Convert Planck Length to Classical Electron Radius
Convert planck lengths to classical electron radii instantly. 1 planck length = 5.73559e-21 classical electron radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Classical Electron Radius to Planck Length converter for the reverse conversion.
Units explained
Planck Length
The Planck length is approximately 1.616×10⁻³⁵ meters — the natural unit of length in Planck's system of natural units. It is constructed from the gravitational constant, the speed of light, and the reduced Planck constant.
Defined by Max Planck in 1899 as part of a natural unit system independent of any human or planetary reference. The current CODATA 2018 value is 1.616255×10⁻³⁵ m, derived from G, ℏ, and c.
The Planck length appears in quantum-gravity research and string theory as the scale at which classical notions of spacetime are expected to break down. It is not measurable directly with current technology.
Defined by Planck in 1899; value derived from fundamental constants, most recently updated by 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.
Planck Length to Classical Electron Radius conversion formula
The relationship between planck lengths and classical electron radii:
To convert planck lengths to classical electron radii, multiply the value in planck lengths by 5.73559e-21. To reverse, multiply classical electron radii by 1.7435e+20.
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 Planck Length converter for the reverse direction.
Step-by-step: convert planck lengths to classical electron radii
- Write down the value in planck lengths (ℓP).
- Multiply that value by the factor 5.73559e-21.
- The product is the equivalent value in classical electron radii (rₑ).
- To reverse, multiply the classical electron radius value by 1.7435e+20.
Worked examples
Example 1 — Convert 1 ℓP to rₑ:
1 × 5.73559e-21 = 5.73559e-21 rₑ
Example 2 — Convert 100 ℓP to rₑ:
100 × 5.73559e-21 = 5.73559e-19 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 planck lengths can be re-expressed in classical electron radii for direct comparison with another instrument's calibration data sheet.
800 ℓP × 5.73559e-21 = 4.588472e-18 rₑ
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 planck lengths) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 ℓP × 5.73559e-21 = 1.147118e-20 rₑ
Planck Length to Classical Electron Radius conversion table
Standard reference values for converting planck lengths to classical electron radii:
| Planck Length [ℓP] | Classical Electron Radius [rₑ] |
|---|---|
| 0.01 | 5.73559e-23 |
| 0.1 | 5.73559e-22 |
| 1 | 5.73559e-21 |
| 2 | 1.147118e-20 |
| 3 | 1.720677e-20 |
| 4 | 2.294236e-20 |
| 5 | 2.867795e-20 |
| 10 | 5.73559e-20 |
| 20 | 1.147118e-19 |
| 30 | 1.720677e-19 |
| 40 | 2.294236e-19 |
| 50 | 2.867795e-19 |
| 100 | 5.73559e-19 |
| 500 | 2.867795e-18 |
| 1000 | 5.73559e-18 |
Frequently asked questions
How many classical electron radii is 1 planck length?
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How do I convert classical electron radii back to planck lengths?
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Sources & references
Conversion factor (1 ℓP = 5.73559e-21 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 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.