E = mc² calculator
Enter a mass, get its energy — or the other way round.
What does E = mc² mean?
Mass and energy are equivalent: an object at rest has rest energy E = m × c², where m is its mass and c = 299,792,458 m/s is the speed of light, an exact value in the SI (OpenStax University Physics, Volume 3).
Example: the energy in one gram
OpenStax works out the rest energy of 1.00 g: 0.001 kg × (3.00 × 10⁸ m/s)² = 9.00 × 10¹³ J. With the exact speed of light it is 8.988 × 10¹³ J — about 25 million kWh, or about 21,500 tons (21.5 kilotons) of TNT.
Does a charged battery weigh more?
Yes, but far too little to measure. In an OpenStax example a car battery storing 600 A·h at 12.0 V holds 2.59 × 10⁷ J, so charging it adds m = E ÷ c² ≈ 2.88 × 10⁻¹⁰ kg. Choose “Mass from energy” to try your own numbers.
What is a ton of TNT in joules?
By convention, 1 ton of TNT equals 4.184 × 10⁹ J exactly; a kiloton is 4.184 × 10¹² J. NIST SP 811 lists this energy-equivalent unit.
How many MeV is one atomic mass unit?
Using the CODATA 2022 value of the atomic mass unit, 1.66053906892 × 10⁻²⁷ kg, one u corresponds to about 931.494 MeV. Nuclear physicists use this to turn mass defects into binding energies.
How much energy is in a kilogram of mass?
8.988 × 10¹⁶ J, which is about 25.0 billion kWh or 21.5 megatons of TNT (taking 1 ton of TNT as 4.184 × 10⁹ J). That figure is the total rest energy. Chemical and nuclear reactions release only the small fraction of mass that is the difference between the reactants and the products; converting a whole mass happens only when matter meets antimatter.
What is the mass of 1 GeV of energy?
Using m = E ÷ c², 1 GeV (10⁹ eV, or 1.602 × 10⁻¹⁰ J) has a mass equivalent of 1.783 × 10⁻²⁷ kg, about 1.07 times the mass of a proton. Particle physicists therefore quote masses in MeV/c² or GeV/c².
What the equation says and does not say
E = mc² gives the rest energy of an object of mass m. A moving object has the total energy E = γmc², where γ = 1 ÷ √(1 − v²/c²), so the kinetic energy is (γ − 1)mc², which reduces to ½mv² at low speed. Mass is not 'turned into' energy in an ordinary chemical or mechanical process; rather, the system's mass changes by Δm = ΔE ÷ c² when it gains or loses energy ΔE. In chemical reactions this Δm is far too small to measure, while in nuclear reactions it is a measurable fraction of the mass.
Worked example: rest energy of an electron and of one atomic mass unit
An electron has a mass of 9.1093837139 × 10⁻³¹ kg, so E = mc² = 8.187 × 10⁻¹⁴ J. Dividing by the electron-volt, 1.602176634 × 10⁻¹⁹ J, gives 511.0 keV, the 511 keV that physicists quote. One atomic mass unit corresponds to 1.492 × 10⁻¹⁰ J, or 931.494 MeV. One kilogram corresponds to 8.988 × 10¹⁶ J. A joule of energy has a mass equivalent of 1 ÷ c² = 1.113 × 10⁻¹⁷ kg.
Common mistakes
The most frequent error is using km/s or km/h for c without converting: c must be in m/s when the mass is in kilograms to give joules. The second is treating the speed of light as approximate: it is exactly 299,792,458 m/s in the SI, so rounding to 3 × 10⁸ changes the answer by about 0.2%. Third, applying E = mc² to a moving object and forgetting the kinetic part gives only the rest energy. Finally, converting 'all' the mass of a fuel gives the theoretical maximum, not what a reaction releases.
Sources: OpenStax University Physics, Volume 3, chapter 5 (relativity, mass-energy equivalence, rest energy); constants — NIST CODATA 2022 and NIST SP 811 (the ton of TNT as 4.184 × 10⁹ J). Related: kinetic energy calculator, time dilation calculator, photoelectric effect calculator and de Broglie wavelength calculator.