Physics Calculators

#1 Free Length Contraction Calculator 2025

3 weeks ago
1 mins
32 Views

Length Contraction Calculator

Introduction to Length Contraction

Length Contraction is a phenomenon predicted by Albert Einstein's Special Theory of Relativity. It describes how the length of an object, when measured by an observer, appears shorter in the direction of its motion compared to its length when measured at rest (its "proper length"). This effect becomes significant only at velocities approaching the speed of light.

How to use this calculator:

  1. Enter the Proper Length (L0) of the object. This is its length when measured in its own rest frame (i.e., if you were moving along with the object).
  2. Enter the Relative Velocity (v) of the object with respect to the observer. This can be entered directly in m/s or as a percentage of the speed of light (c).
  3. Click "Calculate Contraction".
  4. The results will display the contracted length as seen by the observer, the amount of contraction, and a step-by-step derivation.

Theory & Formulas

According to Special Relativity, the measurement of length is not absolute but depends on the relative motion between the object and the observer.

Key Formula:

The contracted length (L) of an object moving at a velocity (v) relative to an observer is given by:

L = L0 × √(1 - v2/c2)

Alternatively, using the Lorentz Factor (γ):

L = L0 / γ

Where:

  • L: Contracted length, measured by the observer. This is the value being calculated. (units depend on L0)
  • L0: Proper length, the length of the object in its rest frame. Your input. (e.g., meters, km)
  • v: Relative velocity between the object and the observer. Your input. (m/s)
  • c: Speed of light in a vacuum (approximately 299,792,458 m/s).
  • γ (gamma): The Lorentz factor, calculated as:
γ = 1 / √(1 - v2/c2)

Important Notes:

  • Length contraction only occurs along the direction of motion. Dimensions perpendicular to the motion are unaffected.
  • The velocity 'v' must be less than 'c'. If v ≥ c, the formulas lead to undefined or imaginary results, which are physically meaningless in this context.

Calculator Inputs

Unit: e.g., meters, kilometers, light-years (ensure consistency)
Select how you want to input velocity.
Shares:

Related Posts