Convert Bohr Radius to Meter
Convert bohr radii to meters instantly. 1 bohr radius = 5.291772e-11 meter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Meter 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.
Meter
The meter is the SI base unit of length. Since 2019, the meter has been defined by fixing the numerical value of the speed of light in vacuum to exactly 299,792,458 meters per second. Every other SI length unit derives from the meter.
The meter was originally defined in 1793 by the French Academy of Sciences as one ten-millionth of the distance from the equator to the North Pole along a meridian through Paris. It has been redefined multiple times — by physical prototype, then by atomic transitions, and finally in 2019 by fundamental physical constants.
The meter is the international standard for length in science, engineering, construction, athletics, and everyday measurement in metric countries. It underpins definitions of area (m²), volume (m³), and most derived SI units.
Established 1793 in France; ratified internationally via the Metre Convention 1875; redefined in 1960, 1983, and most recently 2019 when the SI redefinition fixed it to the speed of light.
Bohr Radius to Meter conversion formula
The relationship between bohr radii and meters:
To convert bohr radii to meters, multiply the value in bohr radii by 5.291772e-11. To reverse, multiply meters by 1.889726e+10.
How to use this converter
Type a value into the calculator. The result in meters updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Meter to Bohr Radius converter for the reverse direction.
Step-by-step: convert bohr radii to meters
- Write down the value in bohr radii (a₀).
- Multiply that value by the factor 5.291772e-11.
- The product is the equivalent value in meters (m).
- To reverse, multiply the meter value by 1.889726e+10.
Worked examples
Example 1 — Convert 1 a₀ to m:
1 × 5.291772e-11 = 5.291772e-11 m
Example 2 — Convert 100 a₀ to m:
100 × 5.291772e-11 = 5.291772e-9 m
Real-world example — Bridging nine orders of magnitude
500 million bohr radii equals a value comfortably in the human-scale meters range. Physics problems that span this gap are common when comparing the wavelength of light to the path length of an experiment.
5e+8 a₀ × 5.291772e-11 = 0.0264588605 m
Real-world example — From sub-micron to human scale
One billion bohr radii equals one meter — the conversion that drives home the gulf between atomic-scale features and everyday objects in physics curricula.
1e+9 a₀ × 5.291772e-11 = 0.0529177211 m
Bohr Radius to Meter conversion table
Standard reference values for converting bohr radii to meters:
| Bohr Radius [a₀] | Meter [m] |
|---|---|
| 0.01 | 5.291772e-13 |
| 0.1 | 5.291772e-12 |
| 1 | 5.291772e-11 |
| 2 | 1.058354e-10 |
| 3 | 1.587532e-10 |
| 4 | 2.116709e-10 |
| 5 | 2.645886e-10 |
| 10 | 5.291772e-10 |
| 20 | 1.058354e-9 |
| 30 | 1.587532e-9 |
| 40 | 2.116709e-9 |
| 50 | 2.645886e-9 |
| 100 | 5.291772e-9 |
| 500 | 2.645886e-8 |
| 1000 | 5.291772e-8 |
Frequently asked questions
How many meters is 1 bohr radius?
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How many meters is 100 bohr radii?
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Sources & references
Conversion factor (1 a₀ = 5.291772e-11 m) 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.