To convert energy into mass, you use Einstein's mass-energy equivalence: E = mc², which rearranges to m = E / c², where c is the speed of light in a vacuum (299,792,458 m/s). Energy and mass are two forms of the same underlying thing, so joules of energy and kilograms of mass are interchangeable through that one equation. Plug any energy value into the formula (after converting it to joules), divide by c², and you get the equivalent mass in kilograms. For everyday amounts of energy the result is vanishingly small because c² is enormous — about 8.99 × 10¹⁶ m²/s² — so an entire kilowatt hour of electricity corresponds to only about 4 × 10⁻¹¹ kg. That is why turning energy into mass in any practical sense only matters inside nuclear reactions, particle colliders, and stellar cores, where enough energy is concentrated in one place for the mass term to become measurable. The other direction — mass into energy — is what powers the Sun and every nuclear reactor on Earth.
The Mass-Energy Equivalence Formula
The formula E = mc² was published by Albert Einstein in 1905 as part of his special theory of relativity. It says that the energy E contained in a mass m at rest equals that mass multiplied by the square of the speed of light. The c² factor is enormous — about 8.99 × 10¹⁶ m²/s² — which is why a tiny amount of mass releases a staggering amount of energy when converted the other way, and why a large amount of energy corresponds to only a minuscule amount of mass when converted this way.
To go from energy to mass you flip the formula:
m = E / c²
Three things matter for the calculation:
- Unit of E. The energy must be in joules (the SI unit of energy), because c is in metres per second and you want m in kilograms. If your value is in calories, kilowatt hours, BTU, or electronvolts, you must first convert it to joules — and that is the step an energy unit converter handles, because the unit list spans roughly 25 orders of magnitude from a sub-attojoule electronvolt to a multi-megajoule kilowatt hour.
- Value of c. The vacuum speed of light is a defined constant: 299,792,458 m/s exactly, so c² ≈ 8.987551787 × 10¹⁶ m²/s².
- Magnitude of the result. The answer is almost always a very small number, usually written in scientific notation so no significant figures are lost.
Run the Energy to Mass Calculation
Here is the exact procedure to convert any amount of energy into its equivalent mass.
- Write down your energy value and the unit it is in. For example, 1 kWh from a utility bill, 2,000 dietary Calories of food energy, or 5 × 10⁶ eV from a particle beam.
- Convert that energy into joules. Use a single base unit. The Energy Converter does this for any of its supported units — J, kJ, cal, kcal, Wh, kWh, BTU, ft·lbf, eV, therm — and shows the joule value. The most common pairings are:
- 1 cal = 4.184 J (thermochemical, what the converter uses)
- 1 kcal = 4,184 J
- 1 Wh = 3,600 J
- 1 kWh = 3,600,000 J
- 1 BTU = 1,055.05585262 J
- 1 eV = 1.602176634 × 10⁻¹⁹ J
- Apply m = E / c². Square c (≈ 8.987551787 × 10¹⁶) and divide E by that number.
- Write the answer in scientific notation if it falls below about 10⁻⁶ kg — anything smaller usually looks cleaner in that form, and the converter itself switches to exponential notation at the extremes for the same reason.
- Double-check the unit you started with. Especially with calories, because the food "Calorie" is really a kilocalorie — a 2,000 Calorie diet is 2,000 kcal = 8,368,000 J, not 2,000 small calories. Mixing those up changes the mass answer by a factor of 1,000.
Worked Example: 1 kWh of Electricity in Mass
One kilowatt hour is a familiar unit — it is what a 1 kW appliance draws if it runs for a full hour. Here is how it converts to mass step by step.
Step 1. The energy in joules. 1 kWh = 3,600,000 J. This is the official, exact relationship: 1 Wh = 3,600 J because a watt is a joule per second and an hour is 3,600 seconds.
Step 2. Apply m = E / c².
m = 3,600,000 ÷ (299,792,458)²
m = 3.6 × 10⁶ ÷ 8.987551787 × 10¹⁶
m ≈ 4.005 × 10⁻¹¹ kg
So 1 kWh of electrical energy is equivalent to about 40 nanograms of mass — roughly the mass of a 40-billionth-of-a-gram speck. You would never register it on a scale, but the equivalence is exact, not approximate. Convert any other energy amount the same way and you get its mass equivalent; a single small calorie drops to about 4.66 × 10⁻¹⁷ kg.
Energy Unit Conversion Factors
Before doing the E = mc² step you almost always need to convert an energy value into joules. The table below lists the exact, officially defined factors the Energy Converter uses to turn any supported unit into joules. With any of these in hand, the conversion to mass is the same single m = E / c² step.
| Energy unit | Symbol | Exact value in joules |
|---|---|---|
| Joule (SI base) | J | 1 |
| Kilojoule | kJ | 1,000 |
| Thermochemical calorie | cal | 4.184 |
| Kilocalorie (food Calorie) | kcal | 4,184 |
| Watt hour | Wh | 3,600 |
| Kilowatt hour | kWh | 3,600,000 |
| British thermal unit (IT) | BTU | 1,055.05585262 |
| Foot pound-force | ft·lbf | 1.3558179483314 |
| Electronvolt | eV | 1.602176634 × 10⁻¹⁹ |
| US therm | thm | 105,480,400 |
The electronvolt row shows why the converter flips to scientific notation at the extremes — 1 eV is about 25 orders of magnitude smaller than 1 kWh, and scientific notation is used at the extremes to keep significant figures intact before you ever reach the mass step.
Two Calorie Traps That Skew the Result
The single most common mistake in energy-to-mass conversions is mixing up the two meanings of "calorie" and the food Calorie. The Energy Converter uses the thermochemical definition, where 1 cal = 4.184 J exactly, and it states that choice up front:
- Small calorie (cal). 1 cal = 4.184 J exactly. Used in chemistry and physics. This is the thermochemical calorie.
- International Table calorie (cal_IT). 1 cal_IT = 4.1868 J. Used in some steam and engineering tables. About 0.067% larger than the thermochemical calorie.
- Food Calorie (kcal, capital C). 1 Calorie = 1 kcal = 1,000 small calories = 4,184 J. This is the value on every US nutrition label.
A snack listed as "200 Calories" therefore holds 200 kcal = 836,800 J, and its mass equivalent via m = E / c² is roughly 9.3 × 10⁻¹² kg. If you accidentally treat the 200 as small calories instead of food Calories, the answer will be off by a factor of 1,000. The converter exposes "cal" and "kcal" as separate units, with kcal labelled "food Calorie" precisely to keep them apart.
When You Actually Need the Energy Converter
For physicists working in a single unit system, the energy-to-mass step is a one-line calculation. For everyone else, almost every practical energy value arrives in a unit that is not the joule: a utility bill in kWh, a nutrition label in kcal, a furnace rating in BTU, a particle-physics paper in eV. The unit conversion is where the errors creep in, especially with the calorie versus Calorie confusion and the kWh ↔ joule 3,600,000 scaling.
The Energy Converter handles that step instantly. You enter the value, pick the source and target units, and it returns the joule equivalent (or any other unit you want) without sending data anywhere — the conversion runs entirely in your browser. Tick "Show all units at once" and you see every supported unit side by side, so you can sanity-check the result against your own estimate before dividing by c². If your energy value came from a frequency — a photon, for instance, where E = h·f — the related guide on converting frequency to energy walks through that first step, and from there the path into mass is the same m = E / c² formula shown above.