Convert Classical Electron Radius to Millimeter
Convert classical electron radii to millimeters instantly. 1 classical electron radius = 2.81794e-12 millimeter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Millimeter 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.
Millimeter
A millimeter is a metric unit of length equal to one thousandth of a meter (1/1000 m). It is the standard small-scale unit in the SI system and is widely used wherever sub-centimeter precision matters.
The millimeter was defined alongside the meter when France adopted the metric system in 1795, using the standard SI prefix milli- (from Latin mille, "thousand") to denote one-thousandth.
Millimeters are used in engineering drawings, machining, manufacturing, paper sizes, rainfall measurement, and any context where dimensions below one centimeter need to be specified clearly. Most rulers worldwide are marked in millimeters.
Adopted in 1795 in France as part of the original metric system; standardized internationally by the Metre Convention in 1875 and confirmed in the SI in 1960.
Classical Electron Radius to Millimeter conversion formula
The relationship between classical electron radii and millimeters:
To convert classical electron radii to millimeters, multiply the value in classical electron radii by 2.81794e-12. To reverse, multiply millimeters by 3.548691e+11.
How to use this converter
Type a value into the calculator. The result in millimeters updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Millimeter to Classical Electron Radius converter for the reverse direction.
Step-by-step: convert classical electron radii to millimeters
- Write down the value in classical electron radii (rₑ).
- Multiply that value by the factor 2.81794e-12.
- The product is the equivalent value in millimeters (mm).
- To reverse, multiply the millimeter value by 3.548691e+11.
Worked examples
Example 1 — Convert 1 rₑ to mm:
1 × 2.81794e-12 = 2.81794e-12 mm
Example 2 — Convert 100 rₑ to mm:
100 × 2.81794e-12 = 2.81794e-10 mm
Real-world example — From wavelengths to millimeter-scale objects
A value of one million classical electron radii sounds vast at the atomic scale but converts to a small everyday quantity in millimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
1000000 rₑ × 2.81794e-12 = 2.81794e-6 mm
Real-world example — Sub-micron to millimeter
500,000 classical electron radii converts to a small everyday quantity in millimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
500000 rₑ × 2.81794e-12 = 1.40897e-6 mm
Classical Electron Radius to Millimeter conversion table
Standard reference values for converting classical electron radii to millimeters:
| Classical Electron Radius [rₑ] | Millimeter [mm] |
|---|---|
| 0.01 | 2.81794e-14 |
| 0.1 | 2.81794e-13 |
| 1 | 2.81794e-12 |
| 2 | 5.635881e-12 |
| 3 | 8.453821e-12 |
| 4 | 1.127176e-11 |
| 5 | 1.40897e-11 |
| 10 | 2.81794e-11 |
| 20 | 5.635881e-11 |
| 30 | 8.453821e-11 |
| 40 | 1.127176e-10 |
| 50 | 1.40897e-10 |
| 100 | 2.81794e-10 |
| 500 | 1.40897e-9 |
| 1000 | 2.81794e-9 |
Frequently asked questions
How many millimeters is 1 classical electron radius?
How do I convert classical electron radii to millimeters?
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How many millimeters is 100 classical electron radii?
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Metric / SI (4 units)
Imperial / US Customary (4 units)
Sources & references
Conversion factor (1 rₑ = 2.81794e-12 mm) 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.