Enter the original length and speed of an object into the calculator to determine the apparent length contraction of an object traveling near the speed of light.

Length Contraction Formula

The following formula is used to calculate an apparent length due to its velocity relative to an observer.

L = L' * Sqrt(1 - (V^2/C^2))
  • Where L is the apparent length
  • L’ is the true or proper length
  • V is the speed of the object
  • C is the speed of light

Length Contraction Definition

What is length contraction?

Length contraction is a term used in special relativity to describe the apparent length of an object as it travels closer to the speed of light with respect to an observer.

In other words, as an object moves faster and faster, it starts to contract and gets shorter and shorter.

Example Problem

How to calculate length contraction?

First, determine the original length of the object. For this example problem, we will say we are looking at a bus with alien technology that can travel close to the speed of light. This bus is measured to be 10 meters.

Next, determine the velocity of the object. In this case, the bus is traveling at 200,000,000 m/s.

Finally, using the information above, along with the speed of light, calculate the apparent length using the formula:

L = L’ * Sqrt(1 – (V^2/C^2))

L = 10 * Sqrt(1 – (200,000,000^2/299,792,458^2))

L = 7.4494