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Lorentz Factor Calculator

Find relativistic time dilation from a speed.

Result

2.2942
0.9000
43.59%

How it is calculated

You enter the speed as a percentage of the speed of light c. The tool converts it to β = v ÷ c = percent ÷ 100 and computes γ = 1 ÷ √(1 − β²). It also reports the contraction figure 1 ÷ γ as a percentage: the length of a moving object along its direction of travel, measured by a stationary observer, as a share of its rest length. γ itself is the factor by which a moving clock appears slower. Valid inputs run from 0 up to, but not including, 100, because γ grows without limit as speed approaches c and no result exists at c. γ is shown with four decimals, β with four, the percentage with two.

Worked example

A spacecraft travels at 90% of the speed of light. Step 1: β = 90 ÷ 100 = 0.9000. Step 2: β² = 0.81, so 1 − β² = 0.19. Step 3: √0.19 = 0.4359, and γ = 1 ÷ 0.4359 = 2.2942. Step 4: 1 ÷ γ = 0.4359, so the ship appears contracted to 43.59% of its rest length, and a clock on board appears to tick about 2.29 times slower.

Try this example →

Common mistakes

  • Entering the speed as a fraction (0.9) when the field expects a percentage; 0.9 means 0.9% of c and gives γ close to 1.0000.
  • Entering a speed in km/h or m/s instead of a percentage of c.
  • Typing 100 and expecting a very large number: at c the formula has no result.
  • Reading the contraction percentage as the amount lost; 43.59% is the length that remains, not the part removed.
  • Assuming relativistic effects matter at everyday speeds: at 1% of c, γ is only about 1.00005.

About this calculator

This calculator finds the Lorentz factor γ from a speed (as a fraction or percentage of the speed of light): γ = 1/√(1 − v²/c²). This factor is central to special relativity — it determines time dilation (moving clocks run slow by a factor of γ) and length contraction (moving objects shrink along their direction of motion by a factor of 1/γ), and it grows without bound as v approaches c.

Physics students and researchers use it to work through relativistic problems in particle physics (where particles routinely reach speeds close to c in accelerators), astrophysics (relativistic jets, cosmic rays), and to understand why GPS satellite clocks need relativistic corrections.

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Comments (1)

  • Editorial team

    To get a feel for the scale, try a few speeds: 50% of c gives a gamma of about 1.15, 99% gives about 7.09, and 99.9% gives about 22.4. Gamma barely moves until you are well past half the speed of light, then climbs steeply. That is why accelerator particles are described by their energy rather than their speed. Which speed range are you working in, and is it for coursework or curiosity?

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