Paper Size Calculator

Understanding the Paper Size Calculator

A paper size reference gives the dimensions of common formats in millimetres and inches. The two systems it spans are genuinely different in design philosophy: the ISO A series is built on a mathematical ratio that survives halving, while US sizes are historical conventions that do not.

How it actually works

Select a size code. The tool returns the dimensions in millimetres and the equivalent in inches. A4 returns 210 by 297 millimetres, which is 8.27 by 11.69 inches.

The deeper context most people miss

A4 is narrower and taller than Letter, which is why documents formatted for one print imperfectly on the other, with content either cropping at the bottom or leaving unexpected margin. The difference is only 6 millimetres wide and 18 tall, and it is enough to break layouts routinely in international document exchange.

Why the A series uses the square root of two

Every ISO A size has an aspect ratio of one to the square root of two, approximately 1.414, and this is the only ratio with a specific useful property: halving the sheet across its longer dimension produces two sheets of the identical ratio. Cut A4 in half and you get two A5 sheets with the same proportions; join two A4 sheets and you get A3. No other ratio does this, and it follows from the algebra, since a sheet of ratio r halved gives a ratio of 2 over r, and setting those equal gives r squared equals 2. The practical consequences are substantial. Scaling between sizes is exact and lossless in proportion, so a document designed for A4 enlarges to A3 or reduces to A5 with no cropping and no empty margin, and photocopiers have dedicated buttons for exactly these ratios, at roughly 141% and 71%. The series is anchored by A0 having an area of exactly one square metre, which makes paper weight arithmetic clean: paper is specified in grams per square metre, so a single A0 sheet of 80 gsm paper weighs 80 grams, an A4 sheet is a sixteenth of that at 5 grams, and a 500-sheet ream weighs 2.5 kilograms, which is why postal weight calculations in metric countries are straightforward. The B and C series follow the same ratio at intermediate sizes, with C series sized so that a C4 envelope holds an A4 sheet unfolded, C5 holds A4 folded once, and so on, which is an elegantly coherent system.

A worked example: what goes wrong between A4 and Letter

A document laid out for A4 printed on Letter loses 18 millimetres of height, which is roughly the last two lines of a full page, so a document that ended neatly at the bottom margin acquires an orphaned line on a new page and the pagination shifts through the whole document. Printed the other way, A4 paper receiving Letter-formatted content leaves 18 millimetres of extra space at the bottom and content sits 6 millimetres narrower than the page allows. Neither is catastrophic and both are persistently irritating, and they are why documents shared internationally should be produced with the destination in mind or with margins generous enough to tolerate either. PDF is the practical solution, since it fixes the layout at the page size it was created for and the printer scales or centres it rather than reflowing. Where a document must work on both, setting margins to at least 20 millimetres on all sides and avoiding content that depends on exact page breaks makes it tolerant. Some word processors offer a scaling option at print time that fits the content to the destination page, which resizes everything slightly and is usually acceptable for text. Legal size at 216 by 356 millimetres is a further complication, being a US format with no ISO equivalent, and Tabloid at 279 by 432 corresponds roughly to A3 without matching it.

Deciding which size to use for what

For everyday documents the answer is whichever your region uses, since paper availability and printer defaults follow it. Beyond that, several choices matter. For documents intended to be printed and bound, the finished size and the binding margin need planning, and printing two A5 pages per A4 sheet is a common approach that the A series makes clean. For posters and large-format work, A3, A2, A1, and A0 scale predictably, and A0 at one square metre is the standard for academic conference posters, where dimensions are frequently specified in the call for papers and are worth checking since portrait and landscape requirements vary. For photographic printing, standard print sizes follow neither system and are based on traditional photographic ratios, which is why photographs cropped to A-series proportions lose content. Business cards, envelopes, and stationery have their own conventions differing by country. For anything sent to a commercial printer, asking about their preferred setup including bleed, trim marks, and colour profile before designing saves rework, since a design laid out to the finished size without bleed cannot be trimmed cleanly. And for anything digital that may be printed, choosing a page size at the outset rather than relying on defaults avoids the reflow problems entirely.

Where the US sizes came from

Letter at 8.5 by 11 inches has no elegant mathematical basis and its origin is not definitively documented, with the most commonly repeated explanation relating to the dimensions a papermaker could produce by hand, where a mould of a size a worker could handle produced sheets subsequently quartered. Whatever the origin, the size became conventional through use and was formalised much later, with US federal government use standardising on 8.5 by 11 in the 1980s having previously used 8 by 10.5. Legal size at 8.5 by 14 similarly emerged by convention for legal documents. The lack of a consistent ratio means US sizes do not scale into one another: two Letter sheets side by side do not make a standard larger size with the same proportions, and reducing Letter to half its area produces a shape different from Letter. This is why the photocopier scaling percentages that work cleanly in metric countries do not have equivalents in the US system, and why enlarging a Letter document to Tabloid involves either distortion or margin. ISO 216 was adopted internationally from a German standard of 1922, itself based on a principle described in the eighteenth century, and it is now used essentially everywhere except the United States, Canada, and a few other countries. Mexico, the Philippines, and Chile use variants or mixtures, which occasionally produces surprises in cross-border document work.

Variations: B and C series, envelopes, and paper weight

The B series sits between A sizes, with B4 falling between A3 and A4, and is used for posters, passports, and some books. The C series is designed for envelopes, sized so that C4 takes an unfolded A4 sheet, C5 takes A4 folded once, and DL, a common business envelope, takes A4 folded twice, which is why the system is coherent for correspondence. US envelope sizes follow their own conventions with numbered formats. Paper weight uses grams per square metre in metric countries, which is a density measure independent of sheet size and therefore directly comparable, while the US uses basis weight in pounds per ream of a basis size that differs by paper type, meaning a 20 lb bond and a 50 lb offset can be similar in actual thickness, which makes US paper weights genuinely confusing to compare across types. Caliper measures thickness directly. For printing, bleed extends artwork beyond the trim line so that trimming variation does not leave white edges, typically 3 millimetres, and any design going to a commercial printer needs it. Trim, safe area, and crop marks are the related conventions.

Working with paper sizes

Use PDF for documents shared internationally, since it fixes layout at its intended page size rather than reflowing to the recipient's default. Set generous margins of at least 20 millimetres if a document must print acceptably on both A4 and Letter, since the 18 millimetre height difference shifts pagination otherwise. Take advantage of the A series ratio when scaling, since A4 to A3 is a clean 141% enlargement and A4 to A5 a 71% reduction with no cropping. Use the C series for envelopes with A series contents, where C4 takes unfolded A4, C5 takes it folded once, and DL folded twice. Compare paper weights carefully across systems, since grams per square metre is directly comparable while US basis weight depends on a basis size that differs by paper type. Add bleed of around 3 millimetres for anything going to a commercial printer, since trimming variation otherwise leaves white edges. And check specified dimensions for conference posters and similar, since requirements vary and A0 portrait and landscape are not interchangeable.

What people get wrong

• Assuming A4 and Letter are interchangeable, when the 18 millimetre height difference shifts pagination and can orphan lines through an entire document.
• Expecting US sizes to scale into one another, when they lack a consistent ratio and halving Letter produces a different shape rather than a smaller Letter.
• Comparing US basis weight across paper types, when the basis sheet size differs by type and a 20 lb bond and 50 lb offset can be similar in actual thickness.
• Sending artwork to a commercial printer without bleed, when trimming variation leaves white edges on anything designed only to the finished size.

Where the math comes from

ISO A series sizes have an aspect ratio of 1 to √2, approximately 1.414, which is the unique ratio preserved when a sheet is halved across its longer dimension. A0 has an area of exactly one square metre, and each subsequent size halves the area. Inch equivalents are derived by dividing millimetres by 25.4. US sizes including Letter and Legal follow historical convention with no consistent ratio between them.

Questions and answers

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