Relativistic Momentum Calculator Formula

Understand the math behind the relativistic momentum calculator. Each variable explained with a worked example.

Use the Relativistic Momentum Calculator

Formulas Used

Relativistic Momentum

rel_momentum = rest_mass * velocity / sqrt(1 - pow(velocity, 2) / pow(2.998e8, 2))

Classical Momentum

classical_momentum = rest_mass * velocity

Variables

VariableDescriptionDefault
rest_massRest Mass(kg)9.109e-31
velocityVelocity(m/s)269800000

How It Works

Relativistic Momentum

Classical momentum (p = mv) is only an approximation at low speeds. The correct formula includes the Lorentz factor.

Formula

p = gamma * m0 * v

As v approaches c, momentum grows without bound even though the velocity barely changes. This is why it takes infinite energy to accelerate a massive particle to c.

Worked Example

Electron at 0.9c.

rest_mass = 9.109e-31velocity = 269800000
  1. 01gamma = 2.294
  2. 02p_rel = 2.294 * 9.109e-31 * 2.698e8
  3. 03p_rel = 5.639e-22 kg m/s
  4. 04p_classical = 9.109e-31 * 2.698e8 = 2.458e-22 kg m/s
  5. 05Relativistic is 2.29x larger

Ready to run the numbers?

Open Relativistic Momentum Calculator