Home › Calculators › E=mc² Calculator
E=mc² Calculator
Convert mass to its rest energy with Einstein’s E = mc², or find the mass equivalent of any amount of energy. Results come in joules, kilowatt-hours, electronvolts and tons of TNT, with every unit listed in the tables.
Last updated:
Convert
Scientific notation works: 9.109e-31
Enter your values to see the result.
Advertisement
Advertisement
How to use the E=mc² Calculator
- Choose the direction: mass to energy or energy to mass.
- Enter the value (scientific notation like 9.109e-31 works).
- Pick the unit from the list.
- Read the result and the step-by-step working.
- Use the tables for every other unit, or copy or download them.
The mass–energy formula
E = m c² and, rearranged, m = E / c²
With E in joules, m in kilograms and c = 299,792,458 m/s exactly, c² = 8.987551787 × 10¹⁶ m²/s². So every kilogram of mass is equivalent to about 89.9 petajoules.
Reference values
| Mass | Rest energy | Other units |
|---|---|---|
| Electron (9.109 × 10⁻³¹ kg) | 8.187 × 10⁻¹⁴ J | 0.511 MeV |
| 1 atomic mass unit (1.6605 × 10⁻²⁷ kg) | 1.492 × 10⁻¹⁰ J | 931.494 MeV |
| Proton (1.6726 × 10⁻²⁷ kg) | 1.503 × 10⁻¹⁰ J | 938.272 MeV |
| 1 microgram | 8.988 × 10⁷ J | ~25 kWh |
| 1 gram | 8.988 × 10¹³ J | ~21.5 kt TNT |
| 1 kilogram | 8.988 × 10¹⁶ J | ~21.5 Mt TNT |
Unit conversions used
| Unit | In joules |
|---|---|
| 1 kWh | 3.6 × 10⁶ J |
| 1 eV | 1.602176634 × 10⁻¹⁹ J (exact) |
| 1 kcal | 4,184 J |
| 1 ton of TNT | 4.184 × 10⁹ J (convention) |
| 1 BTU (IT) | 1,055.056 J |
Frequently asked questions
What does E = mc² mean?
It states that mass and energy are equivalent: a mass m at rest contains energy E equal to m times the speed of light squared. Because c² is about 9 × 10¹⁶ m²/s², a tiny mass corresponds to an enormous energy.
How much energy is in 1 gram of mass?
1 g × c² = 8.988 × 10¹³ J, about 25 million kWh or 21.5 kilotons of TNT.
What is the rest energy of an electron?
The electron mass 9.109 × 10⁻³¹ kg gives 8.187 × 10⁻¹⁴ J, which is 0.511 MeV. A proton's rest energy is about 938.3 MeV, and 1 atomic mass unit is 931.494 MeV.
Is the full mass converted in nuclear reactions?
No. Fission of uranium-235 converts roughly 0.1% of the fuel mass into energy and hydrogen fusion in stars about 0.7%. Only matter–antimatter annihilation converts all of the rest mass.
What is a ton of TNT in joules?
By convention, 1 ton of TNT = 4.184 × 10⁹ J (4.184 GJ). A kiloton is 4.184 × 10¹² J and a megaton 4.184 × 10¹⁵ J.
Does this include kinetic energy?
No. E = mc² gives the rest energy. A moving object has total energy γmc², where γ = 1/√(1 − v²/c²); the extra (γ − 1)mc² is its kinetic energy.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
Related tools
Photon Energy CalculatorPhoton energy in eV and joules from wavelength or frequency, with momentum and color.Kinetic Energy CalculatorSolve KE = ½mv² and PE = mgh for energy, mass, speed or height, with unit conversions.Potential Energy CalculatorGravitational PE = mgh and spring PE = ½kx²: solve for energy, mass, height, k or stretch.Orbital Period CalculatorOrbital period from central mass and semi-major axis with Kepler's third law and presets.Speed Distance Time CalculatorSolve for speed, distance or travel time and get your arrival time.Half Life CalculatorSolve radioactive decay for amount left, half-life, time or initial amount, with a curve.Projectile Motion CalculatorRange, max height, flight time and impact speed of a projectile, with an animated trajectory.Free Fall CalculatorFall time and impact velocity from a height, or height from time or speed, with a chart and table.Meeting Cost CalculatorWork out what a meeting really costs from attendees and salaries, with a live cost ticker.Velocity CalculatorSolve v = d/t and a = Δv/t for any variable, plus a SUVAT solver for any three kinematics values.Torque CalculatorSolve τ = r·F·sin θ for torque, force, lever arm or angle, and convert torque to power at any rpm.Wavelength Frequency CalculatorConvert frequency to wavelength and back for light, radio or sound, with photon energy and band.Acceleration CalculatorAcceleration from velocity change and time, distance and time, or force and mass.Force CalculatorSolve F = ma for force, mass or acceleration, plus weight on every planet.Density CalculatorSolve density, mass or volume with unit conversion and a table of common material densities.Momentum CalculatorCalculate momentum (p = mv), mass, velocity, impulse and momentum change with unit conversion.Power CalculatorCalculate power from work and time, force and velocity, or volts and amps, in W, kW and hp.PPI CalculatorPixel density (PPI), dot pitch and retina viewing distance from resolution and screen size.Download Time CalculatorHow long a file takes to download at your internet speed, or the speed you need.Pressure CalculatorSolve P = F/A for pressure, force or area in Pa, kPa, bar, psi and atm.Work CalculatorSolve W = F·d·cos θ for work, force, distance or angle in J, kWh and ft-lb.Hooke's Law CalculatorSolve F = kx for spring force, spring constant or extension, plus stored spring energy.Centripetal Force CalculatorCentripetal force and acceleration from mass, radius and speed or RPM: F = mv²/r.Gravitational Force CalculatorNewton's law of gravitation F = Gm₁m₂/r² for any two masses, with planet presets.Speed of Sound CalculatorSpeed of sound from air temperature or medium, and distance from an echo or thunder delay.Doppler Effect CalculatorObserved frequency from source and observer speeds, or source speed from a pitch shift.Specific Heat CalculatorSolve Q = mcΔT for heat energy, mass, specific heat or temperature change, with materials.Decibel CalculatorAdd dB levels, convert power or voltage ratios to dB, and find sound level at a distance.Bernoulli Equation CalculatorSolve Bernoulli's equation for pressure, velocity or height, with pipe continuity and flow.Buoyancy CalculatorBuoyant force from fluid density, volume and gravity, with a float or sink check.Escape Velocity CalculatorEscape and orbital velocity for any planet, moon or custom mass and radius.Friction Force CalculatorStatic and kinetic friction from material presets, normal force or mass and incline angle.Inclined Plane CalculatorForces, acceleration and push force for a mass on a slope with friction.Light Travel Time CalculatorHow long light or radio takes to reach the Moon, Sun, Mars, Voyager 1 or any distance.Pendulum Period CalculatorPendulum period and frequency from length and gravity, or length from period.Snell's Law CalculatorRefraction angle, critical angle and total internal reflection from n₁, n₂ and the angle.Speeds and Feeds CalculatorSpindle RPM and feed rate (mm/min, in/min) from tool size, flutes, surface speed and chip load.Terminal Velocity CalculatorTerminal velocity and time to 95% from mass, drag coefficient, area and air density.Water Heating Time CalculatorHow long to heat water: time, energy and cost from volume, temperatures and heater power.Wave Speed CalculatorSolve v = f × λ, find wave speed from distance and time, or from string tension and density.Thin Lens Equation CalculatorSolve 1/f = 1/do + 1/di for any value, with magnification, image type and a ray diagram.Time Dilation CalculatorLorentz factor, dilated time and length contraction from speed and proper time.Displacement CalculatorDisplacement from velocity and time, s = ut + ½at², or start and end coordinates, with steps.Kinematics Calculator (SUVAT)Enter any 3 of s, u, v, a and t to solve the other 2 with the SUVAT equations shown.3D Printer Filament Length CalculatorFilament weight to length and back for PLA, PETG, ABS and more, plus spool remaining.Fuel Injector Size CalculatorInjector size in lb/hr and cc/min from target horsepower, BSFC, cylinders, duty cycle and fuel.Hull Speed CalculatorTheoretical displacement hull speed from waterline length, in knots, mph and km/h.OEE CalculatorOverall equipment effectiveness from time, ideal cycle time and counts: A × P × Q.Scuba Air Consumption CalculatorSAC and RMV from a logged dive, then gas needed, turn pressure and bottom time for the next.Takt Time CalculatorTakt time from available time and demand, plus stations needed and a bottleneck check.Wind Turbine Power CalculatorWind turbine power output and annual kWh from rotor size, wind speed, air density and Cp.Air Density CalculatorMoist air density in kg/m³ and lb/ft³ from temperature, pressure or altitude, and humidity.Angular Velocity CalculatorFind angular velocity in rad/s, deg/s and RPM from angle and time, RPM or linear speed.Antipode MapFind the exact opposite point on Earth for any place, shown on a dual map with land or ocean.Average Velocity CalculatorAverage speed and average velocity over several trip segments, with displacement and direction.Barometric Pressure TodayCurrent air pressure near you with a rising or falling trend and a 48-hour chart in hPa or inHg.Carbon Dating CalculatorEstimate age from percent carbon-14 remaining or activity, or find C-14 left after any age.Coulomb's Law CalculatorElectrostatic force between two charges, attractive or repulsive; solve for charge or distance.Cpk CalculatorCp, Cpk, Pp, Ppk and ppm out of spec from your data or mean and standard deviation.Crosswind Component CalculatorCrosswind and headwind/tailwind components for any runway and wind, with gusts and a diagram.Drag Force CalculatorAerodynamic or hydrodynamic drag force and power from Cd, frontal area, speed and density.E85 Blend CalculatorHow many gallons of E85 and gas to add to hit a target ethanol blend like E30 or E50.Elastic Collision CalculatorGet final velocities after a 1D elastic collision, with momentum and kinetic energy checks.G-Force CalculatorCalculate g-force from turn speed and radius, a speed change over time, or any acceleration.Heat Transfer CalculatorConduction heat flow in W and BTU/h through one or more layers, with R-value and U-value.Helium Balloon Lift CalculatorHow much a helium balloon lifts in grams and how many balloons you need for a payload.Hydrostatic Pressure CalculatorGauge and absolute pressure at any depth in water, seawater, oil or a custom fluid.Impact Force CalculatorAverage impact force and g-force from mass, drop height or speed, and stopping distance/time.