| Inches (in) | Astronomical units (au) |
|---|---|
| 1 Inch | 1.69788512906 × 10-13 au |
| 2 Inches | 3.39577025811 × 10-13 au |
| 3 Inches | 5.09365538717 × 10-13 au |
| 4 Inches | 6.79154051622 × 10-13 au |
| 5 Inches | 8.48942564528 × 10-13 au |
| 10 Inches | 1.69788512906 × 10-12 au |
| 20 Inches | 3.39577025811 × 10-12 au |
| 25 Inches | 4.24471282264 × 10-12 au |
| 50 Inches | 8.48942564528 × 10-12 au |
| 100 Inches | 1.69788512906 × 10-11 au |
| Reference | Inches (in) | Astronomical units (au) |
|---|---|---|
| A sheet of A4 paper (long side) | 11.6929 in | 1.98532 × 10-12 au |
| Average adult human height | 66.9291 in | 1.13638 × 10-11 au |
| A football pitch (length) | 4133.86 in | 7.01882 × 10-10 au |
| A marathon | 1661220 in | 0.000000282056 au |
| Height of Mount Everest | 348386 in | 0.0000000591519 au |
The inch is a unit of length equal to exactly 25.4 millimetres. It is one twelfth of a foot and one thirty-sixth of a yard. The symbol is in, though a double prime is common in technical contexts and a straight double quote is often substituted informally.
The name comes from the Latin uncia, meaning a twelfth part, which also gave English the word ounce. Early definitions were anatomical or agricultural. A statute of Edward II defined the inch as three barleycorns laid end to end, and the width of a man's thumb served as a working approximation in several European languages. Dutch and Swedish still use words for inch that mean thumb.
Its modern precision dates from 1959, when the International Yard and Pound Agreement fixed the yard at exactly 0.9144 metres across the United States, the United Kingdom, Canada, Australia, New Zealand and South Africa. Before that agreement the American and British inches differed very slightly, which mattered in precision manufacturing. The United States retained a separate survey inch for land measurement until it was formally retired at the end of 2022.
The inch remains dominant in several international industries regardless of local measurement systems. Screen sizes are quoted in inches worldwide, measured diagonally. Tyre rim diameters, bicycle wheel sizes, plumbing pipe bores and rack-mounted equipment all use inch designations, and the standard 19-inch rack is a global fixture. Photographic sensor sizes use inch fractions that no longer correspond to any real dimension, a survival from television camera tube measurements.
Subdivision is traditionally binary rather than decimal. An inch is halved repeatedly into eighths, sixteenths and thirty-seconds, which suits ruler markings and fits the fractional sizing of drill bits and spanners. Decimal inches are used in machining, where thousandths of an inch are called thou or mils.
Screens and printing keep it in daily use far outside the countries that use it for anything else. Televisions, monitors and phones are sold by the diagonal in inches everywhere, so a 55-inch television has the same name in Paris as in Chicago. Typography rests on the same base: there are 72 points to the inch, a convention inherited from the printing trade and written into every computer font system, and image resolution is quoted in dots or pixels per inch. Anyone laying out a page in a country that has been metric for a century is therefore working, without particular thought, in twelfths and seventy-seconds of an inch.
One inch equals 25.4 millimetres, 2.54 centimetres, or 0.0254 metres exactly.
The astronomical unit is a length equal to exactly 149,597,870,700 metres, or very nearly 150 million kilometres. The symbol is au. It approximates the mean distance between the Earth and the Sun and is the standard measure for distances within the solar system.
The unit was originally defined by that orbital relationship rather than by a fixed number. Earlier definitions tied it to the properties of a hypothetical body orbiting the Sun, which meant its value depended on the gravitational constant and was subject to revision as measurements improved. The International Astronomical Union ended that dependence in 2012 by fixing the astronomical unit as an exact number of metres. The change simplified calculations and removed an inconvenience: a unit whose length shifted whenever a physical constant was refined.
Determining its value was one of the great problems of observational astronomy. Transits of Venus across the Sun's disc, observed from widely separated points on Earth, allowed the distance to be triangulated. Expeditions were mounted for the transits of 1761, 1769, 1874 and 1882, and James Cook's first Pacific voyage was organised around the 1769 event. Radar ranging to Venus in the 1960s eventually settled the figure far more precisely than any optical method.
The unit makes solar system distances legible. Mercury orbits at 0.39 au, Mars at 1.52 au, Jupiter at 5.2 au and Neptune at 30.1 au. The Kuiper Belt extends to roughly 50 au. Voyager 1, the most distant human-made object, has passed 165 au. Light takes about 499 seconds to cover one astronomical unit, so the Sun is a little over eight light minutes away.
Beyond the solar system the unit becomes unwieldy, and astronomers switch to light years and parsecs. One parsec is 206,265 au.
Spacecraft navigation depends on the unit being exact rather than approximate. Trajectories to the outer planets are computed over distances of tens of astronomical units, and an error in the length of the unit itself would propagate into every position calculation. Fixing the value in 2012 removed that source of drift from the ephemerides used for mission planning.
One astronomical unit equals 149,597,870.7 kilometres, or about 92.956 million miles.