Metre
SI base unit · quantity: length
01 · Definition
The metre began as one ten-millionth of a quarter of the Earth’s meridian. Today it is the distance light travels in 1/299 792 458 of a second — length has become derived from time.
In 1983 metrology made an unexpected move: instead of measuring the speed of light ever more precisely, it was declared exact — 299 792 458 metres per second, no more and no less. From that moment measuring length means measuring the flight time of light, and the platinum-iridium bar at Sèvres, the metre for eighty years, became a museum piece. A side effect: the accuracy of length is now limited by the accuracy of the second — and atomic clocks are five orders of magnitude better than any ruler.
In the laboratory the metre is not laid off — interference fringes of a stabilised laser are counted, its frequency locked to caesium clocks. Geodesy does the same on a planetary scale: GPS measures signal delay, that is, time again.
02 · Conversion
Enter a length — the passport will convert it
Russian measures before 1918 were tied to the English ones: the arshin is exactly 28 inches, the sazhen is three arshins, the versta is five hundred sazhens. The conversion is therefore exact, with no rounding: 1 sazhen = 2.133 6 m by the 1899 definition.
“Micron” and “ångström” have been withdrawn from the SI: write µm and 0.1 nm. The nautical mile stayed — it equals one arcminute of a meridian and is therefore convenient in navigation.
| Unit | Name | Value | Where it occurs |
|---|---|---|---|
| 1 m | metre | 1 m | SI base |
| 1 ft | foot | 0.3048 m | exact, since 1959 |
| 1 in | inch | 0.0254 m | exact, 1/12 ft |
| 1 yd | yard | 0.9144 m | exact, 3 ft |
| 1 mi | mile | 1609.344 m | statute |
| 1 nmi | nautical mile | 1852 m | exact, by definition |
| 1 au | astronomical unit | 149 597 870 700 m | exact, IAU 2012 |
1 m = 3.280839895 ft (exact, by the 1959 agreement)
03 · Orders of magnitude
from the Planck length to the horizon of the UniverseLength
04 · Measuring instruments
How metres are measured
It counts fringes: one fringe is half a wavelength, about 316 nm. The primary realisation of the metre, accuracy 10⁻¹¹.
A femtosecond laser provides a “ruler” of thousands of frequencies and links optics to caesium clocks — a bridge from the second to the metre.
Johansson’s parallel gauge blocks: they wring together and carry the metre into the workshop. Tolerance — tenths of a micrometre.
In the field length is measured by time: a laser rangefinder counts pulse delay, satellites count signal phase. Millimetres over kilometres.
05 · Writing rules
Lowercase m, because capital M is taken by mega
The metre is written as a lowercase Latin m with no full stop; “5 M” means five mega-somethings, and “5 m.” is a newspaper abbreviation. The prefix merges with the symbol: km, cm, µm — never “Km” or “mcm”. Square and cubic metres are m² and m³, not “sq. m” in technical documents.
06 · Neighbouring units
The metre is the most prolific unit of the system: area, volume, speed, acceleration — and through the newton and the joule, the whole of mechanics. Fourteen derived SI units contain the metre in their definition.
metre squared
SI base
metre per second
The metre cannot be removed from the system: it holds up both mechanics and electricity — the volt too reduces to the metre through the watt.
07 · Historical section
How length was measured before the metre
Three arshins, seven feet. Since 1899 tied to the English measures exactly, so the conversion leaves no remainder.
Exactly 28 inches, sixteen vershoks. The main measure in the cloth trade and in building drawings.
Five hundred sazhens. A road measure that left behind milestone posts and the saying “visible a versta away”.
An X-section bar at Sèvres and thirty copies distributed among countries. The metre was an object one could drop.
The metre is the only unit redefined four times
1795 — a fraction of the meridian; 1799 — the platinum bar from the Archives; 1889 — the platinum-iridium prototype; 1960 — 1 650 763.73 wavelengths of krypton-86; 1983 — the path of light in 1/299 792 458 of a second. Every step removed a material carrier, and at the last one the metre ceased to be an independent quantity at all: it is now derived from the second through the constant c. A curious detail: the eighteenth-century survey of the meridian quadrant was off by about 0.2 mm per metre, and that error stayed in the definition for good — the equator is 75 metres longer than 40 000 km.
Catalogue · International System of Units
A passport for every quantity
Seven base units, twenty-two derived ones with their own names, and an archive of systems withdrawn from circulation. Each is a separate sheet: definition, dimension, conversion, instruments, writing rules. In 36 languages.