Length · Unit Converter

Convert Meter to Classical Electron Radius

Convert meters to classical electron radii instantly. 1 meter = 3.548691e+14 classical electron radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Classical Electron Radius to Meter 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

Metric / SI

Meter

What is a meter?

The meter is the SI base unit of length. Since 2019, the meter has been defined by fixing the numerical value of the speed of light in vacuum to exactly 299,792,458 meters per second. Every other SI length unit derives from the meter.

Origin of the meter

The meter was originally defined in 1793 by the French Academy of Sciences as one ten-millionth of the distance from the equator to the North Pole along a meridian through Paris. It has been redefined multiple times — by physical prototype, then by atomic transitions, and finally in 2019 by fundamental physical constants.

Where it is used

The meter is the international standard for length in science, engineering, construction, athletics, and everyday measurement in metric countries. It underpins definitions of area (m²), volume (m³), and most derived SI units.

When and where it was developed

Established 1793 in France; ratified internationally via the Metre Convention 1875; redefined in 1960, 1983, and most recently 2019 when the SI redefinition fixed it to the speed of light.

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.

Meter to Classical Electron Radius conversion formula

The relationship between meters and classical electron radii:

1 m = 3.548691e+14 rₑ
1 rₑ = 2.81794e-15 m

To convert meters to classical electron radii, multiply the value in meters by 3.548691e+14. To reverse, multiply classical electron radii by 2.81794e-15.

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 Meter converter for the reverse direction.

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

  1. Write down the value in meters (m).
  2. Multiply that value by the factor 3.548691e+14.
  3. The product is the equivalent value in classical electron radii (rₑ).
  4. To reverse, multiply the classical electron radius value by 2.81794e-15.

Worked examples

Example 1 — Convert 1 m to rₑ:
1 × 3.548691e+14 = 3.548691e+14 rₑ

Example 2 — Convert 100 m to rₑ:
100 × 3.548691e+14 = 3.548691e+16 rₑ

Real-world example — Meter to nanoscale

One meter equals one billion classical electron radii. Physics curricula use this conversion to teach orders of magnitude when introducing the electromagnetic spectrum.

1 m × 3.548691e+14 = 3.548691e+14 rₑ

Real-world example — Human-scale to atomic dimensions

One meter equals one billion classical electron radii — the canonical metric conversion bridging everyday objects and atomic-scale features in physics, chemistry, and electronics.

1 m × 3.548691e+14 = 3.548691e+14 rₑ

Meter to Classical Electron Radius conversion table

Standard reference values for converting meters to classical electron radii:

Meter [m]Classical Electron Radius [rₑ]
0.013.548691e+12
0.13.548691e+13
13.548691e+14
27.097382e+14
31.064607e+15
41.419476e+15
51.774346e+15
103.548691e+15
207.097382e+15
301.064607e+16
401.419476e+16
501.774346e+16
1003.548691e+16
5001.774346e+17
10003.548691e+17

Frequently asked questions

How many classical electron radii is 1 meter?
1 meter equals 3.548691e+14 classical electron radius.
How do I convert meters to classical electron radii?
Multiply the value in meters by 3.548691e+14 to get classical electron radii.
How do I convert classical electron radii back to meters?
Multiply the value in classical electron radii by 2.81794e-15, or use the Classical Electron Radius to Meter converter.
How many classical electron radii is 100 meters?
100 meters equals 3.548691e+16 classical electron radii, because 100 × 3.548691e+14 = 3.548691e+16.

Convert Meter to other length units

Show all Meter conversions
Metric / SI (17 units)
Imperial / US Customary (27 units)
Nautical (1 units)
Astronomical (9 units)
Atomic / Physics (6 units)
Typographic (3 units)

Sources & references

Conversion factor (1 m = 3.548691e+14 rₑ) verified against the following authoritative sources:

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