Electron Radius (Classical) to Earth's Equatorial Radius Converter
Unit Converter
Instant · Precise · Universal
32 units available
6 categories total
How to Convert Electron Radius (Classical) to Earth's Equatorial Radius
To convert to meters: multiply by 2.8179403262 × 10⁻¹⁵.
re = e²/(4πε₀mec²) ≈ 2.8179 × 10⁻¹⁵ m, where e is electron charge and me is electron mass.
For example, 1 Electron Radius (Classical) (re) = 4.418124e-22 Earth's Equatorial Radius (R⊕ (eq)).
Electron Radius (Classical) to Earth's Equatorial Radius — Common Values
| Electron Radius (Classical) (re) | Earth's Equatorial Radius (R⊕ (eq)) |
|---|---|
| 0.1 | 4.418124e-23 |
| 0.5 | 2.209062e-22 |
| 1 | 4.418124e-22 |
| 2 | 8.836249e-22 |
| 5 | 2.209062e-21 |
| 10 | 4.418124e-21 |
| 25 | 1.104531e-20 |
| 50 | 2.209062e-20 |
| 100 | 4.418124e-20 |
| 500 | 2.209062e-19 |
| 1000 | 4.418124e-19 |
About Electron Radius (Classical) (re)
Definition
The classical electron radius is a theoretical length scale derived from the electron's charge and mass, approximately 2.818 × 10⁻¹⁵ meters.
Mathematical Relationship
re = e²/(4πε₀mec²) ≈ 2.8179 × 10⁻¹⁵ m, where e is electron charge and me is electron mass.
Conversion Formula
To convert to meters: multiply by 2.8179403262 × 10⁻¹⁵.
Practical Applications
Used in calculating X-ray and gamma-ray scattering probabilities off electrons (Thomson and Compton scattering).
Interesting Facts
Despite its name, the electron is a point particle in quantum theory — the 'classical radius' is a theoretical construct, not the electron's actual size.
Common Mistakes
Assuming this is the actual physical size of the electron — quantum mechanics shows the electron has no measurable size.
Educational Tips
Think of it as the scale at which classical electromagnetic self-energy equals the electron's mass-energy.
About Earth's Equatorial Radius (R⊕ (eq))
Definition
The Earth's equatorial radius is the distance from Earth's center to the equator, approximately 6,378.137 km.
Mathematical Relationship
R⊕(eq) = 6,378,137 m = 6,378.137 km. Earth's oblateness = (R_eq − R_pol)/R_eq ≈ 1/298.257.
Conversion Formula
To convert Earth radii to meters: multiply by 6,378,137.
Practical Applications
GPS calculations, satellite orbit determination, map projections, and geophysical modeling.
Interesting Facts
Earth is not a perfect sphere — the equatorial radius is about 21 km (0.3%) larger than the polar radius due to rotational flattening.
Common Mistakes
Using the equatorial radius as if Earth were a sphere — for precision, you must account for the oblate spheroid shape.
Educational Tips
Earth's equatorial radius (6,378 km) vs. polar radius (6,357 km) shows the planet bulges at the equator due to spinning.