Lorentz Factor Calculator Formula

Understand the math behind the lorentz factor calculator. Each variable explained with a worked example.

Use the Lorentz Factor Calculator

Formulas Used

Lorentz Factor (gamma)

gamma = 1 / sqrt(1 - pow(velocity, 2) / pow(2.998e8, 2))

Beta (v/c)

beta = velocity / 2.998e8

1 - beta^2

one_minus_beta2 = 1 - pow(velocity, 2) / pow(2.998e8, 2)

Variables

VariableDescriptionDefault
velocityVelocity(m/s)269800000

How It Works

The Lorentz Factor

Gamma is the cornerstone of special relativity, appearing in time dilation, length contraction, and relativistic energy.

Formula

gamma = 1 / sqrt(1 - beta^2)

where beta = v/c.

  • gamma = 1 at rest
  • gamma = 1.15 at 0.5c
  • gamma = 7.09 at 0.99c
  • gamma approaches infinity as v approaches c

    • Worked Example

    Object at 0.9c.

    velocity = 269800000
    1. 01beta = v/c = 2.698e8 / 2.998e8 = 0.8999
    2. 02beta^2 = 0.8099
    3. 031 - beta^2 = 0.1901
    4. 04gamma = 1 / sqrt(0.1901) = 1 / 0.4360 = 2.294

    Ready to run the numbers?

    Open Lorentz Factor Calculator