Convert Bohr Radius to Kilometer
Convert bohr radii to kilometers instantly. 1 bohr radius = 5.291772e-14 kilometer — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Kilometer to Bohr Radius converter for the reverse conversion.
Units explained
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
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 to Kilometer conversion formula
The relationship between bohr radii and kilometers:
To convert bohr radii to kilometers, multiply the value in bohr radii 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 Bohr Radius converter for the reverse direction.
Step-by-step: convert bohr radii to kilometers
- Write down the value in bohr radii (a₀).
- 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 a₀ to km:
1 × 5.291772e-14 = 5.291772e-14 km
Example 2 — Convert 100 a₀ to km:
100 × 5.291772e-14 = 5.291772e-12 km
Real-world example — Twelve orders of magnitude
A trillion bohr radii 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 a₀ × 5.291772e-14 = 0.0529177211 km
Real-world example — Wavelength to road distance
A trillion bohr radii equals one kilometer — the kind of conversion that appears in physics problems spanning the electromagnetic spectrum across many orders of magnitude.
1e+12 a₀ × 5.291772e-14 = 0.0529177211 km
Bohr Radius to Kilometer conversion table
Standard reference values for converting bohr radii to kilometers:
| Bohr Radius [a₀] | 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 bohr radius?
How do I convert bohr radii to kilometers?
How do I convert kilometers back to bohr radii?
How many kilometers is 100 bohr radii?
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Metric / SI (4 units)
Imperial / US Customary (4 units)
Sources & references
Conversion factor (1 a₀ = 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 Hydrographic Organization — Resolution on the Nautical Mile
International authority that standardised the nautical mile at exactly 1852 m in 1929 — the value adopted worldwide for sea and air navigation.