Paper Sizes and Formats Explained: The Difference Between A4 and Letter

The Difference Between A4 and Letter

Have you ever really taken a look at the packs of computer paper you buy? Or can you automatically eye the standard paper used for letters and academic purposes? You have more than likely heard of A5 or Tabloid, but for many, the only two page sizes that really matter are A4 or Letter. But there exist a number of paper sizes that are relevant to our everyday lives, and knowing them can save you time and money when printing and copying.

• The Systems in Existence
• ISO 216
• Height-to-width Aspect Ratio Alternatives
• ISO Tips to Save You Time
  • Simplified Enlargement and Reduction
  • A Fit for Any Envelope
• North American Sizes
• Printing A4 Documents on Letter and Vice Versa
• Untrimmed Paper Pages
• Something to Think About

The Systems in Existence

Though other paper size standards exist, there are two predominant systems in use today. They are the international and North American systems.

As the term implies, the international standard, also known as the ISO 216 standard, is used throughout the world. It is based on an aspect ratio of the square root of two, like the side of a square and its diagonal. This idea was originally proposed by the German scientist Georg Christoph Lichtenberg in 1786. In 1922, Dr. Walter Porstmann brought Lichtenberg’s ideas into being in Germany. This new standard was known as the DIN 476 standard. The system became widely used during World War II. The most commonly used ISO paper size is A4.

The North American system is used primarily in the USA and Canada. The current sizes are based on traditional sizes such as Letter (8.5 in × 11 in) and Legal (8.5 in × 14 in). The names of North American sizes have started with ANSI ever since the adoption of ANSI/ASME Y14.1 by the American National Standards Institute in 1995. Though the sizes now begin with ANSI, they are nevertheless based on the traditional sizes.

ISO 216

The most convenient and distinguishing characteristic of ISO paper is that each format has an aspect ratio equal to the square root of two (1:4142) which makes it simple to enlarge or reduce a document for printing on another ISO paper format. The most popular series of the ISO standard is the A series. The most widely used paper of this series is the A4 format. All paper sizes of this series have a name that consists of an A followed by a number. The larger that number, the smaller the paper.

The basis for the whole system is the A0 format which has an area of one square meter. With an aspect ratio equal to the square root of two, a sheet of A0 paper ends up being 841 × 1189 millimeters. Figuring out the dimensions of the subsequent paper sizes does not require any real mathematical strain since each ensuing size can be created by simply folding the paper in half with the crease parallel to the shortest sides. If you do this with an A0 sheet of paper, the resulting dimensions will be 594 × 841 millimeters, or the A1 format. Take note that the height of A1 is equal to the width of A0.

Two other ISO paper series exist—B and C. The B series was brought into being to provide a wider range of paper sizes, where as the C series is used only for envelopes. The B paper sizes are a bit larger than their A series counterparts and are based on the geometric mean of two consecutive A series sheets. For example, B4 is between A3 and A4 in size, and B5 is between A4 and A5.

The C series was introduced to provide an envelope with enough space for an A series sheet. The sizes of the A series fit in C series envelopes of the same number. That is, a sheet of A4 easily fits into a C4 envelope. The C sizes are just between the A and B series. Below are tables with the dimensions of all three series. All of them have a height-to-width ratio equal to the square root of two.

Though these are the main formats of the ISO standard, there are other sizes used for printed items such as labels, business cards, and so on. They are often derived by cutting standard sizes into equal parts. This often leads to sizes with an aspect ratio other than the square root of two.

Height-to-width Aspect Ratio Alternatives

Depending on the project purpose, aspect ratios vary. Standard paper formats can be presented in the formula of the square root of two, according to the ISO paper size concept. Once non-standard solutions are required, the same parallel cutting takes place with the only difference being the number of achieved parts. As a result, 3, 4 or 8 equal pieces are obtained. Here are some samples of long sizes.

There are standard ways to apply this or that sub-standard size format. For instance, one-third of A4 is preferable for invitations and personal DL envelopes, while one-fourth of A4 is a nice option for flyers. Small-sized formats aren’t preferable for large volumes of text—it should typically be no more than a simple and brief message.

ISO Tips to Save You Time

Simplified Enlargement and Reduction

Many copy machines have preset magnification factors for enlarging or reducing a copied document in order to print it on a different paper size. These presets typically take the form of buttons labelled A3→A4 and so forth. This eliminates wasted margins and saves you the trouble of trying to guess the right magnification factor, which can lead to a heap of misspent paper. Below is a table of the magnification factors between the most common A sizes in case the copiers at your local library do not have such presets.

A Fit for Any Envelope

The consistent aspect ratio of the ISO papers makes it easy to fit larger paper sizes into smaller envelopes. This can be done by simply folding the larger papers in half (crease parallel to the shorter sides) until you reach the desired size. The difference in the number of the page sizes equals the number of times you should fold it. So if you have a C4 or B4 envelope and a sheet of A2 paper, you should fold it in half twice. The same method works for filing larger paper sizes in file folders of a smaller size.

This works with the B and C envelope formats. Another commonly used format is the DL format. A DL format envelope will accommodate an A4 sheet folded in thirds or an A5 sheet folded in half lengthwise. Read more about common envelope sizes and styles.

North American Sizes

The North American paper sizes are based on traditional formats with arbitrary aspect ratios. The most popular formats of the traditional sizes are the Letter (8.5 × 11 inches), Legal (8.5 × 14 inches) and Tabloid (11 × 17 inches) formats. You more than likely use these formats in your everyday life. Letter is the standard for business and academic documents. The Legal format is used to make legal pads, and the Tabloid format is commonly used to make tabloids or smaller sized newspapers. Very little is known about the origin of the traditional American paper formats.

There have been a few attempts to standardize the paper industry in America. President Hoover brought about the Government size when he ordered that all governmental documents and forms be printed on paper with the dimensions of 8 × 10 ½ inches. The usage of this format did not find its way to the general public, so President Reagan later made the Letter format the standard again.

In 1995, the American National Standards Institute adopted the ANSI/ASME Y14.1 standard. The different formats of this system are denoted by ANSI followed by a letter. Even though this standard exists, the traditional sizes still remain the most widely used.

This relatively young standard is based on the traditional Letter format (ANSI A). The Letter format is comparable to the ISO A4 format in as much as it is widely used for business and academic needs, but the sizes do differ.

The ANSI paper formats are similar to those of the ISO standard in that cutting a sheet in half will produce two sheets of the next size. The difference lies in both size and the aspect ratio. The ANSI sizes have an aspect ratio that alternates between 1.2941 and 1.5455. This makes enlarging and reducing a page to fit other ANSI formats difficult and less systematic than with the ISO layouts. You will more than likely end up with margins differing from the original page.

The use of American paper sizes often leads to many problems when it comes to the international exchange of documents and therefore has become less common in universities where students are more often held to international standards when attending conferences or submitting articles to international journals. Luckily, documents can be prepared to be printed on both ANSI and ISO paper formats.

Printing A4 Documents on Letter and Vice Versa

A business partner from Germany has just sent you a document in the A4 format that you need to print out. You print the document and notice that there are some parts cut off at the top and bottom of each page. This is due to the difference in size between the A4 and Letter (ANSI A) formats. To print or copy an A4 document on Letter, you should set the magnification factor to 94% since the Letter format is 6% less tall than A4. If you plan on printing a Letter document on A4, you should set the magnification factor to 97% since A4 is 3% less wide.

Untrimmed Paper Pages

Unlike trimmed sizes, which are pieces with the final dimensional ratio, untrimmed formats are slightly bigger than the A and B series. This difference comes in handy for commercial printing, allowing the publishing of large volumes of interconnected pages in the right proportions. At the same time, they are functional tools for rotating printing presses.

There are two types of untrimmed sizes—raw format A (shortly RA) and supplementary raw format A (briefly, SRA). They are adjusted to the final trim after binding. Here is a quick sample: if A4 equals 100%, RA is 5% bigger, and SRA is 15% bigger correspondingly. The “square root of two” rule is also valid, although the dimensions of accepted untrimmed formats are rounded.

Something to Think About

Which paper type you use really depends on your physical location. Some people should keep a supply of both ISO and ANSI paper on hand. Such people include university students and those who do business internationally or often send mail abroad. Many of your local office supply stores carry both types of paper regardless of the country, but sometimes it may require special ordering.

Thanks to Markus Kuhn for his wonderful article on paper sizes.