Time Dilation Calculator
Relativistic time dilation and length contraction from a speed — the Lorentz factor, how much a moving clock lags, and what the effect amounts to at everyday and at spacecraft speeds.
A clock moving at speed v runs slow by the Lorentz factor γ = 1/√(1 − v²/c²).
How the time dilation calculator works
A clock moving at speed v runs slow by the Lorentz factor γ = 1/√(1 − v²/c²). At everyday speeds γ is 1 plus a few parts in 10¹⁵ — real, and measurable with atomic clocks on aircraft, but nothing you would notice.
At half the speed of light γ is 1.15; at 99% it is 7; at 99.99% it is 71. Muons created in the upper atmosphere reach the ground only because of this — their 2.2-microsecond lifetime is stretched by a factor of ten or more.
Formula: γ = 1 / √(1 − v²/c²); t_moving = t_rest / γ; L = L₀ / γ
Worked examples
| Inputs | Lorentz factor γ | Note |
|---|---|---|
| Half the speed of light | 1.154701 | γ = 1.155 |
| An airliner | 1 | parts in a trillion |
| 99% of c | 7.088812 | γ = 7 |
FAQFrequently asked questions
What is time dilation?
A moving clock runs slow relative to one at rest, by the Lorentz factor. Both observers see the other's clock as slow; the asymmetry only appears when one turns around.
Is it real?
Measured routinely. GPS satellites correct for it every second; atomic clocks flown around the world come back a few dozen nanoseconds out.
What is the Lorentz factor?
γ = 1/√(1 − v²/c²). It is 1 at rest, rises slowly at first and steeply near c. It also gives length contraction and relativistic mass.
Why can nothing reach the speed of light?
Because γ goes to infinity there — infinite energy would be needed. Massless particles like photons travel at exactly c and never slower.
What is the twin paradox?
A twin who travels fast and returns is younger than the one who stayed. It is not a paradox: the traveller accelerated, and that breaks the symmetry.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.