Einstein’s 1905 equation is the most famous exchange rate in science: mass and energy are the same currency, converted at c² — a rate so steep that a kilogram of anything holds more energy than a city uses in days. This E = mc² calculator converts any mass into its full rest energy in joules, kilowatt-hours and TNT equivalents, and runs in reverse to show how little mass a familiar energy represents.
The Exchange Rate
E = mc², with c = 299,792,458 m/s, so c² ≈ 8.988 × 10¹⁶ J/kg. The default runs it on one kilogram: E = 8.988 × 10¹⁶ joules — about 2.5 × 10¹⁰ kilowatt-hours (a mid-size country’s electricity for days), or 21.5 megatons of TNT. Scale down and the rate stays absurd: one gram of mass is 21.5 kilotons; a single paperclip’s worth of matter, fully converted, out-yields the Hiroshima bomb. The equation’s shock is entirely in the constant — mass is energy at an exchange rate of ninety quadrillion joules per kilogram, which is why the mass side of everyday transactions never visibly moves.
What “Fully Converted” Actually Happens
No real process converts matter wholesale except matter–antimatter annihilation, which converts 100 percent (and is why antimatter is the ultimate rocket fuel and the ultimate storage problem). Nuclear fission releases about 0.09 percent of the fuel’s mass-energy (a uranium nucleus keeps nearly all its mass as fission fragments); fusion manages about 0.7 percent (hydrogen to helium, the Sun’s trade); chemical reactions release mass fractions around 10⁻¹⁰ — burning a kilogram of petrol lightens the products by roughly 5 × 10⁻¹¹ kg, far below any scale’s notice. E = mc² prices the ceiling; each technology’s efficiency is the fraction of that ceiling its physics permits it to touch.
The Sun, Audited by This Equation
The Sun converts about 4.3 million tonnes of mass into energy every second — run it through this calculator in reverse (its luminosity, 3.8 × 10²⁶ W, divided by c²) — and has done so for 4.6 billion years without noticeably slimming: the total spent is under 0.03 percent of its mass. That bookkeeping is the equation’s first great triumph: before it, the Sun’s age was a geological scandal (no chemical or gravitational energy source lasts long enough); after it, the books balanced. Every star is a slow, audited leak of mass into light, at precisely c² per kilogram. The same audit runs on Earth in miniature: a nuclear power station’s fuel emerges from the reactor measurably lighter than it entered, by exactly the mass of the electricity and heat it sold — utilities have been invoicing E = mc², at fission’s modest fraction, all along.
Mass You Can Weigh: The Reverse Direction
Run backwards, the equation says energy itself has mass: a system holding energy E outweighs the same system without it by E/c². A charged phone battery is heavier than a discharged one by about 10⁻¹³ kg; a kettle of boiling water outweighs its cold self by roughly 10⁻¹¹ kg; a compressed spring outweighs a relaxed one. All immeasurably small and all real — and in particle physics, where the masses are attograms, the same arithmetic is the daily bread: particle masses are quoted in energy units (MeV/c²) because at that scale the conversion is not philosophy but lab practice.
What the Equation Does Not Say
It does not say mass can be “turned into” energy as a special trick of bombs: the equivalence is universal and always on — a hot object, a wound clock, a charged capacitor all carry their energy as mass. It does not power stars by “converting hydrogen away”: fusion rearranges nucleons into slightly lighter nuclei, and the difference is what radiates. And E = mc² in this form is the rest energy: a moving object carries more (the full relation is E² = (pc)² + (mc²)², the bridge to the length-contraction and relativistic-energy pages of this hub).
Common Mistakes
Using c in km/s inside an SI calculation and losing ten orders of magnitude. Quoting a fission yield as “the energy in uranium” without the 0.09 percent efficiency honesty. Confusing kilotons with megatons across the gram/kilogram boundary (a factor of a thousand lives there). And treating TNT equivalents as blast predictions — they compare energy totals only; how fast the energy arrives is a different, grimmer science.
Related Tools
The relativity shelf continues in the Physics Calculators hub — the Length Contraction Calculator covers motion’s other famous effect, and the Kepler’s Third Law Calculator weighs the stars that spend this energy.
Frequently Asked Questions
How much energy is in 1 kg of mass?
E = mc² = 1 × (2.998 × 10⁸)² ≈ 8.99 × 10¹⁶ joules — about 25 billion kilowatt-hours, or 21.5 megatons of TNT, if every last atom were converted. Real nuclear fission releases under a thousandth of that per kilogram of fuel.
How much energy is in 1 gram?
About 8.99 × 10¹³ joules — 21.5 kilotons of TNT equivalent, comparable to a wartime atomic bomb’s yield, from a paperclip’s mass. The c² conversion rate is why mass is such concentrated energy.
Does burning fuel convert mass to energy?
Yes, immeasurably little: chemical reactions release about 10⁻¹⁰ of the mass as energy, so burning a kilogram of petrol lightens the products by tens of nanograms. The equation applies to chemistry too — the fraction is just minuscule.
How much mass does the Sun lose per second?
About 4.3 million tonnes per second, from its luminosity divided by c². Over 4.6 billion years that totals under 0.03 percent of the Sun’s mass — fusion is lavish with energy and stingy with mass.
Is a charged battery heavier?
Yes — by E/c², roughly 10⁻¹³ kg for a phone battery. Real, exact, and twelve orders of magnitude below weighing. In particle physics the same equivalence is practical: masses are quoted in MeV/c².
What is the full relativistic energy equation?
E² = (pc)² + (mc²)², where p is momentum. For an object at rest p = 0 and it collapses to E = mc² — the rest energy this calculator computes.