Electron Speed Calculator

Your details

Choose whether you know the accelerating voltage or the kinetic energy directly.
The potential difference the electron is accelerated through. 10 kV gives roughly 19% of the speed of light.
Choose the unit used to display the speed results.
Relativistic speedModerately relativistic
19.4986

Correct speed from special relativity

Classical speed19.7836
Difference (classical - relativistic)0.285
Beta (v/c)0.194986
Lorentz factor (gamma)1.01957
Kinetic energy10,000eV
Relativistic momentum54.2912kg m/s (x10^-24)
de Broglie wavelength12.2047pm
_speedUnit% of c
0.194986 v/c
Non-relativistic<0.01Mildly relativistic0.01-0.1Moderately relativistic0.1-0.5Highly relativistic0.5-0.9Ultra-relativistic0.9+
Relativistic speed19.4986
Classical speed19.7836

The electron travels at 19.50% of the speed of light (beta = 0.1950).

  • The classical formula overestimates the speed by 1.5%. At low voltages the error is small; it grows rapidly above ~50 kV.
  • The Lorentz factor is 1.020, meaning the electron's effective mass is 2.0% heavier than at rest.
  • The de Broglie wavelength is 12.205 pm. At ~100 pm it is comparable to atomic spacings, making the electron a useful probe in electron microscopy.

Next stepThis is the typical range for electron microscopes (TEM/SEM) and medical X-ray tubes. Relativistic corrections meaningfully affect the result.

 = Powered by OnlyCalculators