Lorentz Factor Calculator

Work out lorentz factor instantly with clear inputs, formula shown and shareable results.

About Lorentz Factor Calculator

The Lorentz factor gamma = 1/sqrt(1 - v^2/c^2) governs every relativistic effect. At 0.6c it is 1.25, so a one-second interval on the moving clock stretches to 1.25 s for a stationary observer, and lengths contract to 0.8 of their rest value. Below 0.1c gamma is within 0.5% of one, which is why classical mechanics works so well.

Formulas

Lorentz factor

gamma = 1 / sqrt(1 - v^2 / c^2)

Time dilation

dt = gamma x d(tau)

Worked example

With the default values below, Lorentz Factor Calculator returns Lorentz Factor of 1.25000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Speed as a fraction of light speedaccepts 0–1: 0.6
Proper time intervalminimum 0 s: 1 s

Results

Lorentz Factor: 1.25000
Dilated Time In The Observer's Frame: 1.2500 s
Length Contraction Factor: 0.80000
Speed: 1.7988 × 10⁸ m/s

Step by step

1Values used
2Lorentz factor
3Time dilation
4Lorentz Factor= 1.25000
5Dilated Time In The Observer's Frame= 1.2500 s
6Length Contraction Factor= 0.80000
7Speed= 179,875,000.0000 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

What speed gives gamma = 2?

About 0.866c. Time then runs at half the rate and lengths halve in the observer's frame.

Has time dilation been measured?

Routinely - muon lifetimes in cosmic rays, atomic clocks on aircraft, and GPS satellites all require the correction to work.