Mass-Energy Equivalence Calculator
Enter mass and speed to compute energy via E = m·c² (rest energy) or relativistic kinetic energy E = (γ−1)mc².
Input Data
Results
At a glance:Mass-energy equivalence is the concept from special relativity (Einstein, 1905) that mass and energy are two forms of the same quantity. The rest energy of an object at rest is E = m·c², where m is its mass and c is the speed of light. A moving object has total energy E = γmc² and kinetic energy E_k = (γ−1)mc², with γ = 1/√(1−v²/c²) the Lorentz factor. As v approaches c, γ diverges and arbitrarily large energy would be required to reach light speed, which is why massive objects cannot reach c. Even a tiny mass corresponds to an enormous amount of energy: 1 kg of mass equals about 9×10¹⁶ J.
Formula
Rest energy: E = m·c²
Lorentz factor: γ = 1/√(1−v²/c²)
Total energy: E = γmc²
Kinetic energy: E_k = (γ−1)mc²
$$E_0 = mc^2$$$$E = \sqrt{(pc)^2 + (m_0 c^2)^2}$$$$\gamma = \frac{E}{m_0 c^2} = \frac{1}{\sqrt{1 - v^2/c^2}}$$How to Use
- Enter the mass m (kg).
- Enter the speed v (m/s); use 0 to obtain rest energy only.
- The calculator returns the rest energy, total energy and kinetic energy.
Case Studies
Rest energy of 1 kg
m = 1 kg, v = 0.
E = 1 × (2.998×10⁸)² ≈ 8.99×10¹⁶ J.
Equivalent to roughly 21 megatons of TNT.
Kinetic energy near light speed
m = 1 kg, v = 0.99c.
γ ≈ 7.09, E_k = (7.09−1)×8.99×10¹⁶ ≈ 5.5×10¹⁷ J.
Far exceeds any chemical energy release.
FAQ
What does E = mc² mean?
It states that mass and energy are equivalent and interchangeable. The rest energy of any object equals its mass times the square of the speed of light. A small amount of mass corresponds to a very large amount of energy because c² is huge (≈9×10¹⁶ m²/s²).
Why can nothing exceed the speed of light?
The Lorentz factor γ = 1/√(1−v²/c²) grows without bound as v approaches c, so the kinetic energy required to accelerate a massive object to c is infinite. Therefore massive objects can only approach, never reach, light speed.
What is the difference between rest energy and kinetic energy?
Rest energy E = mc² is the energy an object has simply by existing, regardless of motion. Kinetic energy E_k = (γ−1)mc² is the extra energy due to motion; it reduces to the familiar ½mv² at everyday (non-relativistic) speeds.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.