Convert A.u. of Length to Kilometer
Convert a.u. of length to kilometers instantly. 1 a.u. of length = 5.291772e-14 kilometer — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Kilometer 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.
Kilometer
A kilometer is a metric unit of length equal to one thousand meters. It is the standard unit for measuring road distances, geographic distances, and other large-scale measurements in metric countries.
The kilometer was defined alongside the meter in 1795 using the standard SI prefix kilo- (from Greek chilioi, "thousand"), denoting one thousand units.
Kilometers are used worldwide (except the United States and a few others) for road signage, geographic distance, athletic events, and scientific distances at planetary scale. Speed limits in most countries are given in km/h.
Adopted 1795 in France as part of the original metric system; the kilometer became the global standard for road and geographic distance through the 19th and 20th century metric adoption.
A.u. of Length to Kilometer conversion formula
The relationship between a.u. of length and kilometers:
To convert a.u. of length to kilometers, multiply the value in a.u. of length by 5.291772e-14. To reverse, multiply kilometers by 1.889726e+13.
How to use this converter
Type a value into the calculator. The result in kilometers updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Kilometer to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to kilometers
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 5.291772e-14.
- The product is the equivalent value in kilometers (km).
- To reverse, multiply the kilometer value by 1.889726e+13.
Worked examples
Example 1 — Convert 1 a.u. to km:
1 × 5.291772e-14 = 5.291772e-14 km
Example 2 — Convert 100 a.u. to km:
100 × 5.291772e-14 = 5.291772e-12 km
Real-world example — Wavelength to road distance
A trillion a.u. of length equals one kilometer — the kind of conversion that appears in physics problems spanning the electromagnetic spectrum across many orders of magnitude.
1e+12 a.u. × 5.291772e-14 = 0.0529177211 km
Real-world example — Twelve orders of magnitude
A trillion a.u. of length maps to a single, recognizable distance in kilometers. This kind of conversion arises in cosmology and electromagnetic-spectrum exercises where atomic and astronomical scales sit side by side.
1e+12 a.u. × 5.291772e-14 = 0.0529177211 km
A.u. of Length to Kilometer conversion table
Standard reference values for converting a.u. of length to kilometers:
| A.u. of Length [a.u.] | Kilometer [km] |
|---|---|
| 0.01 | 5.291772e-16 |
| 0.1 | 5.291772e-15 |
| 1 | 5.291772e-14 |
| 2 | 1.058354e-13 |
| 3 | 1.587532e-13 |
| 4 | 2.116709e-13 |
| 5 | 2.645886e-13 |
| 10 | 5.291772e-13 |
| 20 | 1.058354e-12 |
| 30 | 1.587532e-12 |
| 40 | 2.116709e-12 |
| 50 | 2.645886e-12 |
| 100 | 5.291772e-12 |
| 500 | 2.645886e-11 |
| 1000 | 5.291772e-11 |
Frequently asked questions
How many kilometers is 1 a.u. of length?
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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. = 5.291772e-14 km) 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.