Time Dilation Calculator Formula

Understand the math behind the time dilation calculator. Each variable explained with a worked example.

Use the Time Dilation Calculator

Formulas Used

Dilated Time

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

Lorentz Factor

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

Beta (v/c)

beta = velocity / 2.998e8

Variables

VariableDescriptionDefault
proper_timeProper Time (t0)(s)1
velocityVelocity(m/s)269800000

How It Works

Special Relativistic Time Dilation

A moving clock runs slower as observed from a stationary frame.

Formula

t = t0 / sqrt(1 - v^2/c^2) = gamma * t0

  • *t0* = proper time (time measured by the moving clock)
  • *v* = relative velocity
  • *c* = speed of light (2.998 x 10^8 m/s)
  • *gamma* = Lorentz factor

    • At 90% of c, time passes about 2.3 times slower for the moving observer.

    Worked Example

    1 second of proper time at 0.9c.

    proper_time = 1velocity = 269800000
    1. 01beta = v/c = 2.698e8 / 2.998e8 = 0.8999
    2. 02gamma = 1 / sqrt(1 - 0.81) = 1 / sqrt(0.19) = 2.294
    3. 03t = gamma * t0 = 2.294 * 1 = 2.294 s

    Ready to run the numbers?

    Open Time Dilation Calculator