Length Contraction Formula

Length contraction is considered when an object has traveled with the velocity of light. So, relativity arrives into the picture. Therefore, one can say that length contraction happens when an object is traveling at the speed of light. This is described as the decrease in length if a body is traveling with the velocity of light linked to the observer.

Formula of Length Contraction

The formula for length contraction is articulated as

\(\begin{array}{l}L = L_0\sqrt{1-\frac{v^2}{c^2}}\end{array} \)


  • L is the length of an object with is in relativistic speed
  • L0 is the length of an object at rest
  • c is the velocity of light
  • v is the velocity of the object

Length Contraction Solved Example

Problem 1: Compute the contracted length of an object whose initial length 10 m and travel with a velocity 0.75c?

Given parameters are,
L0 = 10 m

v = 0.75c

c = Speed of light (3.0 x 108 m/s)

The formula for length contraction is

\(\begin{array}{l}L = 10\times \sqrt{1-\frac{(0.75c)^2}{c^2}}\end{array} \)

L = 10 × √1- (0.75)2

L = 10 × √(o.438)

L = 6.618 m.


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