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#1 Free Relativistic Kinetic Energy Calculator 2025

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Relativistic Kinetic Energy Calculator

Understanding Relativistic Kinetic Energy

Classical physics, described by Newton's laws, provides a formula for kinetic energy (KE = 0.5mv2) that works well for objects moving at everyday speeds. However, as an object's speed approaches the speed of light (c), Einstein's Special Theory of Relativity reveals that this classical formula is no longer accurate.

Relativistic Kinetic Energy accounts for the increase in an object's effective mass as its velocity increases. It is the total energy of a moving object minus its rest energy (the energy it possesses even when stationary).

How to use this calculator:

  1. Enter the Rest Mass (m0) of the object in kilograms (kg).
  2. Enter the Relative Velocity (v) of the object. This can be entered directly in m/s or as a fraction/percentage of the speed of light (c).
  3. Click "Calculate Energy".
  4. The results will display the Relativistic Kinetic Energy, Classical Kinetic Energy (for comparison), Rest Energy, Total Relativistic Energy, and the Lorentz Factor, along with a step-by-step breakdown.

Theory & Formulas

The core concepts from Special Relativity used here are:

1. Rest Energy (E0):

An object has energy even when at rest, known as its rest energy, given by Einstein's famous mass-energy equivalence formula:

E0 = m0c2

2. Lorentz Factor (γ - Gamma):

The Lorentz factor describes how much quantities like time, length, and relativistic mass of an object change when the object is moving. It's crucial for relativistic calculations:

γ = 1 / √(1 - v2/c2)

3. Total Relativistic Energy (E):

The total energy of a moving object is its rest energy multiplied by the Lorentz factor:

E = γm0c2

4. Relativistic Kinetic Energy (KErel):

This is the energy of motion for a relativistic object. It's the difference between its total relativistic energy and its rest energy:

KErel = E - E0 = (γ - 1)m0c2

5. Classical Kinetic Energy (KEclass):

For comparison, the classical kinetic energy formula is:

KEclass = 0.5m0v2

This formula is an approximation valid only for v << c.

Variables:

  • KErel: Relativistic Kinetic Energy (Joules, J)
  • m0: Rest mass of the object (kilograms, kg)
  • v: Relative velocity of the object (meters per second, m/s)
  • c: Speed of light in a vacuum (approximately 299,792,458 m/s).
  • γ: Lorentz factor (dimensionless).
  • E0: Rest energy (Joules, J)
  • E: Total relativistic energy (Joules, J)

Calculator Inputs

Unit: kilograms (kg)
Select how you want to input velocity.
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