Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 16, 2023

This length contraction calculator will assist you in understanding relativistic effects and the length contraction equation. Lorentz contraction is another name for length contraction.

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Observer velocity (v):

Length Contraction and its Formula

In special relativity, length contraction refers to the perceived length of an object when it approaches the speed of light with regard to an observer.

In the other words, the phenomenon of length contraction occurs when the length of a moving object is measured to be less than its correct length, which is measured in the object's own rest frame. The length contraction can be calculated using the equation below.

Relative Length, L =L0 * γ = L0* √(1 - v2)/c2))

  • where: γ be the Lorentz factor
  • Relative Length, L is defined as the observable length of an object in motion
  • L0 is the length of the object in its rest frame or proper length
  • v is the object's speed
  • c is the speed of light (299 792 458 m/s).

You can checkout more concept with to get quick answers by using this free tool.

What is Proper length?

The distance between two points measured by an observer who is at rest relative to both of the points; Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth. Proper length denoted by L0

How to determine Length Contraction?

The following are the steps to utilising this Length Contraction calculator for finding the relative length:

  • Determine the object's original length first. For example: We'll pretend we're staring at a bus with extra-terrestrial technology that can travel at nearly the speed of light. The length of this bus is 10 metres.
  • Determine the object's velocity next. The bus is going at 200,000,000 m/s in this example.
  • Finally, using the above data and the speed of light, get the apparent length using the formula

Length Contraction Examples

Question 1: Calculate the relative length of an object if the observer travel with the velocity 45m/s and length of the object is 50m.


Consider the problem, we have

Length, L0= 50 m

Observer velocity (v) = 45 m/s

c is the speed of light and its value is (299,792,458 m/s)

The formula for finding the Relative length L=L0* √(1 - v2)/c2))

Relative length = 50.0 m

Therefore,the relative length of an object is 50m

FAQs on Length Contraction Calculator

1. Define Length of Contraction?

Length of Contrction is the shortening of an object's observed length as it moves away from the observer's frame.It can be denoted by L. The formula for Length of Contrction, L = L0 * γ = L0 * √(1 - v2)/c2))


2. What is proper length?

The distance between two points assessed by an observer who is at rest relative to both points is called the proper length denoted by L0.

3. Is it possible to measure length contraction?

According to the second assumption, an observer in any inertial reference frame will measure the speed of light in a vacuum at the same rate. There has never been a direct measurement of length contraction.

4. How can you figure out length of contractions?

When measuring the distance between two places that are stationary relative to the Earth, Earthbound observers use appropriate length. The shortening of the measured length of an item moving relative to the observer's frame is known as length contraction L.