Convert Classical Electron Radius to Kilometer
Convert classical electron radii to kilometers instantly. 1 classical electron radius = 2.81794e-18 kilometer — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Kilometer to Classical Electron Radius converter for the reverse conversion.
Units explained
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.
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.
Classical Electron Radius to Kilometer conversion formula
The relationship between classical electron radii and kilometers:
To convert classical electron radii to kilometers, multiply the value in classical electron radii by 2.81794e-18. To reverse, multiply kilometers by 3.548691e+17.
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 Classical Electron Radius converter for the reverse direction.
Step-by-step: convert classical electron radii to kilometers
- Write down the value in classical electron radii (rₑ).
- Multiply that value by the factor 2.81794e-18.
- The product is the equivalent value in kilometers (km).
- To reverse, multiply the kilometer value by 3.548691e+17.
Worked examples
Example 1 — Convert 1 rₑ to km:
1 × 2.81794e-18 = 2.81794e-18 km
Example 2 — Convert 100 rₑ to km:
100 × 2.81794e-18 = 2.81794e-16 km
Real-world example — Wavelength to road distance
A trillion classical electron radii equals one kilometer — the kind of conversion that appears in physics problems spanning the electromagnetic spectrum across many orders of magnitude.
1e+12 rₑ × 2.81794e-18 = 2.81794e-6 km
Real-world example — Twelve orders of magnitude
A trillion classical electron 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 rₑ × 2.81794e-18 = 2.81794e-6 km
Classical Electron Radius to Kilometer conversion table
Standard reference values for converting classical electron radii to kilometers:
| Classical Electron Radius [rₑ] | Kilometer [km] |
|---|---|
| 0.01 | 2.81794e-20 |
| 0.1 | 2.81794e-19 |
| 1 | 2.81794e-18 |
| 2 | 5.635881e-18 |
| 3 | 8.453821e-18 |
| 4 | 1.127176e-17 |
| 5 | 1.40897e-17 |
| 10 | 2.81794e-17 |
| 20 | 5.635881e-17 |
| 30 | 8.453821e-17 |
| 40 | 1.127176e-16 |
| 50 | 1.40897e-16 |
| 100 | 2.81794e-16 |
| 500 | 1.40897e-15 |
| 1000 | 2.81794e-15 |
Frequently asked questions
How many kilometers is 1 classical electron radius?
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Metric / SI (4 units)
Imperial / US Customary (4 units)
Sources & references
Conversion factor (1 rₑ = 2.81794e-18 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 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.