Mass-energy equivalence calculator
Rest energy of a mass from E=mc² in joules, kilowatt-hours and tonnes of TNT.
Fill in the fields and the result will appear here automatically.
E₀=mc² is the rest energy of the entered mass. Enter grams to compare that same energy in joules, kilowatt-hours and tonnes of TNT equivalent. These units explain the scale; they do not give the electricity obtainable from a fuel. A reaction requires its mass defect Δm, and electricity production also requires a conversion efficiency.
How it works
Formula and logic
E₀=(m in grams/1000)c²; c=299792458 m/s exactly.1 kWh=3.6·10⁶ J;1 tonne TNT equivalent=4.184·10⁹ J by convention.
Example
One gram of matter holds 8.988·10¹³ joules — about 25 million kilowatt-hours.
Fields and units
- Mass — g
How to use
- — The mass field uses grams:1 kg is 1000. The million-kilowatt-hour row only rescales the number. It provides no city demand or number of supplied homes.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax §5.9: rest energy and energy associated with a mass change NIST CODATA 2022: exact h, c, e and measured ε₀ NIST SP811 Appendix B.8: kWh and conventional TNT energy equivalent
- Limitation
- These units explain the scale; they do not give the electricity obtainable from a fuel. A reaction requires its mass defect Δm, and electricity production also requires a conversion efficiency.
FAQ
Does that mean burning a gram of matter releases this much?
No. This calculation gives the rest energy of the entered mass. Energy released by a particular reaction is found from the decrease in total system mass, ΔE=Δmc²; recoverable electricity also depends on the process and its efficiency. Neither fuel composition nor efficiency is an input.
Why is the answer shown as a power of ten?
Because 89,875,517,873,681.8 joules cannot be read. Exponential notation keeps the significant digits and the order of magnitude, and here the order of magnitude is the whole point.
Where do the tonnes of TNT come from?
One tonne of TNT equivalent is defined as 4.184 gigajoules. It is not a property of a particular explosive but a unit of comparison adopted precisely so that numbers like these can be pictured.
Does the formula work for a moving body?
For a moving body the kinetic energy adds to the rest energy, and the total is found through the relativistic factor. What is computed here is the rest energy — the energy locked in the mass itself.
How do I interpret a small mass and a large energy?
Grams and kilograms differ by a factor of 1000. For 1 g the result is≈8.988·10¹³ J,≈24.965 million kWh and≈21480.76 tonnes TNT equivalent. TNT equivalent is an energy unit, not the mass of explosive produced by a reaction.