| Astronomical units (au) | Feet (ft) |
|---|---|
| 1 Astronomical unit | 490806662402 ft |
| 2 Astronomical units | 981613324803 ft |
| 3 Astronomical units | 1472419987205 ft |
| 4 Astronomical units | 1963226649606 ft |
| 5 Astronomical units | 2454033312008 ft |
| 10 Astronomical units | 4908066624016 ft |
| 20 Astronomical units | 9816133248031 ft |
| 25 Astronomical units | 12270166560039 ft |
| 50 Astronomical units | 24540333120079 ft |
| 100 Astronomical units | 49080666240157 ft |
| Reference | Astronomical units (au) | Feet (ft) |
|---|---|---|
| A sheet of A4 paper (long side) | 1.98532 × 10-12 au | 0.974409 ft |
| Average adult human height | 1.13638 × 10-11 au | 5.57743 ft |
| A football pitch (length) | 7.01882 × 10-10 au | 344.488 ft |
| A marathon | 0.000000282056 au | 138435 ft |
| Height of Mount Everest | 0.0000000591519 au | 29032.2 ft |
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.
The foot is a unit of length equal to exactly 0.3048 metres, or twelve inches. Its plural is feet and its symbol is ft, though a single prime is used in technical drawing and a straight apostrophe informally.
Units based on the human foot appear across the ancient world, and their lengths varied considerably. The Roman pes measured about 296 millimetres and was divided into twelve unciae, an arrangement English inherited directly. Medieval Europe supported dozens of local feet, and a merchant crossing a few borders might encounter several. The English foot was standardised in stages, but its exact modern value dates only from the International Yard and Pound Agreement of 1959.
Aviation is the foot's most significant surviving international domain. Aircraft altitude is reported in feet almost everywhere, and flight levels are expressed in hundreds of feet, so FL350 means 35,000 feet. Russia and China historically used metres, and China's transition to feet for most flight levels in 2011 removed a genuine safety hazard at the boundaries of adjoining airspace. Vertical separation standards are defined in feet, and reduced vertical separation minima allow 1000 feet between aircraft above 29,000 feet.
Construction in the United States works in feet and inches throughout, and lumber, ceiling heights and room dimensions all follow. Broadcasting and film retain the foot for lens focus scales and for measuring film stock. Water depth in diving is given in feet in American practice and metres elsewhere, a divergence that dive computers accommodate by offering both.
Twelve as a divisor is the foot's practical strength. It divides evenly by two, three, four and six, which suits carpentry and layout work where thirds and quarters are common. A decimal unit divides cleanly only by two and five.
Water and timber keep two of its derivatives alive. The fathom, six feet, measured the depth of water for as long as a sounding line was thrown by hand, and old charts are still marked in fathoms even where new ones use metres. The board foot, a volume of one foot square by one inch thick, remains the trading unit of sawn timber in North America, so a lumber yard quotes prices per thousand board feet. Both illustrate a general habit of the imperial system: rather than adding prefixes, it names each new quantity after the job it does, which makes the units memorable to those who use them and opaque to everyone else.
One foot equals 12 inches, 0.3048 metres, or 30.48 centimetres exactly.