E=mc\u00B2 Calculator

E=mc² is Einstein's mass-energy equivalence equation, where E is energy (in joules), m is mass (in kilograms), and c is the speed of light (299,792,458 m/s). It shows that mass and energy are different forms of the same thing. A small amount of mass contains an enormous amount of energy because c² is such a large number (about 9×10¹⁶).

One gram of matter contains approximately 9×10¹³ joules or 90 terajoules of energy. To put this in perspective, this equals: 25 million kWh of electricity (enough to power 2,300 homes for a year), 21.5 kilotons of TNT (similar to the Hiroshima bomb), or about 2.2 million gallons of gasoline.

Mass defect is the difference between the mass of an atom and the sum of its individual protons, neutrons, and electrons. When nucleons bind together, some mass is converted to binding energy (per E=mc²). For example, a helium-4 nucleus has less mass than 2 protons + 2 neutrons. This 'missing' mass (0.0304 u) equals 28.3 MeV of binding energy.

In nuclear fission, a heavy nucleus (like uranium-235) splits into lighter fragments. The total mass of the fragments is slightly less than the original nucleus - about 0.1% less. This mass difference is converted to energy via E=mc². Fissioning 1 kg of U-235 releases about 80 terajoules, equivalent to 20,000 tons of TNT.

Nuclear fusion combines light nuclei (like hydrogen isotopes) into heavier ones (like helium). The resulting nucleus has less mass than the sum of the original nuclei - about 0.7% in hydrogen fusion. This mass converts to energy per E=mc². Fusion is more efficient than fission, which is why stars produce such enormous energy over billions of years.

Total mass-to-energy conversion only happens in matter-antimatter annihilation, which requires antimatter (extremely rare and expensive to produce). Nuclear reactions convert only a tiny fraction of mass: fission ~0.1%, fusion ~0.7%. Chemical reactions convert even less (~10⁻¹°%). The rest of the mass remains as matter in different forms.

An atomic mass unit (u or amu) is defined as 1/12 the mass of a carbon-12 atom, approximately 1.66054×10⁻²⁷ kg. Using E=mc², 1 u = 931.494 MeV. This unit is convenient for nuclear calculations because atomic masses are close to whole numbers (hydrogen ≈ 1u, helium ≈ 4u, uranium ≈ 238u).

E=mc² underpins nuclear power plants (fission of uranium), nuclear weapons, PET medical scans (positron-electron annihilation), understanding star energy production, and calculating nuclear reaction energies. Even everyday phenomena like the energy from burning fuel involve tiny mass changes, though too small to measure directly.