Convert Kilometer to Bohr Radius
Convert kilometers to bohr radii instantly. 1 kilometer = 1.889726e+13 bohr radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Bohr Radius 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.
Bohr Radius
The Bohr radius is approximately 5.292×10⁻¹¹ meters — the most probable distance between the proton and electron in a hydrogen atom in its ground state.
Defined by Niels Bohr in his 1913 model of the hydrogen atom. The current CODATA 2018 value of 5.29177210903×10⁻¹¹ m is derived from the elementary charge, electron mass, and Planck's constant.
The Bohr radius is used throughout atomic physics, quantum chemistry, and computational chemistry as the natural length scale for electronic-structure calculations. The atomic unit (a.u.) of length equals the Bohr radius.
Defined by Bohr in 1913; current value via CODATA 2018.
Kilometer to Bohr Radius conversion formula
The relationship between kilometers and bohr radii:
To convert kilometers to bohr radii, multiply the value in kilometers by 1.889726e+13. To reverse, multiply bohr radii by 5.291772e-14.
How to use this converter
Type a value into the calculator. The result in bohr radii updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Bohr Radius to Kilometer converter for the reverse direction.
Step-by-step: convert kilometers to bohr radii
- Write down the value in kilometers (km).
- Multiply that value by the factor 1.889726e+13.
- The product is the equivalent value in bohr radii (a₀).
- To reverse, multiply the bohr radius value by 5.291772e-14.
Worked examples
Example 1 — Convert 1 km to a₀:
1 × 1.889726e+13 = 1.889726e+13 a₀
Example 2 — Convert 100 km to a₀:
100 × 1.889726e+13 = 1.889726e+15 a₀
Real-world example — Geographic to wavelength scale
One kilometer equals one trillion bohr radii — illustrating the 12-order-of-magnitude span between geographic distance and atomic-feature scales.
1 km × 1.889726e+13 = 1.889726e+13 a₀
Real-world example — Kilometres to wavelengths
One kilometer equals one trillion bohr radii — a conversion physics teachers use to convey the gulf between everyday geographic and atomic scales.
1 km × 1.889726e+13 = 1.889726e+13 a₀
Kilometer to Bohr Radius conversion table
Standard reference values for converting kilometers to bohr radii:
| Kilometer [km] | Bohr Radius [a₀] |
|---|---|
| 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 bohr radii is 1 kilometer?
How do I convert kilometers to bohr radii?
How do I convert bohr radii back to kilometers?
How many bohr radii is 100 kilometers?
Popular length unit conversions
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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 a₀) 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.