Convert Bohr Radius to Classical Electron Radius
Convert bohr radii to classical electron radii instantly. 1 bohr radius = 18778.8650449031 classical electron radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Classical Electron Radius 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.
Classical Electron Radius
The classical electron radius is approximately 2.818×10⁻¹⁵ meters. It is the radius an electron would have if its mass were entirely electromagnetic and its charge distributed over its surface.
Defined classically in the early 20th century. The CODATA 2018 value of 2.8179403262×10⁻¹⁵ m is derived from the elementary charge, electron rest mass, and the Coulomb constant.
The classical electron radius appears in scattering theory (Thomson scattering cross-section), particle physics estimates, and historical electromagnetism. It is a calculational tool, not the actual size of an electron, which has no measured extent.
Concept dates to the early 20th-century classical electromagnetism; CODATA 2018 provides the current reference value.
Bohr Radius to Classical Electron Radius conversion formula
The relationship between bohr radii and classical electron radii:
To convert bohr radii to classical electron radii, multiply the value in bohr radii by 18778.8650449031. To reverse, multiply classical electron radii by 5.325135e-5.
How to use this converter
Type a value into the calculator. The result in classical electron 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 Classical Electron Radius to Bohr Radius converter for the reverse direction.
Step-by-step: convert bohr radii to classical electron radii
- Write down the value in bohr radii (a₀).
- Multiply that value by the factor 18778.8650449031.
- The product is the equivalent value in classical electron radii (rₑ).
- To reverse, multiply the classical electron radius value by 5.325135e-5.
Worked examples
Example 1 — Convert 1 a₀ to rₑ:
1 × 18778.8650449031 = 18778.8650449031 rₑ
Example 2 — Convert 100 a₀ to rₑ:
100 × 18778.8650449031 = 1877886.5044903094 rₑ
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 bohr radii) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 a₀ × 18778.8650449031 = 37557.7300898062 rₑ
Real-world example — Wavelengths across the spectrum
Optical and atomic-scale phenomena are routinely cross-converted between sub-micron units. A photon of wavelength 800 bohr radii can be re-expressed in classical electron radii for direct comparison with another instrument's calibration data sheet.
800 a₀ × 18778.8650449031 = 1.502309e+7 rₑ
Bohr Radius to Classical Electron Radius conversion table
Standard reference values for converting bohr radii to classical electron radii:
| Bohr Radius [a₀] | Classical Electron Radius [rₑ] |
|---|---|
| 0.01 | 187.788650449 |
| 0.1 | 1877.8865044903 |
| 1 | 18778.8650449031 |
| 2 | 37557.7300898062 |
| 3 | 56336.5951347093 |
| 4 | 75115.4601796124 |
| 5 | 93894.3252245155 |
| 10 | 187788.6504490309 |
| 20 | 375577.3008980619 |
| 30 | 563365.9513470929 |
| 40 | 751154.6017961238 |
| 50 | 938943.2522451547 |
| 100 | 1877886.5044903094 |
| 500 | 9389432.522451546 |
| 1000 | 1.877887e+7 |
Frequently asked questions
How many classical electron radii is 1 bohr radius?
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How many classical electron radii is 100 bohr radii?
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Sources & references
Conversion factor (1 a₀ = 18778.8650449031 rₑ) 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.