Convert Kilometer to A.u. of Length
Convert kilometers to a.u. of length instantly. 1 kilometer = 1.889726e+13 a.u. of length — use the live calculator, the exact formula, a conversion table and worked examples. Also check the A.u. of Length to Kilometer converter for the reverse conversion.
Units explained
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
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 to A.u. of Length conversion formula
The relationship between kilometers and a.u. of length:
To convert kilometers to a.u. of length, multiply the value in kilometers by 1.889726e+13. To reverse, multiply a.u. of length by 5.291772e-14.
How to use this converter
Type a value into the calculator. The result in a.u. of length updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the A.u. of Length to Kilometer converter for the reverse direction.
Step-by-step: convert kilometers to a.u. of length
- Write down the value in kilometers (km).
- Multiply that value by the factor 1.889726e+13.
- The product is the equivalent value in a.u. of length (a.u.).
- To reverse, multiply the a.u. of length value by 5.291772e-14.
Worked examples
Example 1 — Convert 1 km to a.u.:
1 × 1.889726e+13 = 1.889726e+13 a.u.
Example 2 — Convert 100 km to a.u.:
100 × 1.889726e+13 = 1.889726e+15 a.u.
Real-world example — Kilometres to wavelengths
One kilometer equals one trillion a.u. of length — a conversion physics teachers use to convey the gulf between everyday geographic and atomic scales.
1 km × 1.889726e+13 = 1.889726e+13 a.u.
Real-world example — Geographic to wavelength scale
One kilometer equals one trillion a.u. of length — illustrating the 12-order-of-magnitude span between geographic distance and atomic-feature scales.
1 km × 1.889726e+13 = 1.889726e+13 a.u.
Kilometer to A.u. of Length conversion table
Standard reference values for converting kilometers to a.u. of length:
| Kilometer [km] | A.u. of Length [a.u.] |
|---|---|
| 0.01 | 1.889726e+11 |
| 0.1 | 1.889726e+12 |
| 1 | 1.889726e+13 |
| 2 | 3.779452e+13 |
| 3 | 5.669178e+13 |
| 4 | 7.558904e+13 |
| 5 | 9.448631e+13 |
| 10 | 1.889726e+14 |
| 20 | 3.779452e+14 |
| 30 | 5.669178e+14 |
| 40 | 7.558904e+14 |
| 50 | 9.448631e+14 |
| 100 | 1.889726e+15 |
| 500 | 9.448631e+15 |
| 1000 | 1.889726e+16 |
Frequently asked questions
How many a.u. of length is 1 kilometer?
How do I convert kilometers to a.u. of length?
How do I convert a.u. of length back to kilometers?
How many a.u. of length is 100 kilometers?
Popular length unit conversions
Convert Kilometer to other length units
Show all Kilometer conversions
Metric / SI (17 units)
Imperial / US Customary (27 units)
Nautical (1 units)
Astronomical (9 units)
Atomic / Physics (6 units)
Typographic (3 units)
Sources & references
Conversion factor (1 km = 1.889726e+13 a.u.) 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.