E = mc² Mass–Energy Calculator
Rest energy and signed mass differences with decimal arithmetic and defined units.
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the E = mc² Mass–Energy Calculator
Convert a rest mass to its energy equivalent, convert an energy to a rest-mass equivalent, or compute the signed energy associated with the difference between total reactant and product rest masses. The calculation uses decimal arithmetic so a small entered mass difference is retained even when both totals are large.
The free preview masks computed figures. A Pro pass opens all conversions, copy and reports. Results are rest-energy equivalents, not recoverable electricity, kinetic energy or a blast prediction. Fission and fusion examples below use source-supplied illustrative reaction energies; the inferred mass differences are not independent measurements of the products.
How to use it
- Choose mass to rest energy, energy to mass equivalent, or a reaction mass difference.
- Enter decimal-point numbers or scientific notation and choose the mass or energy unit.
- For a reaction, include all reactant and product rest masses consistently; a larger product total gives a negative released energy.
- Calculate and read J, kWh, eV, MeV and conventional TNT energy equivalents with their limitations.
Examples
Mass 1 kg
Exact model energy 89,875,517,873,681,764 J before display rounding
A rest-energy equivalent does not imply a device can recover all this energy.
Energy 1 kWh
3,600,000 J, equivalent to about 4.00554e-11 kg of rest mass
Energy-to-mass mode: 200 MeV
3.204353268e-11 J and about 3.56532e-28 kg mass equivalent
OpenStax uses 200 MeV as a representative average per uranium-235 fission; individual reaction channels differ.
Energy-to-mass mode: 17.6 MeV
2.81983087584e-12 J and about 3.13748e-29 kg mass equivalent
The source's reaction is deuterium plus tritium producing helium-4 plus a neutron. The reaction energy is approximate.
Equation, units and precision
E = mc², with exact vacuum light speed c = 299792458 m/s. Reaction mode uses Q = (M_before - M_after)c². A positive Q indicates a decrease in rest mass; a negative Q indicates the rest-energy input associated with an increase.
One kWh is 3,600,000 J. One eV is exactly 1.602176634e-19 J; one MeV is one million eV. One conventional tonne of TNT energy equivalent is 4.184e9 J. Calculations keep every digit you enter; figures on screen and in exports are rounded to twelve significant digits, which does not make a measured mass exact.
Worked reaction examples
For the illustrative 200 MeV fission value, multiply by the exact MeV-to-joule coefficient to obtain 3.204353268e-11 J, then divide by c² for about 3.56532e-28 kg. For the source's approximate 17.6 MeV deuterium–tritium reaction, the same steps give 2.81983087584e-12 J and about 3.13748e-29 kg. These examples demonstrate the conversion; no reaction yield, engineering feasibility or operating instructions are inferred.
Sources
Rest energy follows OpenStax: relativistic energy. The worked reaction energies come from OpenStax: fission and OpenStax: fusion. Definitions use NIST: vacuum light speed, NIST: elementary charge, and NIST: energy conversion factors.
Limitations
- This is rest energy, rather than a conversion-efficiency or usable-energy prediction.
- Actual reaction calculations require consistent total rest masses, reaction channels, states and uncertainties.
- A conventional TNT equivalent is only an energy unit; it supplies no blast or safety information.
- The reported digits are rounded; the result is not a professional nuclear or energy-system design.
Privacy
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Frequently asked questions
What do I get without a pass?
Without a pass, E = mc² Mass–Energy Calculator shows the rules, dates and checks that apply to your figures, with every computed amount hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
Does all of a material's mass become usable energy?
The equation gives a rest-energy equivalent. A physical process normally changes only part of the system's rest mass, and its usable output depends on the complete process and losses.
Why can reaction energy be negative?
The defined difference is reactant rest mass minus product rest mass. If the products have more rest mass, this difference is negative and the model indicates energy absorption.
Is this a kinetic-energy calculation?
No. Rest energy is mc². For a moving massive object, kinetic energy is (gamma - 1)mc²; use the related kinetic-energy calculator for that quantity.
Are the fission and fusion example energies exact?
No. They are approximate source values used to illustrate the arithmetic. The unit coefficients and c are defined constants, but the physical reaction data retain their own uncertainty.