Mass–Energy Equivalence Calculator (E = mc²)
Solve Einstein's mass-energy equivalence formula E = mc² for energy or mass. Enter one value and get the other instantly, with the substitution step shown.
Mass–energy equivalence
Albert Einstein's most famous equation states that mass and energy are equivalent — a small amount of mass corresponds to a huge amount of energy, because it is multiplied by the speed of light squared:
- E — energy, in joules (J)
- m — mass, in kilograms (kg) — always positive
- c — the speed of light, a fixed constant, approximately 3 × 10⁸ m/s
Enter either value and leave the other blank; the calculator solves for it and shows the substitution step.
Worked example
How much energy is equivalent to 1 gram (0.001 kg) of mass?
- Formula: E = mc²
- Substitute: E = 0.001 × (3 × 10⁸)²
- Result: E = 9 × 10¹³ J
That is about 90 trillion joules from just one gram — roughly comparable to the energy released by a small nuclear weapon.
Solving in reverse
The same formula rearranges to find mass when energy is known:
- Mass: m = E / c² — enter E, leave m blank.
For example, 9 × 10¹³ J of energy corresponds to m = 9 × 10¹³ / (9 × 10¹⁶) = 0.001 kg.
Common mix-ups
- Forgetting to square c. E = mc (without squaring) is a common slip that dramatically understates the energy.
- Expecting everyday mass-to-energy conversion. This equivalence is real, but converting a significant fraction of an object's mass into usable energy only happens in nuclear reactions, not ordinary chemical or mechanical processes.
- Misreading scientific notation. 9 × 10¹³ means 9 followed by 13 zeros, not 9.13 or 9 × 13 — check the exponent carefully.
Where this shows up
Mass-energy equivalence is the theoretical foundation behind nuclear energy: nuclear fission and fusion reactions convert a tiny fraction of an atom's mass directly into energy, in contrast to ordinary chemical reactions (like burning fuel) which only rearrange kinetic energy and bond energy without touching rest mass. Unlike work (W = Fs) or kinetic energy, which describe energy transferred through motion, E = mc² describes energy inherent in mass itself, at rest.
Frequently asked questions
- What is Einstein's mass-energy equivalence formula?
- E = mc², where E is energy in joules (J), m is mass in kilograms (kg), and c is the speed of light, approximately 3 × 10⁸ metres per second — a fixed constant in the formula, not a field you enter.
- How much energy is in a small amount of mass?
- An enormous amount. Because c² is about 9 × 10¹⁶, even 1 gram (0.001 kg) of mass converts to 9 × 10¹³ joules — roughly the energy released by a small nuclear explosion.
- How do I find the mass equivalent to a given amount of energy?
- Rearrange the formula to m = E / c². Enter the energy and leave mass blank, and the calculator solves it for you automatically.
- Why does the answer show scientific notation like 9 × 10¹³?
- Because c² makes these numbers extremely large or, when solving for tiny masses, the energy values are simply huge — scientific notation keeps them readable instead of a long string of digits.
- Does this mean mass turns into energy in everyday life?
- Not directly — this formula describes the theoretical energy equivalent of a mass. It becomes physically relevant in nuclear reactions (fission and fusion), where a tiny fraction of mass is actually converted into a huge release of energy.
- Why must mass be positive?
- Mass represents a physical amount of matter, which cannot be zero or negative — this calculator only accepts a positive value for mass.
- Why are there only two fields, unlike other physics calculators here?
- Because c is a fixed universal constant, not a variable you can solve for — the formula only relates two quantities, energy and mass, so leaving one blank always solves for it from the other.