Convert A.u. of Length to Astronomical Unit
Convert a.u. of length to astronomical units instantly. 1 a.u. of length = 3.537331e-22 astronomical unit — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Astronomical Unit to A.u. of Length converter for the reverse conversion.
Units explained
A.u. of Length
The atomic unit of length (a.u.) is equal to the Bohr radius — approximately 5.292×10⁻¹¹ m. Despite the abbreviation matching 'astronomical unit', this is a different unit used in atomic and molecular physics.
The atomic unit system was developed in the 1950s for quantum-chemistry calculations. The a.u. of length is defined as the Bohr radius (a₀), the most probable distance between the proton and electron in a hydrogen atom in its ground state.
The atomic unit of length is used throughout quantum chemistry, electronic-structure theory, and computational physics. Most quantum-mechanical equations simplify when expressed in atomic units rather than SI units.
Atomic unit system developed by Hartree in the 1920s; value fixed via CODATA 2018 determination of fundamental physical constants.
Astronomical Unit
The astronomical unit (AU) is a unit of length equal to exactly 149,597,870,700 meters, approximately the average distance from Earth to the Sun. It is the fundamental unit for distance within the solar system.
The AU was originally defined as the semi-major axis of Earth's orbit. In 2012, IAU Resolution B2 redefined the AU as exactly 149,597,870,700 meters, severing its dependence on the actual fluctuating Earth–Sun distance.
AUs are used to express distances within the solar system (Mars: 1.5 AU, Pluto: ~40 AU at perihelion), exoplanet orbital radii, and other planetary-scale distances. Standard in planetary science and astronomy.
Original definition tied to Earth's orbit (Newton, 17th century); fixed at exactly 149,597,870,700 m by IAU Resolution B2 in 2012.
A.u. of Length to Astronomical Unit conversion formula
The relationship between a.u. of length and astronomical units:
To convert a.u. of length to astronomical units, multiply the value in a.u. of length by 3.537331e-22. To reverse, multiply astronomical units by 2.82699e+21.
How to use this converter
Type a value into the calculator. The result in astronomical units updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Astronomical Unit to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to astronomical units
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 3.537331e-22.
- The product is the equivalent value in astronomical units (AU).
- To reverse, multiply the astronomical unit value by 2.82699e+21.
Worked examples
Example 1 — Convert 1 a.u. to AU:
1 × 3.537331e-22 = 3.537331e-22 AU
Example 2 — Convert 100 a.u. to AU:
100 × 3.537331e-22 = 3.537331e-20 AU
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 a.u. of length) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 a.u. × 3.537331e-22 = 7.074662e-22 AU
Real-world example — Wavelengths across the spectrum
Optical and atomic-scale phenomena are routinely cross-converted between sub-micron units. A photon of wavelength 800 a.u. of length can be re-expressed in astronomical units for direct comparison with another instrument's calibration data sheet.
800 a.u. × 3.537331e-22 = 2.829865e-19 AU
A.u. of Length to Astronomical Unit conversion table
Standard reference values for converting a.u. of length to astronomical units:
| A.u. of Length [a.u.] | Astronomical Unit [AU] |
|---|---|
| 0.01 | 3.537331e-24 |
| 0.1 | 3.537331e-23 |
| 1 | 3.537331e-22 |
| 2 | 7.074662e-22 |
| 3 | 1.061199e-21 |
| 4 | 1.414932e-21 |
| 5 | 1.768666e-21 |
| 10 | 3.537331e-21 |
| 20 | 7.074662e-21 |
| 30 | 1.061199e-20 |
| 40 | 1.414932e-20 |
| 50 | 1.768666e-20 |
| 100 | 3.537331e-20 |
| 500 | 1.768666e-19 |
| 1000 | 3.537331e-19 |
Frequently asked questions
How many astronomical units is 1 a.u. of length?
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How many astronomical units is 100 a.u. of length?
Popular length unit conversions
Convert A.u. of Length to other length units
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Metric / SI (4 units)
Imperial / US Customary (4 units)
Astronomical (8 units)
Sources & references
Conversion factor (1 a.u. = 3.537331e-22 AU) verified against the following authoritative sources:
- BIPM — The International System of Units (SI Brochure 9th ed.)
Official BIPM publication defining the seven SI base units (including the meter) and the rules for their use. The global authority on units of measurement.
- NIST — Guide to the SI
US National Institute of Standards and Technology reference covering the SI base and derived units with definitions and usage rules for US technical practice.
- NIST Special Publication 811 — Guide for the Use of the International System of Units
Detailed NIST guide covering exact conversion factors between SI and US customary units along with formatting and rounding conventions.
- NIST — Refinement of values for the yard and pound (Federal Register 1959)
The treaty (signed by US
- International Astronomical Union — System of Astronomical Constants
The IAU defines astronomical units including the AU (149597870700 m exactly) light-year and parsec used in astronomy and astrophysics.