8.9876e+16
J
2.4965e+10
kWh
2.1481e+7
tons TNT
5.6096e+29
MeV
8.9876e+16
J
2.4965e+10
kWh
2.1481e+7
tons TNT
5.6096e+29
MeV
The E=mc² Calculator computes the energy equivalent of mass — and vice versa — using Einstein's most famous equation from special relativity:
$$E = mc^2$$
where $$m$$ is the rest mass and $$c = 299{,}792{,}458\,\text{m/s}$$ is the speed of light in vacuum. Because $$c^2 \approx 9 \times 10^{16}\,\text{m}^2/\text{s}^2$$ is an enormous number, even a tiny amount of mass contains a staggering quantity of energy. One kilogram of matter, if fully converted, would release about 90 petajoules — equivalent to roughly 21.5 megatons of TNT, or the energy output of a large power plant running for several years.
This calculator converts between mass and energy in multiple units: joules, megaelectronvolts (MeV, the standard unit in nuclear and particle physics), kilowatt-hours, and tons of TNT equivalent. It is essential for understanding nuclear reactions, particle physics, stellar energy production, and the fundamental equivalence of mass and energy.
Einstein derived mass-energy equivalence in 1905 as a consequence of special relativity. The full relativistic energy-momentum relation is:
$$E^2 = (pc)^2 + (mc^2)^2$$
For a particle at rest ($$p = 0$$), this reduces to $$E = mc^2$$, the rest energy. Key aspects of the equation:
The equation also explains why accelerating a massive particle to the speed of light requires infinite energy: as velocity approaches $$c$$, the relativistic mass (total energy divided by $$c^2$$) grows without bound according to $$E = \gamma mc^2$$ where $$\gamma = 1/\sqrt{1-v^2/c^2}$$.
The results show the total rest energy contained in the given mass (or the equivalent mass for a given energy). In practice, only a fraction of rest energy is typically released: nuclear fission liberates ~0.09%, fusion ~0.7%, and only matter-antimatter annihilation achieves 100%. The TNT equivalent provides an intuitive scale — the Hiroshima bomb released energy equivalent to converting about 0.7 grams of mass. Conversely, your daily food intake (~8.4 MJ) corresponds to a mass-energy equivalent of only ~93 nanograms.
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One kilogram fully converted to energy yields ~90 petajoules or ~21.5 kilotons of TNT — comparable to the Hiroshima bomb. This illustrates the immense energy locked in ordinary matter.
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1 MeV corresponds to a mass of 1.783 × 10⁻³⁰ kg. The proton rest mass is 938.3 MeV/c², and the electron is 0.511 MeV/c².
It means mass and energy are equivalent and interconvertible. Any object with mass $$m$$ has an intrinsic rest energy $$E = mc^2$$, even when stationary. Conversely, any form of energy (heat, light, kinetic) has an associated mass $$m = E/c^2$$. This is not metaphorical — it is a measurable physical fact confirmed in nuclear reactions and particle physics experiments.
Yes. In nuclear fission, fusion, and radioactive decay, a small fraction of mass converts to kinetic energy. In matter-antimatter annihilation, 100% converts. The Sun converts about 4 million tons of mass to energy every second via hydrogen fusion, producing $$3.8 \times 10^{26}$$ watts.
The speed of light is $$c \approx 3 \times 10^8$$ m/s, so $$c^2 \approx 9 \times 10^{16}$$ m²/s². This enormous factor means tiny mass changes produce vast energies. It reflects the fundamental structure of spacetime — in natural units used by physicists, $$c = 1$$ and $$E = m$$ directly.
Fission of one ²³⁵U nucleus releases about 200 MeV (~3.2 × 10⁻¹¹ J), converting about 0.09% of the uranium mass to energy. One kilogram of ²³⁵U undergoing complete fission releases ~8.2 × 10¹³ J, equivalent to about 20 kilotons of TNT — comparable to the energy of a nuclear weapon.
The complete equation is $$E^2 = (pc)^2 + (mc^2)^2$$, where $$p$$ is momentum. For particles at rest ($$p=0$$), this gives $$E = mc^2$$. For massless particles like photons ($$m=0$$), it gives $$E = pc$$. For moving massive particles, the total energy is $$E = \gamma mc^2$$ where $$\gamma$$ is the Lorentz factor.
In particle physics, masses are expressed in energy units divided by $$c^2$$. The proton mass is 938.3 MeV/c² (= 1.673 × 10⁻²⁷ kg), the electron is 0.511 MeV/c², and the Higgs boson is 125 GeV/c². This notation directly connects mass to its energy equivalent and simplifies relativistic calculations.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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