How this instrument works
Einstein did not publish this as a headline. It arrived in September 1905 as three pages appended to his relativity paper from that June, titled 'Does the inertia of a body depend upon its energy content?' — and he wrote it backwards, as m = L/c², where L stood for energy radiated away as light. His conclusion was that lamps grow lighter as they shine. No balance in 1905 could resolve shifts that small, and Einstein suspected the effect might stay permanently beyond reach of experiment. Radium salts, he suggested, were the one place worth looking.
What the equation claims is that rest mass is not a different substance from energy but a way of storing it, at an exchange rate of c² — spectacularly steep. Since 1983, when the metre was redefined by fixing light speed at 299 792 458 m/s, that rate has been an exact integer: 89 875 517 873 681 764 joules per kilogram. Hold one gram and you hold 8.99 × 10¹³ J, near enough 21 kilotons, which is what Little Boy yielded over Hiroshima. That comparison flatters fission badly. Converting roughly 0.7 g out of 64 kg of uranium, the device cashed about one part in every thousand it carried; fusion manages 0.7 percent; only matter meeting antimatter collects in full.
Two limits deserve stating plainly. First, this is rest energy alone — bodies in motion carry γmc², and anything massless obeys the wider relation E² = (pc)² + (mc²)², which is how a photon holds energy and momentum with no mass whatever. Second, nothing here gets destroyed. Fuse hydrogen inside a perfectly sealed box, weigh that box afterwards, and it weighs precisely what it did before. Rest mass falls only once photons and neutrinos have escaped, carrying their share across your scale's boundary.
- Enter Rest mass and choose its unit — milligrams or grams for laboratory samples, tonnes when you want an answer in absurd territory.
- Read Rest energy in joules, or switch that field to kWh if you would rather compare against an electricity bill.
- Divide the joules figure by 4.184 × 10¹⁵ to restate it in megatons of TNT, the unit weapons literature uses.
- Particle physicists quote masses the other way round — an electron as 0.511 MeV/c². Convert to kilograms before entering.
- Use a rest value. Anything travelling fast enough to matter needs a γ factor that this sheet deliberately leaves out.
Worked example — rest energy of one kilogram
Set Rest mass to 1 kg. A litre of water, a bag of sugar, a thick paperback — deliberately unremarkable. Substitution needs one multiplication: E = 1 × 299 792 458² = 89 875 517 873 681 764 J. Every digit of that is exact, because light speed is a defined constant rather than a measured one, so whatever uncertainty appears in your answer came off your scale.
Restated, 8.99 × 10¹⁶ J is 24.96 billion kilowatt-hours, enough to run about 2.3 million average American homes for a year. Detonated rather than metered, it is 21.5 megatons — well under half a Tsar Bomba. Nothing in engineering comes close to extracting it: burning a kilogram of petrol yields 4.6 × 10⁷ J, nine orders of magnitude short, and the exhaust weighs half a nanogram less than what went in.
Questions
Does this work for something moving?
Only for bodies at rest. Total energy of a moving object is γmc², where γ = 1/√(1 − v²/c²), so E = mc² is simply the v = 0 case. At one tenth of light speed γ reaches 1.005, half a percent high; at nine tenths it is 2.29. Below roughly 3000 km/s the correction stays under one part in 20 000, which covers every satellite, bullet and centrifuge you are likely to meet.
Why does c² come out as an exact integer?
Because c is defined, not measured. The 17th General Conference on Weights and Measures fixed light speed at exactly 299 792 458 m/s in 1983 and rebuilt the metre around that number, so squaring it gives 89 875 517 873 681 764 m²/s² with no error bar whatever. Any uncertainty in your result traces back to the mass you typed, and nowhere else.
Is mass really converted into energy?
That phrasing causes more confusion than it clears. Mass is a form of energy, so nothing changes species. What happens in a nuclear reaction is that the system's rest mass drops because binding energy departs as radiation and as kinetic energy of fragments. Total energy is conserved throughout, and so is total mass, provided you draw your boundary wide enough to keep every escaping photon inside it.
Does charging a battery make it heavier?
Yes, by an amount no laboratory can weigh. A 100 Wh laptop cell stores 3.6 × 10⁵ J, which divided by c² is 4 × 10⁻¹² kg — four nanograms. Best mass comparators resolve near a tenth of a microgram, some 25 000 times coarser. A wound clock spring, a compressed gas cylinder and a hot cup of tea are all fractionally heavier than their relaxed, cold selves for exactly this reason.
Has anyone tested E = mc² directly?
Yes, to about four parts in ten million. A 2005 experiment led by Simon Rainville compared two quantities measured by entirely separate means: gamma-ray energies released when sulphur-32 and silicon-29 nuclei capture a neutron, against corresponding mass differences weighed in a Penning ion trap. They agreed within 0.00004 percent. Less directly, every accelerator on Earth depends on this relation holding, which is why particle masses get quoted in MeV/c² — energy is what those machines actually see.
Where does a proton's mass come from?
Not mostly from its quarks. Adding up rest masses of two up quarks and one down quark accounts for around one percent of a proton's 938.272 MeV/c². Remaining 99 percent is field energy of the gluons and confined motion of quarks inside, appearing as mass through precisely this relation. Almost all of your body weight, then, is binding energy wearing a disguise.