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Electron Speed Calculator.

Invert the relativistic kinetic-energy equation to calculate speed from explicit kinetic energy and rest mass.

On-device calculationNo signup
01

Set your values

Results update as you type.

Speed: 164,267,382.3803549 m/s

Speed

0.00000000m/s
Speed as fraction of c: 0.54793701 c

Speed as fraction of c

0.00000000c
Lorentz factor: 1.19542926 ×

Lorentz factor

0.00000000×

Results update automatically as you type.

This is a special-relativity energy-to-speed calculation. Rest mass is an explicit input; no electron charge, field, or accelerator model is assumed.

Use Cases

Particle physics calculations

Determine the speed of electrons or other particles in accelerators or cosmic rays when their kinetic energy is known.

Example: An electron with 1 MeV kinetic energy (1.602e-13 J) and rest mass 9.109e-31 kg.

Educational demonstrations

Illustrate relativistic effects by comparing speeds at different energies, showing how speed approaches the speed of light.

Example: Calculate speed for 10 J and 100 J kinetic energy for a proton.

Frequently Asked Questions

How does the Electron Speed Calculator work?
It inverts the relativistic kinetic-energy formula E_k = (γ - 1)mc² to solve for speed v. Given kinetic energy in joules and rest mass in kilograms, it computes v = c * sqrt(1 - (1/(E_k/(mc²) + 1))²).
What units should I use for kinetic energy and rest mass?
Kinetic energy must be in joules (J) and rest mass in kilograms (kg). The calculator returns speed in meters per second (m/s).
Can I use this calculator for non-relativistic speeds?
Yes, it works for any speed. For low energies, the result will be close to the classical speed sqrt(2E/m), but it remains accurate for relativistic speeds as well.

Tips & Common Mistakes

Tips

  • Ensure kinetic energy is in joules; convert from eV by multiplying by 1.602e-19.
  • Rest mass must be in kilograms; for electrons use 9.109e-31 kg.
  • The calculator returns speed in m/s; compare to c (3e8 m/s) to see relativistic effects.
  • For very low energies, the result may be extremely small; use scientific notation for precision.

Common Mistakes to Avoid

  • Using electron mass in atomic mass units (u) instead of kilograms.
  • Forgetting to convert kinetic energy from electronvolts (eV) to joules.
  • Assuming the calculator gives speed as a fraction of light speed; it gives m/s.

Last updated: August 13, 2026