The exact inch
One inch equals exactly 25.4 millimeters, or exactly 0.0254 meters. This is not a rounded approximation of some other underlying relationship -- it is the actual definition of the modern inch, fixed by international agreement so that converting between inches and millimeters (multiply by 25.4) introduces no error at any level of precision.
The 1959 international yard and pound agreement
Before 1959, the yard and the pound were each defined slightly differently by the national standards laboratories of different English-speaking countries, having drifted apart in small ways since earlier physical prototype standards were made and distributed. In 1959, the national standards bodies of the United States, United Kingdom, Canada, Australia, New Zealand and South Africa agreed to eliminate that drift by adopting a single, common definition: the international yard was fixed at exactly 0.9144 meters, and the international pound was fixed at exactly 0.45359237 kilograms.
Every other US customary and imperial unit of length in common use today follows as an exact fraction or multiple of that single 0.9144 m yard: the foot is 1/3 of a yard (0.3048 m exactly), the inch is 1/36 of a yard (0.0254 m exactly), and the statute mile is 1,760 yards (1,609.344 m exactly). Because all of these units trace back to the same 1959-fixed yard, they are all exact relative to the meter, not independently rounded figures.
What 'exact by definition' actually means
Before 1959, the exact length of a yard or a pound in a given country was, in a strict sense, an empirical question: it depended on measuring a specific physical prototype bar or weight held by that country's standards laboratory, a process that carries some (very small) measurement uncertainty, and different countries' prototypes had drifted to give very slightly different answers. After 1959, the question changed entirely: the yard is 0.9144 meters because the responsible national standards bodies agreed to define it that way, not because anyone measured a prototype and got that number.
This distinction matters because a defined value has zero uncertainty by construction -- 25.4 mm per inch is exact to as many decimal places as anyone cares to write, forever, unless the definition itself is changed by a similar international agreement. A measured value, by contrast, always carries some margin of uncertainty reflecting the precision of the measurement process used to obtain it.
The survey foot note
A separate, very slightly different 'US survey foot' persisted in some historical US land-survey and geodetic work even after the 1959 agreement fixed the standard international foot at exactly 0.3048 m. The US survey foot, defined as exactly 1,200/3,937 meters (about 0.3048006 m), differs from the international foot by roughly 2 parts per million -- a difference too small to matter for most everyday purposes, but non-zero and potentially significant when compounded over the very long distances used in geodetic surveying and mapping.
The National Institute of Standards and Technology (NIST) and the National Geodetic Survey formally retired the US survey foot, effective December 31, 2022, in favor of using the international foot throughout, which removed this small legacy discrepancy from US survey and mapping work going forward. This site's length converter uses the standard international foot definition throughout, consistent with that retirement.
How modern SI units are defined
The 1959 yard-and-pound agreement was an early example of a broader pattern in modern measurement science: fixing units by an exact defined numerical relationship rather than by a physical prototype that must be periodically re-measured and can drift over time. The meter itself has followed this path further than the yard -- since 1983, the meter has been defined by fixing the speed of light in vacuum at exactly 299,792,458 meters per second, meaning the meter is now derived from a fundamental physical constant rather than from any physical bar.
The 2019 revision of the International System of Units (SI) extended this same defining-constant approach to the kilogram, ampere, kelvin and mole, fixing each of them via an exact numerical value of a fundamental physical constant (such as the Planck constant for the kilogram) rather than a physical prototype object. Because the inch is defined as an exact fraction of the meter, and the meter is now defined via the speed of light, the modern inch is ultimately anchored to a fundamental physical constant rather than to any object that could be lost, damaged or subject to measurement uncertainty.
Worked example: converting a length
Because 1 inch = 25.4 mm exactly, converting any length in inches to millimeters is a single exact multiplication: 12 inches converts to 12 x 25.4 = 304.8 mm, which also confirms that 1 foot (12 inches) equals exactly 0.3048 meters, consistent with the foot's definition as 1/3 of the 1959-fixed 0.9144 m yard.
| Unit | Exact meters-equivalent | Basis |
|---|---|---|
| 1 yard | 0.9144 m | 1959 international yard and pound agreement |
| 1 foot | 0.3048 m | 1/3 yard, exact |
| 1 inch | 0.0254 m | 1/36 yard, exact |
| 1 mile | 1,609.344 m | 1,760 yards, exact |
Häufig gestellte Fragen
Why is an inch exactly 25.4 mm and not approximately 25.4 mm?
Because the international yard was fixed at exactly 0.9144 meters under the 1959 international yard and pound agreement between the US, UK, Canada, Australia, New Zealand and South Africa, and the inch is defined as exactly 1/36 of that yard -- which works out to exactly 0.0254 m, or 25.4 mm, with no rounding involved.
What was the 1959 international yard and pound agreement?
It was an agreement among the national standards bodies of the United States, United Kingdom, Canada, Australia, New Zealand and South Africa to adopt a single, common definition for the yard (exactly 0.9144 m) and the pound (exactly 0.45359237 kg), ending small discrepancies that had developed between each country's own physical prototype standards.
What does it mean for a unit to be 'exact by definition'?
It means the relationship between two units is fixed by an agreed definition rather than obtained by physically measuring one against the other, so it carries zero uncertainty and never needs to be re-measured or refined -- 25.4 mm per inch is exact to any number of decimal places, unlike a value derived from comparing physical prototype objects.
What is the US survey foot, and is it still used?
The US survey foot was a very slightly different foot definition (about 0.3048006 m, roughly 2 parts per million larger than the standard international foot) used historically in some US land-survey and geodetic work. NIST and the National Geodetic Survey formally retired it, effective December 31, 2022, in favor of the standard international foot used throughout this site's converters.
How is the meter itself defined today?
Since 1983, the meter has been defined by fixing the speed of light in vacuum at exactly 299,792,458 meters per second. Because the inch is an exact fraction of the meter (via the 1959-fixed yard), the modern inch is ultimately anchored to this fundamental physical constant rather than to a physical prototype bar.
Quellenangaben
- National Institute of Standards and Technology (NIST) -- Special Publication 811: Guide for the Use of the International System of Units (SI), 2008 Edition.
- Bureau International des Poids et Mesures (BIPM) -- The International System of Units (SI Brochure), 9th edition, 2019.
- NIST / National Geodetic Survey -- notice on the retirement of the U.S. survey foot, effective December 31, 2022.