Time Dilation Calculator
Lorentz factor, dilated time and contracted length.
Work out Time Dilation. Lorentz factor, dilated time and contracted length. Free, with no account and nothing to download.
As a fraction of the speed of light. 0.866 gives a Lorentz factor of exactly 2.
Optional — gives the relativistic mass.
Lorentz factor γ
1.99982
Time runs 2× slower, lengths shrink to 50.0%
γ = 1/√(1 − v²/c²), and it stays almost exactly 1 until the speed becomes genuinely enormous. At a tenth of light speed it is 1.005; at 87% it is 2; at 99.9% it is 22.4. That flatness is why relativity went unnoticed for two centuries and then became unavoidable all at once. Time dilation and length contraction are the same factor applied in opposite directions — moving clocks run slow by γ, moving lengths shrink by γ. This is not an illusion or a measurement error. Muons created in the upper atmosphere reach the ground in numbers that only make sense with dilation, and GPS satellites would drift by about 10 km a day if their clocks were not corrected for it.
How the Time Dilation Calculator works
Enter a speed as a fraction of light speed for the Lorentz factor, along with dilated time, contracted length and relativistic mass. γ stays almost exactly 1 until the speed becomes enormous, which is why nobody noticed relativity for two centuries.
Also known as: lorentz factor calculator · length contraction calculator · special relativity calculator · gamma factor calculator
Frequently asked questions
What is the Lorentz factor?
γ = 1/√(1 − v²/c²). It is 1.005 at a tenth of light speed, exactly 2 at 86.6%, and 22.4 at 99.9%.
Is time dilation real or just an illusion?
Entirely real. Muons created high in the atmosphere reach the ground in numbers that only make sense with dilation, and GPS satellite clocks would drift about 10 km worth of error per day without the correction.
What is length contraction?
The same factor applied the other way — moving objects are shortened along their direction of travel by γ. Time stretches by γ, length shrinks by γ.
Why can nothing reach the speed of light?
Because γ diverges at exactly v = c. The energy needed to accelerate a massive object rises without limit as it approaches, so it would take infinite energy to arrive.
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