# units of length

Figure 1. The parsec.

## angstrom

The angstrom (Å) is the CGS unit used to express
optical, or near-optical, wavelengths.
It is named after the Swedish physicist Anders Ångström.
One angstrom is equal to 0.1 nm (nanometers), or 10^{-10} m.

## astronomical unit

An astronomical unit (AU) is the mean distance between Earth and the Sun. 1 AU = 149,597,870 kilometers = 92,955,806 miles = 499 light-seconds. light-year equals 63,240 AU.

## cubit

A cubit is a measure of length used in the ancient world. It is approximately equal to the length of a person's forearm, i.e., the part of the arm from the elbow to the fingers. The Romans used a cubit equal to 17.4 modern inches; the Egyptians used one of 20.64 inches.

## fermi

The fermi is a unit of length equal to 10^{-13} cm. One fermi is approximately
the diameter of a proton.

## foot

The foot is an old Imperial and US Customary unit of length equal to one-third of a yard or 0.3048 meter. There are 12 inches to 1 foot.

## furlong

A furlong is an Imperial unit of measurement, equal to 220 yards (about 210 meters). There are 8 furlongs to 1 mile. The word derives from a 'furrowlong'; it represented the standard length of a furrow on a square field of 10 acres in medieval times.

## inch

An inch is a unit of length in the US customary and Imperial systems. Since 1959 it has been defined exactly equal to 25.4 millimeters.

## light-year

A light-year (ly) is the distance traveled by light, moving at 300,000 kilometers per second (186,282 miles per second), in one year – about 9.406 trillion kilometers (5.88 trillion miles or 63,240 astronomical units). The nearest star, Proxima Centauri, lies at a distance of 4.28 light-years or just over 40 trillion kilometers (25 trillion miles). A unit generally preferred by professional astronomers is the parsec.

## meter

The meter (m) is the base unit of length in the SI system of units. 1 meter = 39.3701 inches. It is defined by the International Bureau of Weights and Measures as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

A **kilometer** (1 km) = 1,000 m = 0.62 mile. Alternatively, 1 mile = 1.609 km.

A **micron** is a unit of length in the CGS system, equal
to one millionth of a meter. In SI units
it is replaced by the micrometer (μm).

One billionth (10^{-9}) of a meter.
It used, for example, in the measurement of intermolecular distances and wavelengths.
A sheet of paper is about 100,000 nanometers thick. The nanometer has superceded
the angstrom as the accepted unit
for such measurements.

### History of the meter

It was originally intended that the meter ('meter' in European
spelling) represent one ten millionth of the distance from the North Pole
to the equator on the meridian passing through Paris. But the surveyors
got their sums wrong and for 162 years (to 1960), the meter was defined
as an arbitrary distance between two marks on a bar of platinum kept in Paris – the so-called "international prototype metre". From
1960 to 1983, the meter was defined as the length equal to 1,650,763.73
times the wavelength of radiation corresponding to the transition between
the energy levels 2p_{10} and 5d_{5} of the krypton-86 atom

## mile

The mile is a measure of distance, the name of which is an abbreviation of the Latin *mille passuum* or 'one thousand paces.' Since the paces (one step
with each foot) of the Roman army were supposed to be two steps, each 2.5
feet long, one thousand paces is very close to the length now called a statute
mile – 5,280 feet. A **nautical mile** was developed
to be a distance equal to one minute of arc (1/60 of a degree) distance
along a great circle and is equal to 6,076 feet. 1 mile = 1.609 kilometers.

## parsec

The parsec (pc) is an astronomical unit of length, equal to the distance at
which the radius of Earth's orbit subtends an angle of one arcsecond (see Figure 1).
The name is a contraction of "parallax-second."

1 parsec = 3.259 light-years = 206,265 astronomical units (AU) = 30.83 trillion km = 19.16 trillion miles.

The parsec is generally used by astronomers in preference to the light-year.
For larger distances, the **kiloparsec** (kpc) = 1,000 pc or **megaparsec** (Mpc)
= 1,000,000 pc are used.

It is a popular misconception that light-year and parsec are units of time. For example, in the Star Wars movie Episode IV: A New Hope, Han Solo says to Obi-Wan: "You've never heard of the Millennium Falcon?... It's the ship that made the Kessel Run in less than twelve parsecs."

## yard

The foot is an old Imperial and US Customary unit of length equal to one-third of a yard or 0.3048 meter. There are 12 inches to 1 foot.

The yard is a unit of distance equal to 3 feet (36 inches) or 0.9144 meters.
The name originates with the old German word *gazdaz* for a staff
or stick, which could be used for measurement. This changed to *gierd* in old English and eventually to yard. The yard-arm of a sailing ship –
a tapered spar used to support a square sail – harkens back to the
earlier meaning. In France, the equivalent of the yard measure is called
a "verge," from the Latin *virga* for a stick or rod.