Free Time Dilation Calculator

Calculate relativistic time dilation: t = t0 / sqrt(1 - v^2/c^2), the time observed by a stationary observer.

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s
m/s

Dilated Time

2.293433 s

Lorentz Factor2.293433
Beta (v/c)0.89993329

Dilated Time vs Proper Time (t0)

View formula & 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.

    Example Calculation

    1 second of proper time at 0.9c.

    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

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