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

    Frequently Asked Questions

    Has time dilation been experimentally confirmed?

    Yes, many times. Muons created in the upper atmosphere reach the ground because their decay time is dilated. Atomic clocks on aircraft and satellites also confirm it.

    What is the twin paradox?

    If one twin travels at high speed and returns, they age less than the stay-at-home twin. The apparent paradox resolves because the travelling twin accelerates, breaking the symmetry.

    Does GPS use time dilation corrections?

    Yes. GPS satellites move fast enough (and are in a weaker gravitational field) that both special and general relativistic corrections are essential for accuracy.

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