The Metre That Used to Be a Bar of Metal
Until 2019, the kilogram was a lump of platinum-iridium in a vault outside Paris. If that cylinder gained a fingerprint's worth of contamination, the kilogram itself changed — by definition, because the object was the definition.
The metre had already escaped that problem. It stopped being a physical bar in 1960 and, since 1983, has been defined by something that can't drift:
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.
That number looks arbitrary. It is, in a specific sense — it was chosen to make the new metre match the old one as closely as measurement allowed, so nothing built to the previous standard suddenly became wrong.
The consequence is subtle and worth understanding: the speed of light is no longer measured. It's defined. Exactly 299,792,458 metres per second, with no uncertainty, because the metre is derived from it. Any improvement in measurement precision now refines our knowledge of the second and of lengths, not of the speed of light.
Why the Inch Is Exactly 2.54 cm
The same logic explains a fact that surprises people: imperial units are defined in terms of metric ones.
The International Yard and Pound Agreement of 1959 fixed the yard at exactly 0.9144 metres. Everything else follows:
1 yard = 0.9144 m (exact, by definition)
1 foot = 0.3048 m (exact)
1 inch = 0.0254 m (exact)
1 mile = 1609.344 m (exact)
So an inch isn't approximately 2.54 cm. It is 2.54 cm, exactly, by international agreement. There's no rounding and no uncertainty in the conversion — which means any decimal expansion beyond that is arithmetic, not measurement error.
The Length Converter applies these exact factors:
- Enter your value.
- Select the source unit.
- Read the equivalents.
Conversions between metric and imperial are exact in one direction and repeating decimals in the other. 10 inches is exactly 25.4 cm. 25 cm is 9.842519685... inches, repeating — because dividing by 2.54 doesn't terminate.
The Survey Foot Problem
A wrinkle worth knowing if you work with US land data.
Before 1959, the US defined the foot slightly differently. When the international foot was adopted, surveying and geodetic work in the US kept the old definition to avoid invalidating existing land records. This became the US survey foot:
International foot: 0.3048 m exactly
US survey foot: 1200/3937 m ≈ 0.30480061 m
The difference is about two parts per million. Negligible over a room. Over a state plane coordinate system spanning hundreds of kilometres, it produces discrepancies of several centimetres — enough to matter for boundary surveys and infrastructure alignment.
The US formally deprecated the survey foot at the end of 2022, but legacy datasets and older survey records still use it. If you're converting coordinate data, check which foot the source used.
The general lesson: a unit name isn't always sufficient. Nautical miles, statute miles, and various historical local miles all share a name and differ substantially.
Precision, Accuracy and Significant Figures
Converting units doesn't create information. This is the point people most often miss.
Measure a table as "1.2 metres" — two significant figures, implying accuracy to about a centimetre. Convert to inches and a calculator gives 47.244094488189 inches.
Fourteen digits from a two-digit measurement. Thirteen of them are noise.
The rule: a conversion result should carry the same number of significant figures as the input. 1.2 m becomes 47 inches, not 47.244094488189.
Related concepts that get conflated:
Precision is how finely you can resolve a measurement — how many digits your instrument reports.
Accuracy is how close the measurement is to the true value.
They're independent. A miscalibrated laser rangefinder is precise and inaccurate: it will give you 2.8471 m consistently, and the table might be 2.9 m. A tape measure read to the nearest centimetre is less precise and possibly more accurate.
Reporting more digits doesn't improve either. It just implies a precision you don't have.
Tolerance: Where Length Actually Matters
In manufacturing, a dimension without a tolerance is incomplete. "50 mm" doesn't specify anything a machinist can work to. "50 ± 0.1 mm" does.
Rough orders of magnitude:
- Construction: millimetres
- General machining: ±0.1 mm
- Precision machining: ±0.01 mm
- Optical and semiconductor work: micrometres and below
The tolerance drives cost far more than the nominal dimension does. Tightening a tolerance by an order of magnitude typically means different equipment, more measurement, higher scrap rates, and temperature-controlled facilities.
Tolerances stack. Assemble five parts each at ±0.1 mm and the worst-case accumulated error is ±0.5 mm. Statistical tolerance analysis gives a more realistic figure than worst-case stacking, since errors partially cancel, but the principle holds: an assembly is looser than any of its components.
Thermal expansion
Materials change length with temperature. Steel expands roughly 12 micrometres per metre per degree Celsius; aluminium around 23.
A one-metre steel part measured at 30°C and used at 10°C is about 0.24 mm shorter at the working temperature. That's outside a precision tolerance from temperature alone.
This is why metrology labs are temperature controlled and why the standard reference temperature for dimensional measurement is 20°C. A dimension without a stated temperature is ambiguous at precision scales.
Choosing How Many Digits to Keep
A practical procedure for any conversion:
1. Identify the precision of your input. How was it measured, and to what resolution?
2. Convert with full precision. Don't round intermediate steps.
3. Round the final result to match the input's significant figures.
4. State the unit and, where it matters, the tolerance and temperature.
An example: a part measured with digital callipers reading to 0.01 mm gives 63.47 mm. Converting to inches: 63.47 / 25.4 = 2.4988188... The input had four significant figures, so report 2.4988 inches — not 2.499, which loses information, and not the full expansion, which invents it.
Common Mistakes
Rounding intermediate values. Round once, at the end. Rounding at each step accumulates error, particularly in multi-step conversions.
Assuming a unit name is unambiguous. Survey foot versus international foot. Nautical versus statute mile. US versus imperial fluid measures. Check the definition.
Reporting a calculator's full output. It's arithmetic precision, not measurement precision.
Converting back and forth repeatedly. Each round trip through a rounded value drifts. Store one canonical unit and convert only for display.
Ignoring temperature at precision scales. Below about ±0.05 mm on metal parts, thermal expansion is a real term in the error budget.
Mixing units within a calculation. The Mars Climate Orbiter is the famous case, and it was a units mismatch between two systems that each worked correctly in isolation.
FAQ
Is an inch exactly 2.54 cm? Yes, exactly, by the 1959 international agreement. There is no rounding in the conversion factor.
Why is the speed of light an exact number? Because the metre is defined in terms of it. Since 1983 the speed of light is fixed by definition rather than measured.
What's the difference between the survey foot and the international foot? About two parts per million. Negligible at small scales, significant across large coordinate systems. The US survey foot was deprecated at the end of 2022.
How many decimal places should I keep in a conversion? Match the significant figures of your input. Extra digits imply precision the measurement doesn't have.
What's the difference between precision and accuracy? Precision is resolution — how finely you can distinguish values. Accuracy is closeness to the true value. A measurement can be one without the other.
Does temperature affect length measurements? Yes. Steel changes about 12 micrometres per metre per degree Celsius. At precision tolerances, the measurement temperature must be specified.
The Takeaway
Length conversions between metric and imperial are exact — the factors are defined, not measured — which means every digit beyond your input's precision comes from arithmetic rather than reality. Keeping the significant figures honest, checking which definition of a unit you've been handed, and stating tolerance and temperature where they matter covers most of what goes wrong.
Convert between millimetres, centimetres, metres, inches, feet and miles free with the Length Converter at sadiqbd.com — no sign-up, instant results.
