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Relativistic Energy Calculator

Calculate Special & General Relativity time dilation, Lorentz factor γ, length contraction, relativistic mass E=mc², and Einsteinian velocity addition for relativistic energy.

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Input Relativistic Parameters

Enter velocity as fraction of light speed c, rest mass, or proper time.

Dilated Time t / Lorentz Factor γ

16.67 seconds
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Einstein's Special Relativity

As velocity v approaches speed of light c, the Lorentz factor γ = 1 / √(1 - v²/c²) approaches infinity, dilating moving clock time and contracting lengths along direction of motion.

Calculation Methodology & Details

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Formula

Lorentz Factor: γ = 1 / √(1 - v² / c²) Time Dilation: t = γ × t₀ Length Contraction: L = L₀ / γ Mass-Energy Equivalence: E = m c² = γ m₀ c² Einstein Velocity Addition: u = (u' + v) / (1 + u'v / c²)

Applies Einstein's 1905 Special Relativity Lorentz transformation equations and General Relativity Schwarzschild spacetime curvature metrics.

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Important Disclaimer

Calculations assume inertial non-accelerating frames of reference unless gravitational field potential Φ or proper acceleration g is provided.

How to Calculate Step-by-Step

Follow these steps to complete the calculation:

1

Step 1

Enter velocity v as a fraction or percentage of speed of light c (e.g. 0.80c = 80%).

2

Step 2

Input proper rest time t₀ (seconds/years), rest length L₀ (meters), or rest mass m₀ (kg).

3

Step 3

View Lorentz factor γ, dilated time t, contracted length L, relativistic momentum p, or total rest mass energy E in Joules/MeV.

Detailed Insights & Expert Guide

ℹ️ About this Calculation

The Relativistic Energy Calculator calculates Special Relativistic Lorentz transformations, time dilation, length contraction, E = mc² mass-energy equivalence, and gravitational time dilation near massive bodies.

Variable Glossary

Input

Lorentz Factor (γ)

Dimensionless scale factor measuring relativistic magnitude: γ = 1 / √(1 - v²/c²).

Parameter

Proper Time (t₀)

Time interval measured by a clock at rest in the moving object's frame of reference.

FAQ

What is the Twin Paradox?
The Twin Paradox is a thought experiment where one twin travels into space at near light speed and returns to find the stay-at-home twin has aged more. Resolved because the traveling twin undergoes non-inertial acceleration during turnarounds.
Why can nothing travel faster than the speed of light c?
As an object with rest mass m₀ approaches c, its Lorentz factor γ and relativistic kinetic energy approach infinity, requiring infinite energy to accelerate to light speed c.
What is gravitational time dilation?
According to General Relativity, clocks run slower in stronger gravitational fields: t_g = t₀ / √(1 - 2GM / rc²). GPS satellites must adjust their atomic clocks for this effect daily.