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How It Works
Einstein's mass-energy equivalence E = mc² shows that mass and energy are two forms of the same thing. Because the speed of light squared (~9 × 10¹&sup6;) is enormous, even a tiny amount of mass contains a vast amount of energy. This equation underpins nuclear power, particle physics, and our understanding of stellar processes.
The speed of light in a vacuum is exactly 299,792,458 m/s. You can rearrange the equation to solve for mass or the speed of light when the other values are known.
Example Problem
How much energy is contained in 1 kg of matter?
- E = 1 × (3 × 10&sup8;)² = 9 × 10¹&sup6; J
- That is 90 petajoules — roughly the energy of 21.5 megatons of TNT.
Frequently Asked Questions
What does E = mc² mean in simple terms?
It means mass can be converted into energy and vice versa. The amount of energy locked inside matter is its mass multiplied by the speed of light squared, which is why nuclear reactions release so much energy from so little fuel.
Is mass actually destroyed in a nuclear reaction?
The total mass of the products is slightly less than the reactants. That missing mass (called mass defect) has been converted into energy according to E = mc². In a uranium fission event, about 0.1% of the mass is converted to energy.
Does E = mc² apply to everyday objects?
Technically yes — every object has rest energy equal to mc². However, converting that mass into usable energy requires nuclear or subatomic processes. Chemical reactions convert negligibly small amounts of mass.
Related Calculators
- Radioactive Decay Calculator — calculate decay rates and half-lives of nuclear materials.
- Kinetic Energy Calculator — find the energy of a moving object from mass and velocity.
- Power Calculator — determine the rate of energy conversion.
- Potential Energy Calculator — calculate stored energy due to position or configuration.
- Energy Converter — convert between joules, eV, kWh, and other energy units.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.