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Length Contraction Calculator

Work out length contraction instantly with clear inputs, formula shown and shareable results.

About Length Contraction Calculator

A moving object is measured shorter along its direction of travel by the Lorentz factor: L = L0/gamma. At 0.8c gamma is 1.667, so a 100 m rod measures 60 m. The contraction is real in the measuring frame but the object's own rest length is unchanged - it is the geometry of spacetime, not compression.

Formulas

Length contraction

L = L0 / gamma

Lorentz factor

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

Worked example

With the default values below, Length Contraction Calculator returns Contracted Length of 60.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Length at restminimum 0 m
100 m
Speed as a fraction of light speedaccepts 0–1
0.8

Results

Contracted Length
60.0000 m
Lorentz Factor
1.6667
Amount Of Contraction
40.0000 m
Speed
2.3983 × 10⁸ m/s

Step by step

  1. 1Values used
  2. 2Length contraction
  3. 3Lorentz factor
  4. 4Contracted Length= 60.0000 m
  5. 5Lorentz Factor= 1.6667
  6. 6Amount Of Contraction= 40.0000 m
  7. 7Speed= 239,834,000.0000 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 4 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

Is the object actually squashed?

No. Nothing about the object changes; different frames simply disagree about simultaneity, which is what measuring a length requires.

Does contraction apply in all directions?

Only along the motion. Transverse dimensions are unaffected, which is why a moving sphere is measured as an oblate ellipsoid.

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