Article — Paper Size Converter
A paper size converter translates a sheet between two coordinate systems — ISO 216 (A4, A3, B5, C4) used almost everywhere in the world, and ANSI/U.S. (Letter, Legal, Tabloid) used mainly in North America and the Philippines — while expressing dimensions in millimeters, centimeters, inches, and typographic points. The headline number to memorize: A4 is 210 × 297 mm, or 8.27 × 11.69 inches; Letter is 8.5 × 11 inches, or 215.9 × 279.4 mm. They are similar in feel but not interchangeable. This guide explains the math behind each system, the √2 ratio that makes ISO sizes nest cleanly, and the print and PDF pitfalls that catch designers and printers when a document hops between standards.
ISO 216 vs ANSI: two paper-size families
ISO 216 is the international paper-size standard adopted in 1975. It defines three series. A-series sizes (A0 through A10) are the everyday office and print sheets used in offices, schools, and publishers across Europe, Asia, Africa, Australia, and South America. B-series sizes sit between consecutive A sizes — useful when the A-series step from 297 mm to 420 mm leaves too big a gap. C-series sizes are envelopes sized to hold A-series sheets unfolded, folded once, or folded twice.
ANSI/ASME Y14.1, the U.S. counterpart, runs Letter (8.5 × 11 in), Legal (8.5 × 14 in), Tabloid or ANSI B (11 × 17 in), Ledger (the same sheet rotated to landscape), and the larger ANSI C, D, and E sizes used in engineering drawings. The Letter format traces back to 19th-century U.S. paper mills, was standardized as 8.5 × 11 inches by the Hoover Commission in 1921, and never adopted the √2 math of the ISO system.
Why ISO A sizes use the √2 ratio
The defining property of the A series is that every sheet has the same aspect ratio: 1: √2 ≈ 1: 1.4142. The motivation, first proposed by the German physicist Georg Christoph Lichtenberg in a 1786 letter, is that folding such a sheet in half along the long edge produces a smaller rectangle with the same ratio. The German DIN 476 standard codified this in 1922; ISO adopted it as 216 fifty-three years later.
A0 is sized so its area equals exactly one square meter, with the √2 ratio fixing the rest: 841 × 1189 mm. From there each step halves the area — A1 is 0.5 m², A2 is 0.25 m², A4 is 1⁄16 m² (625 cm²), and A10 falls to 0.97 cm². The practical payoff is that two A4 sheets fit on one A3 with no waste, four fit on A2, and so on all the way up to A0. Print shops can stock a single roll size and cut all standard sheets from it.
The A0 sheet is sized so its area is exactly 1 m² — not 1.0000 m² rounded, but mathematically exact. The dimensions 841 × 1189 mm are integer millimeters chosen because their product (999,949 mm²) is the closest you can get to 1 m² while keeping the √2 ratio and whole-millimeter sides.
A4 vs Letter: where they overlap and where they collide
A4 and U.S. Letter are roughly the same physical size, which makes the differences sneak up on documents that move between systems. The exact numbers: A4 measures 210 × 297 mm (8.27 × 11.69 in); Letter measures 215.9 × 279.4 mm (8.5 × 11 in). Letter is wider by 5.9 mm and shorter by 17.6 mm.
A document laid out for Letter and printed unmodified onto A4 loses 17.6 mm of margin at the foot and gains 5.9 mm of empty strip down the right side. PDF readers and printers typically scale the page to fit instead of cropping, which solves the safety issue but compresses fonts and figures by about 6%. The reverse — A4 onto Letter — clips text in the top or bottom margin if scaling is disabled.
- A4 — 210 × 297 mm, 8.27 × 11.69 in, area 623.7 cm²
- Letter — 215.9 × 279.4 mm, 8.5 × 11 in, area 603.2 cm²
- Difference — Letter is 5.9 mm wider but 17.6 mm shorter
- Area gap — A4 is 3.4% larger by surface area
- Aspect ratio — A4 is 1.414, Letter is 1.294 (slightly squarer)
- Practical rule — A4 fits Letter trays in most printers, but margins shift
The 17.6 mm height difference means an A4 document printed onto Letter at 100% scale will lose text at one end of the page — usually the bottom on most drivers. Either set the PDF reader to "fit to printable area" or, for legal and contractual documents, print on actual A4 stock to preserve original layout dimensions.
B-series, C-series, and matching envelope pairs
The B and C series are the lesser-known half of ISO 216. B-series sizes (B0 = 1000 × 1414 mm, B1 = 707 × 1000 mm, and so on) sit at the geometric mean between consecutive A sizes — useful for posters, magazines, paperback books, and passports (B7 is the ICAO passport size). The Japanese JIS B series is slightly different (JIS B5 is 182 × 257 mm, while ISO B5 is 176 × 250 mm); check which standard your supplier uses before bulk ordering.
C-series sheets exist almost entirely as envelopes. C4 (229 × 324 mm) holds an A4 sheet flat. C5 (162 × 229 mm) holds A4 folded once. C6 (114 × 162 mm) holds A4 folded in quarters or A5 flat. A common postal mistake is buying C5 envelopes for unfolded A4 letters — the sheet has to be folded to fit. For an unfolded A4, ask for C4.
The recurring mailroom mistake: someone buys C5 envelopes assuming they hold A4 paper because "A5 is half of A4." A5 fits flat in C5, but A4 must be folded once. For unfolded A4 you need C4 (229 × 324 mm). For an A4 folded in thirds (the usual business-letter fold), buy DL envelopes at 110 × 220 mm.
Typographic points: the DTP unit explained
The point (pt) is the typographer's native unit. Modern desktop publishing uses the PostScript point defined by Adobe in the 1980s: 1 pt = 1⁄72 inch = 0.35278 mm exactly. An A4 sheet measures 595.28 × 841.89 points; Letter measures 612 × 792 points. PDF coordinates, CSS print styles, and most layout tools report dimensions in this point.
Historical typography used several different points. The Didot point (mainly Continental Europe, 0.376 mm) and the older American "printer's point" (0.351 mm) both predate the PostScript point and are still encountered in trade publications and metal-type catalogs. Unless you are specifically dealing with vintage typesetting, the 0.3528 mm PostScript point is the one to use.
The font size you set in pixels in a web browser is not the same as a typographic point. CSS pixels are defined as 1⁄96 inch, so 12 pt = 16 px. PDF readers, Word, and InDesign use points natively; web browsers default to pixels and translate when printing.
Common paper-size mistakes
It is true that A5 has exactly half the area of A4, and that folding A4 along its long edge yields an A5 outline. But the dimensions are 148 × 210 mm, not 105 × 297 mm — the long edge of A4 becomes the short edge of A5. People sketching layouts on a napkin sometimes flip the wrong dimension.
The Japanese Industrial Standards (JIS) B series uses different math: JIS B sheets are sized so the area is 1.5× the corresponding A sheet, not the geometric mean. JIS B5 is 182 × 257 mm; ISO B5 is 176 × 250 mm. The 6–7 mm difference matters for cut-to-fit operations and binder hole positions.
ISO 216 specifies whole-millimeter dimensions: A4 is exactly 210 × 297 mm, not 21 × 30 cm. A 3 mm error per side becomes a 6 mm error across the sheet, which is more than the trim tolerance on most commercial guillotines and is enough to misregister a duplex print or a saddle-stitch fold.
Sources
- ISO 216:2007 — Writing paper and certain classes of printed matter (official standard)
- NIST Handbook 44 — Specifications, Tolerances, and Other Technical Requirements (US measurement standards)
- BIPM — International System of Units (the metric basis for ISO dimensions)
- U.S. Library of Congress — Care, Handling, and Storage of Paper