The E = mc2 calculator above applies the most quoted equation in physics in both directions. Give it a mass and it returns the rest energy that mass represents. Give it an energy and it returns the mass that energy is equivalent to. The arithmetic is a single multiplication or division, but the constant involved is so large that the results are easy to misread, which is most of what this page is about.
Arb Digital builds free tools that pick one job and finish it properly. This one does the mass-energy conversion and then expresses the answer four ways — joules, electronvolts, TNT equivalent and kilowatt hours — because a number like 90 trillion joules means nothing on its own. The boundary against the site's existing pages is simple: an energy converter rescales an energy you already have between units, while this page derives an energy that was never entered from a mass, and vice versa.
What This Mass Energy Equivalence Calculator Does
In mass-to-energy mode it multiplies a mass by the square of the speed of light. You can enter that mass in tonnes, kilograms, grams, milligrams, pounds or atomic mass units, which covers everything from an industrial quantity down to a single nucleon. The result appears as a headline figure in the most readable SI prefix, with the raw joules, the electronvolt equivalent, the TNT equivalent and the mass in kilograms alongside.
In energy-to-mass mode the division runs the other way. Enter an energy in joules, kilojoules, kilowatt hours, kilotons of TNT, electronvolts or megaelectronvolts, and the headline becomes the mass that energy corresponds to. These figures are startlingly small. A kilowatt hour of electricity, enough to run a fan heater for an hour, is equivalent to about forty billionths of a gram.
Both directions use the exact defined value of the speed of light. Since the 2019 revision of the SI, the metre is defined by fixing that speed, so the number carries no experimental uncertainty at all. The NIST CODATA entry for the speed of light in vacuum gives it as 299,792,458 metres per second and marks the standard uncertainty as exact.
How to Use It
- Choose the direction. Mass to energy is the usual question. Energy to mass is the one that shows how little mass any everyday quantity of energy corresponds to.
- Enter the value in the row that matches. The tool reads only the row for the selected direction, so the other row can be left holding whatever you last used.
- Pick a unit that suits the scale. Atomic mass units for particles, grams for laboratory quantities, tonnes for anything industrial. Megaelectronvolts are the natural energy unit in nuclear physics.
- Read the TNT equivalent for a sense of scale. Joules at this magnitude are meaningless to intuition. Kilotons of TNT are still large but at least comparable to things people have measured.
- Remember this is a ceiling, not a yield. Rest energy is the total energy content if every last bit of mass were converted, which no process on Earth comes close to achieving.
The Formula: How Rest Energy Is Calculated
The relation is E0 = mc2, where m is rest mass in kilograms, c is the speed of light in metres per second and E0 is rest energy in joules. OpenStax University Physics Volume 3, section 5.9 on relativistic energy, states that the rest energy of an object is E0 = mc2, and that this is the energy stored in an object at rest.
Squaring the speed of light gives 8.98755 × 1016 square metres per second squared. Multiplying a one gram mass by that gives 8.98755 × 1013 joules, or about 89.9 terajoules. Dividing by 4.184 × 1012 joules per kiloton of TNT gives an equivalent of roughly 21.5 kilotons, which is close to the yield of the earliest fission weapons. Dividing instead by 3.6 million joules per kilowatt hour gives about 25 million kilowatt hours.
The reverse direction divides. A kilowatt hour is 3.6 × 106 joules, so the equivalent mass is 3.6 × 106 divided by 8.98755 × 1016, which is 4.0 × 10−11 kilograms — forty nanograms. That is the mass a perfect battery would gain when charged with one kilowatt hour, and it is far too small to weigh with any instrument that exists.
Rest Energy Is a Ceiling, Not a Yield
The most common misreading of this calculation is treating the answer as the energy you could get out of a kilogram of something. It is not. It is the total energy content of that mass if the mass were entirely annihilated, which requires matter meeting antimatter and essentially never happens outside a particle accelerator or a very brief moment in a laboratory.
Real processes convert a tiny fraction. Nuclear fission of uranium-235 converts roughly one thousandth of the fuel mass into energy. Fusion of hydrogen into helium, the process powering the Sun, converts about seven thousandths. Chemical reactions such as burning petrol convert something on the order of one part in ten billion, which is why chemical energy densities are so far below nuclear ones and why nobody notices that a burnt log weighs fractionally less than the wood and oxygen that went into it.
This is also why the equation does not imply that everyday objects are dangerous. A one gram paperclip contains 21 kilotons of rest energy in the same sense that the Atlantic Ocean contains a great deal of gold. The quantity is real, and the route to extracting it does not exist.
Mass Is Not Converted Into Energy — It Is Energy
Popular accounts describe mass being converted into energy, as though the two were different substances and one turned into the other. The modern reading is stronger and simpler: mass is a form of energy, and the equation is a statement of units rather than a recipe for transformation. A system's mass is a measure of its total internal energy content divided by c2.
This has a consequence people often find surprising. A hot object weighs marginally more than the same object cold, because the thermal energy contributes to its mass. A compressed spring weighs more than a relaxed one. A nucleus weighs less than the sum of its separate nucleons, and the missing mass is exactly the binding energy holding it together, which is where the energy released in fission and fusion actually comes from.
Nothing about this depends on relativity being exotic. The mass defect of a nucleus is measured routinely with mass spectrometry, and the numbers match the energy released to high precision. If you are working with nuclear masses, the molar mass calculator handles the chemistry side and the weight converter deals with unit changes.
Why Electronvolts Are the Right Unit for Particles
The joule is the coherent SI unit of energy, but it is absurdly large for a single particle. One electronvolt is the energy an electron gains crossing a potential difference of one volt, and since 2019 it is a defined quantity because the elementary charge is a fixed constant. That makes 1 eV exactly 1.602176634 × 10−19 joules.
Particle masses are quoted in energy units for exactly this reason. An electron has a rest energy near 511 kiloelectronvolts, a proton near 938 megaelectronvolts. Dividing those by c2 recovers the mass, which is why particle physicists write masses as MeV/c2 and treat the two as interchangeable. Enter one atomic mass unit into this tool and you get about 931.5 megaelectronvolts, the standard conversion factor used throughout nuclear physics.
What the TNT Equivalent Actually Means
A kiloton of TNT is a defined energy unit, not a measured property of any real explosive batch. By convention one gram of TNT releases 4,184 joules — the same number as a thermochemical kilocalorie, which is not a coincidence — so a kiloton is 4.184 × 1012 joules. Actual trinitrotoluene varies a little around that figure, and the convention exists so that yields can be compared consistently.
Using it here is a scale aid rather than a claim about weapons. It converts a number with no intuitive handle into one that can be compared with events people have heard measured. If you would rather stay in civil units, the kilowatt hour figure does the same job: it puts the answer on the same scale as an electricity bill, which the electricity bill calculator can then price out at a real tariff, and the power converter handles rate units if you want to know how long a given power output would take to deliver it.
Where This Sits Among the Site's Physics Tools
This page derives an energy from a mass through a fixed constant. That is a different job from every other energy tool Arb Digital publishes. The kinetic energy calculator handles energy of motion, which depends on velocity and vanishes when the object stops. The potential energy calculator handles energy of position in a gravitational field, which depends on height and on a choice of reference level. Rest energy depends on neither and never goes away.
For the relativistic neighbours, the time dilation calculator covers what happens to clocks at high speed and the Schwarzschild radius calculator covers the gravitational radius of a mass. On the quantum side, the photon energy calculator gives the energy of a massless particle from its wavelength, which is the one case where mass-energy equivalence gives zero and the energy comes entirely from momentum.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Reading rest energy as an achievable yield — total annihilation is the only process that releases all of it, and no ordinary reaction converts more than a fraction of a per cent.
- Using weight instead of mass — the equation takes mass in kilograms. A pound is a mass unit here, but a reading in newtons or kilograms-force is a force and must be divided by gravity first.
- Forgetting to square the speed of light — using c rather than c squared understates the answer by a factor of three hundred million.
- Applying it to relativistic mass — the m in this equation is rest mass. For a moving object the total energy is larger, and the extra part is kinetic energy rather than rest energy.
- Comparing TNT equivalents across conventions — the kiloton is a defined unit of 4.184 terajoules, so a figure quoted against a different assumed energy density is not directly comparable.
Related Free Tools From Arb Digital
Rescale results with the energy converter, the weight converter and the power converter. For other forms of energy, the kinetic energy calculator and the potential energy calculator cover motion and position, and the photon energy calculator covers light. The time dilation calculator and the Schwarzschild radius calculator handle the rest of the relativistic set, and the molar mass calculator connects atomic masses to laboratory quantities. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
About 8.99 × 10 to the thirteenth joules, or 89.9 terajoules, which is roughly 21.5 kilotons of TNT equivalent or 25 million kilowatt hours. That figure is the total rest energy and assumes complete annihilation, which no ordinary process achieves.
The modern reading is that mass is a form of energy rather than something that converts into it. A system's mass measures its total internal energy divided by the speed of light squared, which is why a hot object is marginally heavier than a cold one.
About 4.0 × 10 to the minus eleventh kilograms, which is forty nanograms. That is the mass a perfect battery would gain on being charged with one kilowatt hour, and it is far below what any instrument can weigh.
Because since the 2019 revision of the SI the metre is defined by fixing the speed of light at 299,792,458 metres per second. It is a defined constant rather than a measured one, so the conversion factor carries no experimental uncertainty.
Rest mass. The equation as written gives the rest energy of an object that is not moving. For a moving object the total energy is higher, and the difference is relativistic kinetic energy, which is a separate calculation.
Roughly 931.5 megaelectronvolts. This is the standard conversion used throughout nuclear physics, and it is why nuclear binding energies and mass defects can be quoted interchangeably in mass units or energy units.
The energy converter rescales an energy you already have between joules, calories, kilowatt hours and other units of the same quantity. This page derives an energy that was never entered, from a mass, using a physical constant rather than a unit factor.
This tool is provided for educational use. The rest energy it reports is a theoretical total, not an achievable output from any real process, and nothing on this page describes how energy could be released from matter.
