Relativistic Velocity Calculator

Relativistic Velocity Calculator calculator can be used to calculate the relativistic velocity addition, Lorentz factor, and final velocity when two velocities are known.

Input Parameters

Calculation Results

Calculation Formula

For velocities in the same direction: v = (v1 + v2)/(1 + v1*v2/c²)

For velocities in opposite directions: v = (v1 - v2)/(1 - v1*v2/c²)

Where:
v = Final relativistic velocity
v1 = First velocity
v2 = Second velocity
c = Speed of light in vacuum (≈3×10⁸ m/s)

Final Relativistic Velocity (v) in m/s:

Lorentz Factor (γ):

Relativistic Velocity Calculator Usage Guide

Learn how to use the Relativistic Velocity Calculator and its working principles

How to Use the Calculator

  1. Enter the first velocity (v1) in meters per second (m/s).
  2. Enter the second velocity (v2) in meters per second (m/s).
  3. Select the direction of the second velocity relative to the first velocity (same direction or opposite direction).
  4. Click the "Calculate" button to compute the relativistic velocity and Lorentz factor.
  5. The results will be displayed in the respective fields.

Working Principle

The calculator uses the relativistic velocity addition formula to compute the final velocity when two velocities are combined. This formula accounts for the effects of special relativity when velocities approach the speed of light.

For velocities in the same direction:

v = (v1 + v2)/(1 + v1*v2/c²)

For velocities in opposite directions:

v = (v1 - v2)/(1 - v1*v2/c²)

Where:

  • v = Final relativistic velocity
  • v1 = First velocity
  • v2 = Second velocity
  • c = Speed of light in vacuum (approximately 3×10⁸ m/s)

Lorentz Factor

The Lorentz factor (γ) is a key concept in special relativity that describes how time, length, and mass are perceived differently at relativistic speeds. It is calculated as:

γ = 1/√(1 - v²/c²)

The Lorentz factor increases as the velocity approaches the speed of light, indicating more significant relativistic effects.