Length Contraction Calculator

Your details

Load a well-known relativistic scenario to populate the inputs automatically.
The length of the object measured in its own rest frame - the longest it can ever appear.
Choose the unit for the proper length input and the contracted-length output.
Choose how you want to enter the relative velocity.
Relative velocity as a fraction of the speed of light. Must be less than 1 (i.e., less than c).
Observed (contracted) lengthRelativistic
86.60254m

The length measured by an observer watching the object move past them.

Lorentz factor (gamma)1.154701
Velocity (fraction of c)0.5
Length contraction0.134%
Length difference13.39746m
Velocity (km/s)149,896.229
0.5 c
Non-relativistic<0.1Mildly relativistic0.1-0.5Relativistic0.5-0.9Highly relativistic0.9-0.999Ultra-relativistic0.999+

Observed length: 86.602540 m (contracted by 13.3975%)

  • At 0.500000c the Lorentz factor is 1.1547, so the object appears 13.3975% shorter than its rest length of 100 m.
  • Contraction is substantial. At these speeds, an object would visibly appear significantly shorter along its direction of travel - though actually seeing this is complicated by the finite travel time of light (the Penrose-Terrell rotation effect).
  • Length contraction is real and measurable: cosmic-ray muons created 10 km up in the atmosphere survive to sea level partly because, in our frame, the atmosphere is length-contracted in their direction of travel.

Next stepTry the time dilation calculator to see the complementary effect: how much slower a moving clock ticks relative to a stationary one.

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