Energy Calculator

Energy takes many forms, but it is always measured in the same unit, the joule. This calculator works out five common forms: the kinetic energy of something moving, the gravitational potential energy of something raised, the elastic energy stored in a stretched spring, the heat needed to change the temperature of a material, and the electrical energy used by a device over time. It then expresses the result in joules, kilojoules, calories, food Calories, watt-hours, kilowatt-hours, BTU, electronvolts and foot-pounds, so you can compare a moving car with a cup of tea or an hour of heating.

The chart places your result on a logarithmic scale beside familiar amounts such as a food Calorie, a battery and a liter of gasoline.

Kinetic: E = 1 over 212mv²; gravitational: E = mgh; elastic: E = 1 over 212kx²

Heat: E = mcΔT; electrical: E = Pt

m is mass in kilograms, v speed in m/s, g gravitational acceleration, h height, k a spring constant in N/m, x the stretch, c the specific heat in J/(kg·K), ΔT the temperature change, P power in watts and t time in seconds. A temperature change in kelvin equals the same change in degrees Celsius. Each formula gives joules when the inputs are in SI units, which the calculator handles for you.

A moving car. A 1,000 kg car at 72 km/h (20 m/s) carries 200 kJ of kinetic energy, all of which the brakes must turn into heat to stop it.

Lifting a box. Raising 10 kg by 5 m stores 490.332 J, about one-ninth of a food Calorie.

Boiling water. Heating 1 kg of water from 20 °C to 100 °C takes 334.72 kJ, or 0.093 kWh, before any of it turns to steam.

A space heater. 1.5 kW for one hour is 5.4 MJ, exactly 1.5 kWh.

A spring. A 200 N/m spring stretched 10 cm stores 1 J.

The food Calorie on nutrition labels is a kilocalorie. The kilowatt-hour is the unit on electricity bills, the BTU is common for heating and cooling equipment, and the electronvolt is used in atomic and particle physics.

Energy is never created or destroyed, only converted. A falling object turns gravitational potential energy into kinetic energy; a car's brakes turn kinetic energy into heat; a power station turns chemical or nuclear energy into electricity, and a heater turns it back into heat. In practice each conversion loses some energy as heat that is hard to use, which is why efficiencies are below 100%. These formulas let you follow energy through such chains, for example to check how high a dropped ball could bounce or how long a battery could run a motor.

Everyday energies span a huge range. A heartbeat does about a joule of work. A slice of bread provides roughly 300 kJ of food energy, enough in principle to lift an adult up a few hundred meters, though the body converts only part of it into useful work. A typical home in the United States uses on the order of 10,000 kWh of electricity a year, about 36 billion joules, and a full tank of gasoline holds more than a billion joules of chemical energy. Converting everything to the same unit, as this calculator does, is the easiest way to compare such different quantities and to spot an answer that is off by a factor of a thousand.

For problems focused on one form of energy, the kinetic energy calculator and the potential energy calculator solve for any variable, the specific heat calculator handles heating and cooling, and the work and energy calculator connects force, distance and power.