Physics

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Length Contraction Calculator.

Calculate relativistic length contraction from proper length and speed.

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Results update as you type.

Contracted length: 9.427274 m

Contracted length

0.000000m
Lorentz factor: 1.060752

Lorentz factor

0.000000

Results update automatically as you type.

Use Cases

Physics Education and Problem Solving

Students and educators can use this calculator to quickly compute length contraction for homework problems or to visualize how length changes with speed in special relativity.

Example: Calculate the contracted length of a 10 m spaceship traveling at 0.8c (240 million m/s).

Science Fiction and Conceptual Exploration

Writers and enthusiasts can explore the effects of relativistic travel on perceived distances and sizes, aiding in realistic depictions of near-light-speed travel.

Example: Determine how much a 100 m long spacecraft would shrink at 99% of the speed of light.

Frequently Asked Questions

What is length contraction in relativity?
Length contraction is a phenomenon in special relativity where an object's length is measured to be shorter when it is moving relative to the observer. The contraction occurs only along the direction of motion and becomes significant at speeds close to the speed of light.
How does this calculator compute contracted length?
The calculator uses the formula L = L0 * sqrt(1 - v^2/c^2), where L0 is the proper length (in meters), v is the relative speed (in m/s), and c is the speed of light (299,792,458 m/s). It automatically computes the contracted length in meters.
What is proper length?
Proper length (L0) is the length of an object measured in its own rest frame, i.e., when the object is at rest relative to the observer. It is the maximum length an object can have; any motion relative to the observer will cause it to appear shorter.

Tips & Common Mistakes

Tips

  • Ensure the proper length is in meters and the speed is in meters per second. The calculator uses these units directly, so no conversion is needed.
  • Remember that length contraction only applies along the direction of motion. Perpendicular dimensions are unaffected.
  • For speeds much less than the speed of light (e.g., everyday speeds), the contraction is negligible and the length is essentially the proper length.
  • Use the speed of light as a reference: at v = c, the contracted length would be zero, but such speeds are physically impossible for massive objects.

Common Mistakes to Avoid

  • Using speed in kilometers per hour or miles per hour without converting to meters per second. Always input speed in m/s.
  • Confusing proper length with contracted length. Proper length is the length in the object's rest frame, not the measured length when moving.
  • Forgetting that the contraction factor is sqrt(1 - v^2/c^2). Some may mistakenly use (1 - v/c) or other approximations.

Last updated: August 13, 2026