Convert Bohr Radius to Centimeter
Convert bohr radii to centimeters instantly. 1 bohr radius = 5.291772e-9 centimeter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Centimeter 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.
Centimeter
A centimeter is a metric unit of length equal to one hundredth of a meter (1/100 m). It is one of the most commonly used SI sub-units in daily life, especially for measuring small objects, body dimensions, paper sizes, and short distances.
The centimeter emerged from the French metric system established by the French Academy of Sciences in 1793. The metric system introduced decimal-based prefixes (milli-, centi-, deci-, deca-, hecto-, kilo-) to create proportional sub-units of the meter.
Centimeters are the standard unit for everyday measurement in nearly every country outside the United States. They are used for body height, clothing sizes, rainfall, paper formats (A4 is 21 × 29.7 cm), screen dimensions, and most consumer product specifications.
Developed in France during the late 18th century as part of the metric system designed by the French Academy of Sciences. Formally adopted in France in 1795 and ratified internationally through the Metre Convention signed in Paris in 1875.
Bohr Radius to Centimeter conversion formula
The relationship between bohr radii and centimeters:
To convert bohr radii to centimeters, multiply the value in bohr radii by 5.291772e-9. To reverse, multiply centimeters by 1.889726e+8.
How to use this converter
Type a value into the calculator. The result in centimeters updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Centimeter to Bohr Radius converter for the reverse direction.
Step-by-step: convert bohr radii to centimeters
- Write down the value in bohr radii (a₀).
- Multiply that value by the factor 5.291772e-9.
- The product is the equivalent value in centimeters (cm).
- To reverse, multiply the centimeter value by 1.889726e+8.
Worked examples
Example 1 — Convert 1 a₀ to cm:
1 × 5.291772e-9 = 5.291772e-9 cm
Example 2 — Convert 100 a₀ to cm:
100 × 5.291772e-9 = 5.291772e-7 cm
Real-world example — From wavelengths to millimeter-scale objects
A value of one million bohr radii sounds vast at the atomic scale but converts to a small everyday quantity in centimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
1000000 a₀ × 5.291772e-9 = 0.0052917721 cm
Real-world example — Sub-micron to millimeter
500,000 bohr radii converts to a small everyday quantity in centimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
500000 a₀ × 5.291772e-9 = 0.0026458861 cm
Bohr Radius to Centimeter conversion table
Standard reference values for converting bohr radii to centimeters:
| Bohr Radius [a₀] | Centimeter [cm] |
|---|---|
| 0.01 | 5.291772e-11 |
| 0.1 | 5.291772e-10 |
| 1 | 5.291772e-9 |
| 2 | 1.058354e-8 |
| 3 | 1.587532e-8 |
| 4 | 2.116709e-8 |
| 5 | 2.645886e-8 |
| 10 | 5.291772e-8 |
| 20 | 1.058354e-7 |
| 30 | 1.587532e-7 |
| 40 | 2.116709e-7 |
| 50 | 2.645886e-7 |
| 100 | 5.291772e-7 |
| 500 | 2.645886e-6 |
| 1000 | 5.291772e-6 |
Frequently asked questions
How many centimeters is 1 bohr radius?
How do I convert bohr radii to centimeters?
How do I convert centimeters back to bohr radii?
How many centimeters is 100 bohr radii?
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Imperial / US Customary (4 units)
Sources & references
Conversion factor (1 a₀ = 5.291772e-9 cm) 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.