Length · Unit Converter

Convert Classical Electron Radius to Centimeter

Convert classical electron radii to centimeters instantly. 1 classical electron radius = 2.81794e-13 centimeter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Centimeter to Classical Electron Radius converter for the reverse conversion.

Written by Sunith Babu L, Ph.D., Lead Engineer Reviewed by Girish V Kulkarni Ph.D.
Length category 2 min read Published Last reviewed Updated

Units explained

Atomic / Physics

Classical Electron Radius

What is a 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.

Origin of the classical electron radius

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.

Where it is used

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.

When and where it was developed

Concept dates to the early 20th-century classical electromagnetism; CODATA 2018 provides the current reference value.

Metric / SI

Centimeter

What is a 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.

Origin of the centimeter

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.

Where it is used

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.

When and where it was developed

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 to Centimeter conversion formula

The relationship between classical electron radii and centimeters:

1 rₑ = 2.81794e-13 cm
1 cm = 3.548691e+12 rₑ

To convert classical electron radii to centimeters, multiply the value in classical electron radii by 2.81794e-13. To reverse, multiply centimeters by 3.548691e+12.

How to use this converter

Type a value into the calculator. The result in centimeters updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Centimeter to Classical Electron Radius converter for the reverse direction.

Step-by-step: convert classical electron radii to centimeters

  1. Write down the value in classical electron radii (rₑ).
  2. Multiply that value by the factor 2.81794e-13.
  3. The product is the equivalent value in centimeters (cm).
  4. To reverse, multiply the centimeter value by 3.548691e+12.

Worked examples

Example 1 — Convert 1 rₑ to cm:
1 × 2.81794e-13 = 2.81794e-13 cm

Example 2 — Convert 100 rₑ to cm:
100 × 2.81794e-13 = 2.81794e-11 cm

Real-world example — Sub-micron to millimeter

500,000 classical electron radii converts to a small everyday quantity in centimeters — useful when relating optical-wavelength specifications to physical mounting hardware.

500000 rₑ × 2.81794e-13 = 1.40897e-7 cm

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 centimeters — useful when relating optical-wavelength specifications to physical mounting hardware.

1000000 rₑ × 2.81794e-13 = 2.81794e-7 cm

Classical Electron Radius to Centimeter conversion table

Standard reference values for converting classical electron radii to centimeters:

Classical Electron Radius [rₑ]Centimeter [cm]
0.012.81794e-15
0.12.81794e-14
12.81794e-13
25.635881e-13
38.453821e-13
41.127176e-12
51.40897e-12
102.81794e-12
205.635881e-12
308.453821e-12
401.127176e-11
501.40897e-11
1002.81794e-11
5001.40897e-10
10002.81794e-10

Frequently asked questions

How many centimeters is 1 classical electron radius?
1 classical electron radius equals 2.81794e-13 centimeter.
How do I convert classical electron radii to centimeters?
Multiply the value in classical electron radii by 2.81794e-13 to get centimeters.
How do I convert centimeters back to classical electron radii?
Multiply the value in centimeters by 3.548691e+12, or use the Centimeter to Classical Electron Radius converter.
How many centimeters is 100 classical electron radii?
100 classical electron radii equals 2.81794e-11 centimeters, because 100 × 2.81794e-13 = 2.81794e-11.

Convert Classical Electron Radius to other length units

Show all Classical Electron Radius conversions

Sources & references

Conversion factor (1 rₑ = 2.81794e-13 cm) verified against the following authoritative sources:

Results are provided for general reference. Verify critical measurements against an authoritative standard.