International Paper Sizes & Formats
The purpose of this site is to explain current international standard paper sizes, covered by the ISO 216 Standard, and to provide size charts to allow a quick lookup of sizes.
If you are looking for the specific size of a particular paper format these are available on the following pages:
- A Series Paper Sizes
- B Series Paper Sizes
- C Series Envelope Sizes
- US Paper Sizes
- Newspaper Sizes
- Postcard Sizes
ISO Paper Sizes Standard Overview & Rationale
The ISO paper size A standard is based on each size being half of the size of the previous one, when folded parallel to the shorter lengths. This system allows for a variety of useful applications, such as the enlarging and reducing of images without any cutoff or margins, or folding to make a booklet of the next size down.
The mathematics behind this useful feature is that the sheets have an aspect ratio (that's the ratio of the length to the width) of the square root of 2.
Image courtesy of Office 365.
A Series Paper Sizes Formal Definition
The ISO 216 definiton of the A paper sizes is based on the following basis:
- 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: The last item is there because the root 2 aspect ratio doesn't always give a whole number.
Extensions - B Series Paper Sizes
There are some requirements for paper sizes where the A series isn't suitable and to take these into account the B series paper sizes were introduced. In order to explain the rationale behind the B paper sizes, we are going to need a bit more maths.
The B series paper standards are also based around the 1:root 2 aspect ratio, but in order to provide sizes not covered by the A series, the length and width of size B(n) are defined as being the geometric mean of size A(n) and size A(n-1).
Note: The geometric mean of two numbers is the square root of the product of those two numbers. e.g. The geometric mean of 6 and 4 is root(6x4) or the square root of 24. (For those who are interested - this link explains Geometric Means in more detail.)
The benefit of using the geometric mean is that the magnification factor between A1 and B1 sizes is that same as the one that scales B1 to A0.
The C Series Envelope Sizes
The C series sizes were introduced to define the sizes of envelopes suitable for the A series paper sizes. This is also based on the root 2 aspect ratio and the size of a C(n) envelope is defined as the geometric mean of paper sizes A(n) and B(n). This leads to a C(n) envelope which nicely holds a sheet of A(n) paper unfolded.
This sizing also has some neat properties when dealing with folded paper, so a C4 envelope will hold a sheet of A4 paper unfolded, a C5 envelope will hold a sheet of A4 paper folded in half once parallel to its shortest sides and a C6 envelope will hold the same piece of paper folded twice.
Conversions Between Paper Sizes
The ISO 216 paper sizes have some useful properties for reducing and enlarging in print or photocopying such that the scale factor needed to convert from A3 to A4, at 71% is the same as the scale factor to convert between A4 and A5, A5 and A6 and so on. The following link covers Full Tables of Magnification Scale Factors for A & B Paper Sizes.
ISO 536 defines paper weights and grammage, which determine the thickness of the paper. The US and North America use an entirely different definition for paper weights based on basis weight and stock types. Tables of conversions between basis weight by stock type and grammage are also provided.
Paper Whiteness, Brightness & Shade
Not all paper is the same shade of white and Whiteness, Brightness and Shade are different measures used to discriminate between various shades of paper.
Portrait & Landscape Paper
Paper can be viewed as Portrait paper or Landscape paper depending on how you look at it. Viewed with the shorter sides at the top and bottom it is said to be Portrait and viewed with the longer sides at the top and bottom it is said to be Landscape.
Historical Paper Sizes
Before the introduction of ISO 216 many paper sizes were in use around the world. British Imperial paper sizes were common in countries which had been part of the British Empire, Japan had traditional paper sizes and a variety of sizes were used across European countries.