Paper Size Converter
Convert between A-series (A4, A3), US Letter, Legal, and other paper sizes in mm and inches. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Paper Size Converter
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Formula: ISO A-series: Width = 1000 / 2^((2n+1)/4) mm, Height = 1000 / 2^((2n-1)/4) mm
Worked example โ A4 = 8.27 x 11.69 inches | Taller and narrower than US Letter (8.5 x 11.0)
Formula
ISO A-series: Width = 1000 / 2^((2n+1)/4) mm, Height = 1000 / 2^((2n-1)/4) mm
ISO A-series paper sizes follow a mathematical progression where each size has an area equal to half the next larger size. All sizes maintain a width-to-height ratio of 1 to the square root of 2 (approximately 1:1.4142). A0 has an area of exactly 1 square meter.
Worked Examples
Example 1: Converting A4 for US Printer Setup
Problem:A European document is designed for A4 paper. What dimensions should be set on a US printer in inches?
Solution:A4 = 210 mm x 297 mm Width: 210 / 25.4 = 8.268 inches Height: 297 / 25.4 = 11.693 inches US Letter = 8.5 x 11 inches A4 is narrower (8.27 vs 8.5) but taller (11.69 vs 11.0)
Result:A4 = 8.27 x 11.69 inches | Taller and narrower than US Letter (8.5 x 11.0)
Example 2: Setting Up A3 Poster for Print at 300 DPI
Problem:Create a digital design for an A3 poster at 300 DPI. What pixel dimensions are needed?
Solution:A3 = 297 mm x 420 mm = 11.693 in x 16.535 in At 300 DPI: Width: 11.693 x 300 = 3,508 pixels Height: 16.535 x 300 = 4,961 pixels File size (RGB): 3508 x 4961 x 3 = ~52 MB uncompressed
Result:A3 at 300 DPI = 3,508 x 4,961 pixels (approximately 52 MB uncompressed RGB)
Frequently Asked Questions
What is the difference between A4 and US Letter paper size?
A4 paper measures 210 by 297 millimeters (8.27 by 11.69 inches), while US Letter measures 215.9 by 279.4 millimeters (8.5 by 11 inches). Letter is slightly wider but shorter than A4. This difference of about 6 mm in width and 18 mm in height creates real problems when printing documents designed for one size on the other. A4 documents printed on Letter paper may have the bottom cut off, while Letter documents on A4 may have excessive top and bottom margins. The A4 standard is used in virtually every country except the United States, Canada, and parts of Mexico. This size difference is one of the most common sources of formatting problems in international document exchange.
How does the ISO A-series paper size system work?
The ISO 216 A-series is based on a mathematically elegant system where each size is exactly half the area of the next larger size. A0 paper has an area of exactly one square meter (841 by 1189 mm). Folding A0 in half gives A1, folding A1 gives A2, and so on down to A10. The key mathematical principle is that the aspect ratio of all A-series sizes is 1 to the square root of 2 (approximately 1:1.4142). This constant ratio means that when you scale a document from one A-size to another, nothing is cropped and proportions are maintained. This system was first proposed by German scientist Georg Lichtenberg in 1786 and was adopted as the international ISO standard in 1975. It is now the dominant paper sizing system worldwide.
What is the B-series paper size and when is it used?
The ISO B-series paper sizes are intermediate sizes between the A-series, designed for applications where A-series sizes are not quite right. B-series sizes are geometric means between consecutive A-series sizes, meaning B1 is between A0 and A1 in area. B-series paper is commonly used for passports (B7), books (B5 and B6), posters (B1 and B2), and envelopes (where a B-size envelope perfectly fits an A-size document). B0 measures 1000 by 1414 mm, making each B-size larger than the same-numbered A-size. Like the A-series, each B-size has the 1-to-square-root-of-2 aspect ratio, maintaining the same scaling advantages. The B-series is particularly popular in Japan where B4 and B5 are standard sizes for magazines, manga, and official documents.
Why does the United States use different paper sizes from the rest of the world?
The United States uses Letter (8.5 by 11 inches) and Legal (8.5 by 14 inches) paper sizes based on historical traditions dating back to the early American paper-making industry. These sizes were standardized in the 1980s by ANSI (American National Standards Institute) but had been in common use for over a century before that. The original dimensions likely came from the size of paper molds used in 18th-century American mills. Despite the mathematical advantages of the ISO system, the US has not adopted it due to the enormous cost of converting millions of printers, filing cabinets, binders, and other office infrastructure. Canada officially adopted ISO sizes for government use in 1976 but Letter remains dominant in everyday use due to American influence on commerce and technology.
How do you convert paper sizes to pixels for digital design?
Converting paper sizes to pixels requires knowing the desired resolution in dots per inch (DPI or PPI). Multiply each dimension in inches by the DPI value. For screen display (72 DPI), A4 becomes 595 by 842 pixels. For standard printing (150 DPI), A4 becomes 1240 by 1754 pixels. For high-quality printing (300 DPI), A4 becomes 2480 by 3508 pixels. For professional press work (600 DPI), A4 becomes 4960 by 7016 pixels. In graphic design software like Adobe InDesign and Illustrator, you typically work at 300 DPI for print projects and 72 to 150 DPI for digital distribution. Always set up your document at the final print size and resolution from the beginning rather than scaling later, which can cause quality loss.
What paper sizes are used for architectural and engineering drawings?
Architectural and engineering drawings use specific paper sizes that differ from standard office sizes. In the US, ARCH sizes are used: ARCH A (9 by 12 inches), ARCH B (12 by 18 inches), ARCH C (18 by 24 inches), ARCH D (24 by 36 inches), and ARCH E (36 by 48 inches). The ANSI engineering sizes are ANSI A through ANSI E, with ANSI A matching Letter size and each subsequent size doubling one dimension. Internationally, the ISO A-series is used for technical drawings, with A1 (594 by 841 mm) being the most common for architectural plans and A3 for detailed drawings. Large-format plotters can print on rolls up to 42 or 60 inches wide, and drawings are typically produced at standardized scales like 1:50, 1:100, or 1:200.
How do envelope sizes relate to paper sizes?
Envelope sizes are designed to accommodate specific paper sizes, with standardized dimensions that allow paper to fit with appropriate clearance. For ISO A-series paper, C-series envelopes provide exact fit: a C4 envelope (229 by 324 mm) holds unfolded A4, C5 (162 by 229 mm) holds A4 folded once, and C6 (114 by 162 mm) holds A4 folded twice. DL envelopes (110 by 220 mm) are the most common business envelope, holding A4 folded into thirds. In the US, the No. 10 envelope (4.125 by 9.5 inches) holds Letter paper folded into thirds, and the 9 by 12 envelope holds unfolded Letter paper. When mailing documents internationally, choosing the correct envelope size prevents damage from folding or excessive movement inside an oversized envelope.
What are the most common paper sizes for printing photographs?
Photo printing uses specific sizes that differ from standard document paper. Common US photo sizes include 4 by 6 inches (the standard snapshot), 5 by 7 inches, 8 by 10 inches (portrait size), 11 by 14 inches, 16 by 20 inches, and 20 by 24 inches. These sizes have different aspect ratios, so cropping is necessary when printing from a single digital image to different sizes. A 4-by-6 has a 2:3 ratio (matching most DSLR cameras), while 8-by-10 has a 4:5 ratio. International photo sizes include 10 by 15 cm (similar to 4 by 6), 13 by 18 cm (similar to 5 by 7), and 20 by 25 cm (similar to 8 by 10). Professional photo labs often accept both metric and imperial size specifications.
How does paper weight or thickness relate to paper size?
Paper weight and thickness are independent of paper size but the units used can cause confusion. In the metric system, paper weight is expressed as grams per square meter (gsm or g/m2), which is consistent regardless of sheet size. Standard copy paper is 80 gsm, cardstock is 200 to 300 gsm, and poster board can be 400+ gsm. In the US, paper weight is expressed as the weight of 500 sheets (a ream) in a basis size, which varies by paper type. The basis size for bond/writing paper is 17 by 22 inches, while for cover stock it is 20 by 26 inches. This means 20 lb bond paper and 20 lb cover stock have different actual thicknesses. A 20 lb bond paper is approximately equivalent to 75 gsm, while 80 lb cover stock is approximately 216 gsm.
What are the standard paper sizes for books and publications?
Book sizes vary by genre and region, though several standard sizes dominate publishing. In the US, mass-market paperbacks are typically 4.25 by 6.875 inches. Trade paperbacks range from 5.5 by 8.5 inches to 6 by 9 inches. Hardcovers commonly use 6 by 9 inches or 6.125 by 9.25 inches. Children's picture books are often 8.5 by 11 inches or 10 by 10 inches square. In Europe and internationally, book sizes often correspond to ISO standards: A5 (148 by 210 mm) for paperbacks, B5 (176 by 250 mm) for academic texts, and A4 (210 by 297 mm) for textbooks. Art books and coffee table books use larger custom formats. Print-on-demand services like Amazon KDP support specific trim sizes that must be selected before formatting the interior layout.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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