Centimetre ⇄ Millimetre ⇄ Inch Converter

The millimetre, centimetre, and inch are the three small-length units that show up everywhere from spec sheets to clothing tags to screen sizes. Paper is measured in millimetres (A4 = 210 × 297 mm), phone screens are quoted in inches (a 6.1-inch display measures 154.94 mm diagonally), and product dimensions are often printed in centimetres on the back of the box. Working fluently between all three saves a lot of mental arithmetic, especially when a single measurement is given in just one of the units and you need its equivalent in the others. This page walks through the exact definitions behind the conversions, why the units are mixed this way in practice, and how the calculator on Solved resolves the three values into one consistent answer.

The exact definition: 1 inch equals 25.4 millimetres

The relationship between the inch and the millimetre is defined exactly by international agreement. In 1959 the English-speaking nations, the United States, the United Kingdom, Canada, Australia, New Zealand, and South Africa, signed the International Yard and Pound Agreement at the request of their standards laboratories, harmonising the imperial units they had been using. The agreement redefined the inch as exactly 25.4 millimetres and the pound as exactly 0.45359237 kilograms. Before that, the United States used a slightly different inch based on the 1893 Mendenhall order, which in turn derived from the older English imperial yard; the difference was tiny (about two parts per million) but mattered for surveying and for some high-precision manufacturing.

Because the 1959 agreement makes the relationship exact rather than approximate, every conversion factor in the chain (1 in = 25.4 mm = 2.54 cm; 12 in = 1 ft = 30.48 cm = 304.8 mm) is a rational integer multiplication by definition. There is no rounding error to chase. If you have an inch value and want it in millimetres, you multiply by 25.4 and you have the exact answer; if you have a millimetre value and want it in inches, you divide by 25.4 and you have an exact answer that may have a repeating decimal but is otherwise lossless. This is why a length stored in any of the three units can be converted to the other two with full precision, the only place rounding ever enters is in how many digits of the result you choose to display.

The same 1959 agreement fixed the foot at exactly 0.3048 m and the yard at exactly 0.9144 m, so 1 ft = 12 in = 30.48 cm = 304.8 mm exactly and 1 yd = 3 ft = 91.44 cm exactly. The metre, the centimetre, and the millimetre are defined by the SI (the modern metric system), with 1 m = 100 cm = 1000 mm exactly, defined since 1960 by the distance light travels in 1/299792458 of a second, and since 2019 defined by fixing the numerical value of Planck's constant.

Why paper uses millimetres and screens use inches

If you have ever wondered why an A4 sheet is "210 mm × 297 mm" but your phone is "6.1 inches", the answer is historical and regional. The metric system, formalised in France in 1795 and now used in nearly every country, standardised on the metre as a single base unit and defined the centimetre and millimetre as prefix subdivisions. The international ISO 216 paper standard (A4, A3, A5, etc.) was first formalised in 1922 (DIN 476 in Germany) and is built around an aspect ratio of √2:1, the long side of an A-sheet is √2 times the short side, so folding in half keeps the same proportions. The chosen base size, A0, has an area of one square metre and dimensions 841 mm × 1189 mm. A4, the next size down after two folds, is 210 mm × 297 mm. Every measurement in the ISO system is therefore a clean multiple of a base SI length, and millimetres are the natural unit.

Inch-based measurements for screens come from the cathode-ray-tube (CRT) era, when CRT diagonal measurements were universally quoted in inches. Monitor manufacturers in the United States, Japan, and Taiwan adopted the inch early on, and the convention stuck even when the underlying display technology changed to LCD and OLED. TV and laptop screens are still measured in inches (a 15.6-inch laptop screen is 396.24 mm diagonally, a 55-inch TV is 1397 mm diagonally), and phones followed. A 6.1-inch display has a diagonal of 6.1 × 25.4 = 154.94 mm. The metric sizes sometimes appear on spec sheets, Apple's iPhone pages list dimensions in millimetres, but the headline screen-size number stays in inches.

Centimetres sit in the middle and are most common on consumer-product packaging in metric-system countries: a coffee mug labelled "9 cm tall", a picture frame sold in centimetres, a paperback book measured by its centimetre height. Because 1 cm = 10 mm and 1 cm ≈ 0.3937 in, the centimetre is the everyday "human-scale" metric sub-unit. Switching between the three is unavoidable when you are doing anything cross-cultural, installing a 19-inch rack-mount device into a metric cabinet, ordering a TV that needs to fit a 100 cm shelf, or specifying a printed part that will be inspected in either unit.

A worked example: how a single length resolves

Take the simple case of an iPhone-style 6.1-inch screen diagonal. The inch value is exact (6.1 in). Convert to millimetres: 6.1 × 25.4 = 154.94 mm. Convert to centimetres: 6.1 × 2.54 = 15.494 cm. In metres, the same screen is 0.15494 m; in feet, 6.1 / 12 = 0.50833 ft. Every one of these numbers is exact to as many decimal places as you care to write, with the only rounding being display formatting.

Now try A4 paper. The standard width is 210 mm = 21 cm = 210 / 25.4 = 8.2677165354… inches. The 21 cm is exact (an integer number of centimetres); the inch value has a repeating decimal because 25.4 does not divide 210 evenly. If you measure an A4 sheet with a ruler graduated in inches, you will read approximately 8.27 inches, which is the right answer to two decimals but is an approximation. The "exact" answer of 8.2677165… inches reflects the fact that A-series paper dimensions are defined by powers of 2 applied to an area-of-one-square-metre reference, not by any inch-based reference.

A third worked example: a US 8.5 × 11 letter sheet. The long side is 11 inches = 11 × 25.4 = 279.4 mm = 27.94 cm exactly. 8.5 inches = 215.9 mm = 21.59 cm exactly. Letter paper is defined in inches, so all three of those values are exact (no repeating decimals). This is the kind of inversion that the converter handles automatically: type 8.5 into the inches field and it shows 21.59 in the centimetre field with the same precision; type 21.59 into the centimetre field and the inches field reads 8.5 exactly.

Live cross-update: how the three fields stay in sync

A bidirectional converter has to be careful about feedback loops. If typing into the millimetre field recomputes the centimetre and inch fields, and the centimetre field then re-fires an update of the millimetre field, the chain of updates can oscillate or simply feel broken (the cursor jumps as the field keeps overwriting itself mid-typing). The Solved calculator uses a simple "last-edited" pattern: a small piece of state records which field the user is currently typing into, and only that field shows the raw user input. The other two fields show the value computed from the canonical millimetre basis. When the user clicks into a different field and starts typing, the just-edited field becomes a new canonical source, and the two non-edited fields update to match.

This avoids both the obvious problem (round-trip values drifting because of rounding during typing) and the subtle problem (a mid-typing decimal point being clobbered by the recompute loop). The canonical basis is the millimetre because the relationship from millimetres to the other two units involves only division by small exact integers (10 and 25.4), no rounding error is introduced, and the converter's display rounding is a single consistent choice applied uniformly to all read-outs.

Common pitfalls and small mistakes

The most common mistake is rounding 25.4 to 25. Inches-to-millimetre calculations done by multiplying by 25 instead of 25.4 produce answers that are off by 1.6%, invisible for casual work, but enough to make a 19-inch rack-mount device not actually fit a 19-inch-by-12-inch cut-out once you account for the real dimensions. Memory shortcuts like "1 in ≈ 25 mm" are useful for quick estimates but should never be used in code, in drawings, or when ordering physical parts.

The US survey inch is different from the international inch. Since 2023 the US has been phasing out its "survey" units, the US survey foot was defined as 1200/3937 metres (about 0.3048006096 m), giving a US survey inch of 1/0.3937 m ≈ 25.4000508 mm. The US survey foot was used for the State Plane Coordinate System and for some legacy land-survey work. As of January 1, 2023, the National Geodetic Survey officially deprecated the US survey foot in favour of the international foot, so this difference is largely historical now, but old survey records may still use it. If you are working from a 19th- or early-20th-century land description, double-check which inch is being used.

Truncating to the nearest whole millimetre in display can mislead. A 6.1-inch screen might be quoted as "155 mm diagonal" in marketing copy, but the exact value is 154.94 mm. If you are matching the screen to a phone case, the difference matters. The calculator reports more digits by default; rounding for display (whether to the nearest mm, 0.1 mm, or the full IEEE 754 double-precision value) is a choice you make deliberately, and the converter on Solved lets you see all the digits when needed.

Mixing paper standards. ISO A-series paper is defined by the √2 area-preserving fold and the one-square-metre A0 base, so A4 is exactly 210 × 297 mm. US Letter is exactly 8.5 × 11 inches, and is not the same as A4, at 215.9 × 279.4 mm, it is slightly wider and slightly shorter than A4. They are not interconvertible. The converter turns an 8.5-inch dimension into 215.9 mm, which is the correct number for Letter, but Letter ≠ A4 even though their areas are close.

Foot-inch confusion. A 6-foot-tall person is 72 inches = 1828.8 mm = 182.88 cm, not 182 cm. The exact centimetre equivalent of 6 ft is 182.88, often rounded to "about 183 cm" in casual conversation. The foot is defined as exactly 12 international inches (since 1959), so the conversion is lossless: 6 × 12 × 25.4 / 10 = 182.88 cm exactly.

Why the precision matters in 2026

Modern manufacturing tolerates a few thousandths of a millimetre (a few micrometres) in metal and plastic parts, and the international inch is defined to enough precision that any inch-to-millimetre conversion is good to under a nanometre. When CAD software or 3D-printing software converts units for you, it does so by multiplying or dividing by 25.4 in IEEE 754 double precision, which gives you about 15 decimal digits of exact arithmetic. The output you see in a typical CAM software window is usually rounded to 0.001 mm or 0.0001 inch, but the internal stored value is the full-precision number.

For everyday conversions, measuring furniture, fitting a screen to a desk, ordering a frame, two or three decimal places are plenty. A centimetre is about 0.3937008 inches; if you remember "1 cm ≈ 0.4 inch" you can work intuitively in either unit. A millimetre is 0.03937008 inches, so 10 mm is about 0.4 inches. These ballpark factors are useful for quick mental arithmetic, and the converter on Solved is the right tool when you need the exact value.

Related references and standards

The exact 1959 international yard and pound agreement is published by each country's standards body: NIST in the United States (as part of NIST Handbook 44 and SP 811), the National Physical Laboratory in the UK, the National Research Council of Canada, and so on. The current redefinition of SI units (since 2019) is published by the Bureau International des Poids et Mesures (BIPM) in the SI Brochure, currently in its 9th edition (2019, with subsequent updates). The relevant BIPM reference for length conversions is §2.3.3 of the brochure, "Decimal multiples and submultiples of the SI units", which defines the SI prefixes including centi- (10⁻²) and milli- (10⁻³).

ISO 216 is the international standard for paper sizes (A series, B series, C series) and is maintained by the International Organization for Standardization. It codifies the √2:1 aspect ratio and the one-square-metre A0 base that gives the A-series dimensions. ANSI/ASME Y14.5 is the US standard for engineering drawings and dimensioning. NIST SP 811 (the NIST Guide for the Use of the International System of Units, sometimes called the "NIST Metric Guide") is the authoritative US reference for SI usage and conversion factors in technical work, including the 25.4 mm = 1 in definition.

For surveying, the National Geodetic Survey's 2023 announcement on the deprecation of the US survey foot is the relevant modern reference. Before that, the Federal Register notice from 1959 published the US adoption of the international yard and pound, and the Mendenhall order of 1893 (which originally set the US inch as 25.400051 mm) remained in force as the "US survey" basis until 2023.

Direct sources:

• NIST Special Publication 811, Guide for the Use of the International System of Units (SI), https://www.nist.gov/pml/od/unit-conversion
• BIPM, The International System of Units (SI Brochure), 9th edition, https://www.bipm.org/en/publications/si-brochure
• ISO 216:2007, Writing paper and certain classes of printed matter, trimmed sizes, A and B series, https://www.iso.org/standard/36631.html
• NIST Handbook 44, Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices, https://www.nist.gov/pml/owm/handbook-44
• National Geodetic Survey, Deprecation of the US survey foot, 2023, https://www.ngs.noaa.gov/OPUS/
• International Yard and Pound Agreement, 1959, published via the US Federal Register and NIST SP 811 Appendix B

Worked examples for common sizes

For quick reference, here are the exact and rounded conversions for several everyday objects:

Each of these is exactly the value reported by the converter on Solved, the converter is using the canonical 25.4 mm-per-inch relationship throughout.

When to use this converter

Use this converter whenever you have a number in one unit and need it in another, especially when the value is not a clean round number (so mental arithmetic fails). Typical use cases include:

• Specifying a screen size in a metric-system country (millimetres) when the catalogue lists it in inches.
• Comparing paper sizes between ISO A-series and US Letter or Legal.
• Ordering a frame, a shelf, or a piece of furniture sized in one unit but needed in another.
• Reading engineering drawings that mix metric and imperial callouts on the same diagram.
• Verifying dimensions on product detail pages or user manuals where the units might not match the conventions you expect.
• Working out tyre, screen, or ring sizes that span two measurement systems.

For lengths above about 100 cm, i.e. when you start needing metres and feet, consider a longer-range length converter that includes yards, miles, and kilometres. For lengths below about 1 mm, wire gauges, paper thickness, machine tolerances, micrometres and "mils" (thousandths of an inch) are the right units, and the standard conversions there are 1 µm = 0.001 mm = 0.00003937 in and 1 mil = 0.0254 mm = 25.4 µm.

Frequently Asked Questions

What is the exact conversion from inches to millimetres?

1 inch = 25.4 millimetres exactly, by international agreement signed in 1959. The factor is defined, not measured, so there is no rounding error in the conversion. Multiplying any inch value by 25.4 gives the exact millimetre equivalent.

What is the exact conversion from millimetres to centimetres?

1 centimetre = 10 millimetres exactly, by SI definition. To convert millimetres to centimetres, divide by 10. The inverse (centimetres to millimetres) is a multiplication by 10, also exact.

Why are paper sizes quoted in millimetres but screen sizes in inches?

Paper sizes follow the international ISO 216 standard (A4, A3, etc.), which is built around the SI metre, so paper dimensions are naturally whole-millimetre numbers. Screen sizes follow a tradition from the cathode-ray-tube era in the United States and East Asia, where displays were historically quoted in inches. The convention has stuck despite the underlying technology changing multiple times.

Is 1 cm the same as 10 mm?

Yes, the centi- prefix means one hundredth, so 1 cm = 1/100 m and 1 mm = 1/1000 m. Since 1/100 m = 10 × 1/1000 m, 1 cm = 10 mm exactly.

Is the US inch the same as the British inch?

Since 1959 the US, UK, Canada, Australia, New Zealand, and South Africa all use the same international inch = 25.4 mm exactly. Before 1959 the US used a slightly different "survey" inch (about 25.4000508 mm) for some surveying work; that unit was officially deprecated by the National Geodetic Survey on 1 January 2023 in favour of the international inch.

What is 5 feet 9 inches in centimetres?

5 ft 9 in = 69 in = 69 × 2.54 cm = 175.26 cm exactly. (Or 5 × 30.48 + 9 × 2.54 = 152.4 + 22.86 = 175.26 cm.) Two common rough approximations: 5'9" is about 175 cm, or "just under 1.75 m".

How many millimetres in a quarter inch?

1/4 in = 25.4 / 4 = 6.35 mm exactly. Similarly, 1/8 in = 3.175 mm, 1/16 in = 1.5875 mm, and 1/32 in = 0.79375 mm. These are common drill-bit and sheet-metal sizes.

What is 1 inch in metres?

1 in = 25.4 mm = 0.0254 m exactly. So 1 m = 39.37007874… in exactly (with the inch representation having a repeating decimal).

Why does A4 paper measure 8.27 inches and not 8.5?

A4 follows the ISO 216 √2:1 area-preserving fold and starts from an A0 base of one square metre. A4 is exactly 210 × 297 mm, which equals 8.2677165… × 11.6929134… inches, not a clean inch value. US Letter is exactly 8.5 × 11 inches (215.9 × 279.4 mm), which is a clean inch value but not a clean millimetre value. They are similar but not identical, and neither converts to the other exactly.

Is 1 foot still 12 inches?

Yes, 1 foot = 12 inches exactly, both since the 1959 international yard and pound agreement. The 12-inch foot is a very old convention (the Romans used a 12-unit foot in some regions), and it has been standardised as exactly 12 modern international inches = 304.8 mm = 30.48 cm.

What's the fastest way to convert inches to millimetres in my head?

Multiply by 25, close enough for most casual use (you're off by 1.6%, or about 0.4 mm per inch). For a more accurate mental approximation, multiply by 25.4, or remember that 4 in = 101.6 mm, so 1 inch is "about 25 mm and a bit". For anything that has to be precise, engineering, manufacturing, order specifications, use the calculator or multiply by 25.4 exactly.

What's the difference between a metric inch and an imperial inch?

There is no such thing as a separate "metric inch" used in modern measurements. The international inch (25.4 mm) is used by every country that uses inches today. Some historical metrication proposals in the 19th and early 20th centuries suggested using 25 mm as a "metric inch" for easier arithmetic, but none was ever widely adopted, and the international inch remains the only inch used in current standards.