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E = mc² Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


You can bet that anyone you meet will at least have heard about this famous equation. You have probably come across it a hundred times yourself. But what does E equals mc squared actually mean? What is the mysterious mass-energy equivalence principle? What had Einstein to do with it? Continue reading to find out!

Einstein's theory of relativity

In 1905, Albert Einstein proposed a theory that stated that mass and energy are equivalent. It meant that the law of conservation of energy (it says that the sum of potential energy and kinetic energy of a body is constant) and the law of conservation of mass are, in fact, the same. Also, Einstein stated that even a particle at rest has some energy, called its rest energy.

💡 You can find more information about the energy of an object in our potential energy calculator and our kinetic energy calculator.

Mass energy equivalence formula

All right, you probably know that:

E=mc2E = mc^2

But what exactly do the letters in this famous equation stand for?

  • mm – Mass of an object in kilograms (kg);

  • cc – Speed of light – a constant value of 299,792,458 m/s; and

  • EE – Rest energy of the object in joules (J).

Make sure that the mass of the object is in the unit of kilograms. If not, you can use our weight converter to express the object's mass value in kilograms easily.

💡 You can visit our energy conversion calculator if you want to learn how to convert the calculated energy value into other units of energy.

Consequences of E = mc²

Once you start to think about it, the consequences of the formulation of E = mc² equation were astounding. Einstein proposed a world in which mass is just energy waiting to be 'set free'. And not just some energy – an enormous amount of it.

The average adult weight is 62 kg. Such a person, according to Einstein, has a rest energy of 5.6 × 1012 megajoules (MJ). You can check it with our E = mc² calculator. Just for comparison, the bomb dropped on Nagasaki had the energy of 8.4 × 107 MJ. In essence, if you managed to explode and set all of your rest energy free (which is not achievable... yet), you would cause the same destruction as over 66,000 nuclear bombs. Saying it's a lot is definitely an understatement.

This formula was a lifesaver for everyone trying to understand how the universe works. It explained why radioactive materials don't 'melt' while emitting streams of particles (it is because of the extreme efficiency of converting mass to energy). It also explains why the stars don't run out of hydrogen, their primary fuel, for billions of years. Suddenly, the age of the universe appeared much more credible.

🙋 To learn more about this topic, you can also explore our relativistic kinetic energy calculator, where the formula is almost identical.

FAQ

What is c in E=mc²?

c denotes the speed of light in vacuum (299,792,458 m/s). That means that even a tiny mass is equivalent to a significant amount of rest energy.

What is the meaning of E=mc²?

Mass and energy are interchangeable. On the one hand, we can turn mass into energy as in nuclear power plants. On the other hand, high-energy photons can create matter (usually as the particle-antiparticle pair, e.g., electron and positron).

How much energy does a Uranium-235 fission reaction yields?

Assuming that 0.1% of the total mass of Uranium-235 converts to energy through fission reaction:

  1. Take the 235U mass, which is about 235 u.
  2. Convert the mass to kilograms: m = 235 × 1.66×10⁻²⁷ kg = 3.9×10⁻²⁵ kg.
  3. Evalue the mass that converts to energy: Δm = 0.1% × 3.9·10⁻²⁵ kg = 3.9×10⁻²⁸ kg.
  4. Multiply it by the squared speed of light, c² = 9×10¹⁶ m²/s².
  5. The resulting energy equals about 3.51×10⁻¹¹ J or 219 MeV.

What is the mass deficit for the D-T fusion reaction?

The deuterium-tritium fusion reaction yields 17.6 MeV energy. To find the mass deficit:

  1. Convert the energy to joules: 17.6 MeV = 2.82×10⁻¹² J.
  2. Divide it by the squared speed of light: 2.82×10⁻¹² / 9×10¹⁶ = 3.13×10⁻²⁹ kg.
  3. We can also write it using the atomic unis: 3.13×10⁻²⁹ / 1.66×10⁻²⁷ = 0.019 u.
Bogna Szyk
The equation, energy equals mc squared
Mass
lb
Energy
MJ
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