Length · Unit Converter

Convert Kilometer to Classical Electron Radius

Convert kilometers to classical electron radii instantly. 1 kilometer = 3.548691e+17 classical electron radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Classical Electron Radius to Kilometer 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

Kilometer

What is a 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.

Origin of the kilometer

The kilometer was defined alongside the meter in 1795 using the standard SI prefix kilo- (from Greek chilioi, "thousand"), denoting one thousand units.

Where it is used

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.

When and where it was developed

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.

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.

Kilometer to Classical Electron Radius conversion formula

The relationship between kilometers and classical electron radii:

1 km = 3.548691e+17 rₑ
1 rₑ = 2.81794e-18 km

To convert kilometers to classical electron radii, multiply the value in kilometers by 3.548691e+17. To reverse, multiply classical electron radii by 2.81794e-18.

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 Kilometer converter for the reverse direction.

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

  1. Write down the value in kilometers (km).
  2. Multiply that value by the factor 3.548691e+17.
  3. The product is the equivalent value in classical electron radii (rₑ).
  4. To reverse, multiply the classical electron radius value by 2.81794e-18.

Worked examples

Example 1 — Convert 1 km to rₑ:
1 × 3.548691e+17 = 3.548691e+17 rₑ

Example 2 — Convert 100 km to rₑ:
100 × 3.548691e+17 = 3.548691e+19 rₑ

Real-world example — Kilometres to wavelengths

One kilometer equals one trillion classical electron radii — a conversion physics teachers use to convey the gulf between everyday geographic and atomic scales.

1 km × 3.548691e+17 = 3.548691e+17 rₑ

Real-world example — Geographic to wavelength scale

One kilometer equals one trillion classical electron radii — illustrating the 12-order-of-magnitude span between geographic distance and atomic-feature scales.

1 km × 3.548691e+17 = 3.548691e+17 rₑ

Kilometer to Classical Electron Radius conversion table

Standard reference values for converting kilometers to classical electron radii:

Kilometer [km]Classical Electron Radius [rₑ]
0.013.548691e+15
0.13.548691e+16
13.548691e+17
27.097382e+17
31.064607e+18
41.419476e+18
51.774346e+18
103.548691e+18
207.097382e+18
301.064607e+19
401.419476e+19
501.774346e+19
1003.548691e+19
5001.774346e+20
10003.548691e+20

Frequently asked questions

How many classical electron radii is 1 kilometer?
1 kilometer equals 3.548691e+17 classical electron radius.
How do I convert kilometers to classical electron radii?
Multiply the value in kilometers by 3.548691e+17 to get classical electron radii.
How do I convert classical electron radii back to kilometers?
Multiply the value in classical electron radii by 2.81794e-18, or use the Classical Electron Radius to Kilometer converter.
How many classical electron radii is 100 kilometers?
100 kilometers equals 3.548691e+19 classical electron radii, because 100 × 3.548691e+17 = 3.548691e+19.

Convert Kilometer to other length units

Show all Kilometer 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 km = 3.548691e+17 rₑ) verified against the following authoritative sources:

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