Convert Centimeter to Classical Electron Radius
Convert centimeters to classical electron radii instantly. 1 centimeter = 3.548691e+12 classical electron radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Classical Electron Radius to Centimeter converter for the reverse conversion.
Units explained
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.
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.
Centimeter to Classical Electron Radius conversion formula
The relationship between centimeters and classical electron radii:
To convert centimeters to classical electron radii, multiply the value in centimeters by 3.548691e+12. To reverse, multiply classical electron radii by 2.81794e-13.
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 Centimeter converter for the reverse direction.
Step-by-step: convert centimeters to classical electron radii
- Write down the value in centimeters (cm).
- Multiply that value by the factor 3.548691e+12.
- The product is the equivalent value in classical electron radii (rₑ).
- To reverse, multiply the classical electron radius value by 2.81794e-13.
Worked examples
Example 1 — Convert 1 cm to rₑ:
1 × 3.548691e+12 = 3.548691e+12 rₑ
Example 2 — Convert 100 cm to rₑ:
100 × 3.548691e+12 = 3.548691e+14 rₑ
Real-world example — Small-scale to atomic-scale
One centimeter equals 10 million classical electron radii — useful for physics curricula that relate everyday measurements to atomic and optical scales.
1 cm × 3.548691e+12 = 3.548691e+12 rₑ
Real-world example — Centimeter to wavelength scale
One centimeter equals 10 million classical electron radii. Physics curricula use this kind of conversion to relate everyday measurements to atomic and optical scales.
1 cm × 3.548691e+12 = 3.548691e+12 rₑ
Centimeter to Classical Electron Radius conversion table
Standard reference values for converting centimeters to classical electron radii:
| Centimeter [cm] | Classical Electron Radius [rₑ] |
|---|---|
| 0.01 | 3.548691e+10 |
| 0.1 | 3.548691e+11 |
| 1 | 3.548691e+12 |
| 2 | 7.097382e+12 |
| 3 | 1.064607e+13 |
| 4 | 1.419476e+13 |
| 5 | 1.774346e+13 |
| 10 | 3.548691e+13 |
| 20 | 7.097382e+13 |
| 30 | 1.064607e+14 |
| 40 | 1.419476e+14 |
| 50 | 1.774346e+14 |
| 100 | 3.548691e+14 |
| 500 | 1.774346e+15 |
| 1000 | 3.548691e+15 |
Frequently asked questions
How many classical electron radii is 1 centimeter?
How do I convert centimeters to classical electron radii?
How do I convert classical electron radii back to centimeters?
How many classical electron radii is 100 centimeters?
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Sources & references
Conversion factor (1 cm = 3.548691e+12 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.