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.
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Adjust values & calculateAll Paper Sizes Reference
Formula
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.
Last reviewed: December 2025
Worked Examples
Example 1: Converting A4 for US Printer Setup
Example 2: Setting Up A3 Poster for Print at 300 DPI
Background & Theory
The Paper Size Converter applies the following established principles and formulas. Unit conversion is the process of expressing a quantity in a different unit of measurement while preserving its physical meaning. At the foundation of modern measurement lies the International System of Units (SI), which defines seven base units: the meter for length, kilogram for mass, second for time, ampere for electric current, kelvin for thermodynamic temperature, mole for amount of substance, and candela for luminous intensity. All other units, called derived units, are defined as algebraic combinations of these seven. Dimensional analysis is the principal method for performing unit conversions. By treating units as algebraic quantities that can be multiplied, divided, and cancelled, a conversion factor chain allows a value expressed in one unit to be rewritten in another without altering its physical magnitude. For example, to convert 60 miles per hour to meters per second, one multiplies by a chain of conversion factors each equal to one: (1609.34 m / 1 mile) × (1 hour / 3600 s). Metric prefixes enable compact expression of quantities across extreme ranges of magnitude. Standard prefixes span from nano (10^-9) through micro (10^-6) and milli (10^-3) up through kilo (10^3), mega (10^6), and giga (10^9), and beyond in both directions. These prefixes are strictly multiplicative and apply consistently to any SI base or derived unit. Temperature conversions require affine transformations rather than simple scaling. To convert Celsius to Fahrenheit the formula is °F = (°C × 9/5) + 32, while the conversion to the absolute Kelvin scale is K = °C + 273.15. These formulas reflect the different zero points and degree-size conventions of each scale. Significant figures govern how precision is preserved through calculations. A result should not express more precision than the least precise input value permits. In digital storage, IEEE and IEC standards distinguish between decimal prefixes (kilobyte = 1000 bytes) and binary prefixes (kibibyte = 1024 bytes), a distinction that has practical consequences for how storage capacity is reported by manufacturers versus operating systems. Unit coherence — ensuring that all quantities in an equation share a consistent unit system — is essential for obtaining correct results.
History
The history behind the Paper Size Converter traces back through the following developments. Human beings have been measuring and comparing quantities since before recorded history. The earliest known measurement units were body-based: the cubit (the distance from elbow to fingertip), the foot, the hand, and the digit. The furlong originated as the length of a furrow a team of oxen could plow without resting. These anthropomorphic standards were practical for local use but differed between regions and kingdoms, creating persistent difficulties in trade and construction. The ancient Egyptians standardized the royal cubit at approximately 52.4 centimeters and distributed calibrated granite rods to ensure consistency across building projects, including the pyramids. Roman engineers used the mile (mille passuum, one thousand double paces) and spread these standards throughout their empire via road networks. Despite these efforts, measurement diversity persisted across medieval Europe, hampering commerce. The French Revolution created political will for radical standardization. In 1795 France officially adopted the metric system, defining the meter as one ten-millionth of the distance from the equator to the North Pole along the Paris meridian. This gave the world its first fully decimal, rationally constructed measurement system. The Metre Convention of 1875 established the International Bureau of Weights and Measures (BIPM) in Sevres, France, creating a permanent international body to maintain physical artifact standards and coordinate global metrology. For over a century, the kilogram was defined by a platinum-iridium cylinder locked in a vault near Paris. In 1999, a stark demonstration of what unit inconsistency costs occurred when NASA's Mars Climate Orbiter was lost because one engineering team used pound-force seconds while another used newton seconds. The spacecraft entered the Martian atmosphere at the wrong angle and was destroyed, at a cost of 327 million dollars. In 2019 the SI underwent its most significant revision, redefining all seven base units in terms of fixed numerical values of fundamental physical constants such as the speed of light, Planck's constant, and the elementary charge. This eliminated any reliance on physical artifacts and made the measurement system permanently stable and universally reproducible.
Frequently Asked Questions
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\nWidth: 210 / 25.4 = 8.268 inches\nHeight: 297 / 25.4 = 11.693 inches\nUS Letter = 8.5 x 11 inches\nA4 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\nAt 300 DPI:\nWidth: 11.693 x 300 = 3,508 pixels\nHeight: 16.535 x 300 = 4,961 pixels\nFile 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.
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.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy