Relativistic Momentum Calculator Formula
Understand the math behind the relativistic momentum calculator. Each variable explained with a worked example.
Formulas Used
Lorentz Factor (gamma)
lorentz_factor = 1 / sqrt(1 - pow(velocity_fraction, 2))Classical Momentum
classical_momentum = mass * velocity_fraction * 299792458Relativistic Momentum
relativistic_momentum = mass * velocity_fraction * 299792458 / sqrt(1 - pow(velocity_fraction, 2))Variables
| Variable | Description | Default |
|---|---|---|
mass | Rest Mass(kg) | 9.109e-31 |
velocity_fraction | Velocity (fraction of c) | 0.9 |
How It Works
Relativistic Momentum
At speeds approaching the speed of light, classical momentum (p = mv) is insufficient. Special relativity modifies the formula.
Formula
p = gamma * m * v = m * v / sqrt(1 - v²/c²)
As v approaches c, momentum approaches infinity, which is why massive objects cannot reach the speed of light.
Worked Example
An electron (m = 9.109e-31 kg) at 0.9c.
mass = 9.109e-31velocity_fraction = 0.9
- 01gamma = 1/sqrt(1 - 0.81) = 1/sqrt(0.19) = 2.294
- 02v = 0.9 * 2.998e8 = 2.698e8 m/s
- 03Classical p = m*v = 9.109e-31 * 2.698e8 = 2.458e-22 kg·m/s
- 04Relativistic p = gamma*m*v = 2.294 * 2.458e-22 = 5.639e-22 kg·m/s
Ready to run the numbers?
Open Relativistic Momentum Calculator