Electron Speed Calculator

Find an electron's speed after acceleration through a voltage.

Speed 18,727,896.64

Fraction of c (c) 0.0625

Formula: Relativistic: KE = eV = (γ − 1)·m_e·c²

Step-by-step with your numbers:

1. Values used:

2. Accelerating voltage = 1,000 V

4. Speed = 18,727,896.64

5. Fraction of c = 0.0625c

Did we solve your problem today?

Accelerating an electron through a voltage gives it kinetic energy and speed (relativistically).

The math behind it

The energy gained is eV = (γ − 1)·m_e·c². Solve for γ, then the speed v = c·√(1 − 1/γ²).

1000 V → about 1.87 × 10⁷ m/s (0.0625c).

When do relativistic effects matter?

Above a few kilovolts, electrons move fast enough that γ noticeably exceeds 1.