C10 | 28 × 40 | 1.1 × 1.6 |

As you may have already noticed, the area of series C paper is actually the geometric mean of the areas of series A and series B paper size of the same sequence or number. For example, C4 is larger than A4 but smaller in area than B4.

Each C size envelope is meant to fit its corresponding A-sized sheet unfolded. For example, an unfolded A4 letter (and hence an A3 paper folded in half) will fit inside a C4 envelope. A flat A5 sheet or an A4 folded in half will fit inside a C5 envelope.

The below image provides a better understanding of the sizes of A and B series paper and the C series envelope sizes.