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Time Dilation Calculator

Calculate relativistic time dilation between a moving frame and a stationary observer.

About Time Dilation Calculator

A moving clock runs slow relative to a stationary observer by exactly the Lorentz factor. At 0.8c the factor is 1.667, so one year aboard corresponds to twenty months outside. Time dilation is measured routinely in particle lifetimes and must be corrected for in satellite navigation, where it is a real engineering constraint.

Formula

Time Dilation

Δt = γ Δτ, with γ = 1 ÷ √(1 − v²/c²)

Δτ
Proper time, measured by a clock travelling with the object
γ
Lorentz factor

Worked example

With the default values below, Time Dilation Calculator returns Time Measured by the Stationary Observer of 1.66667. Change any input above and every figure here is recalculated in your browser.

Inputs used

Speed as a fraction of light speedaccepts 0–1
0.8
Time measured in the moving frameminimum 0 years
1 years

Results

Time Measured by the Stationary Observer
1.66667 years
Lorentz Factor
1.66667
Difference in Elapsed Time
0.66667 years
Length Contraction Factor
0.60000
Speed
239,833,966 m/s

Step by step

  1. 1Values used
  2. 2Time Dilation
  3. 3Time Measured by the Stationary Observer= 1.66667 years
  4. 4Lorentz Factor= 1.66667
  5. 5Difference in Elapsed Time= 0.66667 years
  6. 6Length Contraction Factor= 0.60000
  7. 7Speed= 239,833,966 m/s

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Time Dilation calculated?

Δt = γ Δτ, with γ = 1 ÷ √(1 − v²/c²) A moving clock runs slow relative to a stationary observer by exactly the Lorentz factor. At 0.8c the factor is 1.667, so one year aboard corresponds to twenty months outside.

Why does Time Dilation matter?

Time dilation is measured routinely in particle lifetimes and must be corrected for in satellite navigation, where it is a real engineering constraint.

What values do I need to enter?

This calculator takes 2 inputs: Speed as a fraction of light speed, Time measured in the moving frame. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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