Energy Calculator

Kinetic energy (KE) is the energy an object has because of its motion. It is calculated as KE = ½mv², where m is mass (in kg) and v is speed (in m/s); the result is in joules (J). The formula shows that doubling speed quadruples kinetic energy, so speed has a large effect. It applies in classical mechanics; at very high speeds, relativistic effects would be used instead.

Kinetic energy is the energy of motion (KE = ½mv²). Potential energy is stored energy due to position or configuration: gravitational potential energy (PE = mgh) from height, elastic potential energy from a compressed or stretched spring, and chemical potential energy in bonds. Energy can convert between forms—for example, a falling object gains kinetic energy as it loses gravitational potential energy—while the total energy in a closed system stays constant (conservation of energy).

The work-energy theorem says that the net work done on an object equals its change in kinetic energy: W = ΔKE = ½m(v² − v₀²), where v is final speed and v₀ is initial speed. So if you know the mass and the initial and final speeds, you can find the work done (in joules). Conversely, if you know the work done and the initial kinetic energy, you can find the final speed. Friction and other non-conservative forces change mechanical energy; the theorem still holds when all forces are included in the net work.

Potential energy is energy stored due to position or configuration. Gravitational potential energy is PE = mgh, where m is mass in kilograms, g is the gravity you enter in m/s² (about 9.8 near Earth), and h is height in meters. The result is in joules before the result-unit switch. You need to choose a reference level for h (e.g., the ground). Elastic potential energy in a spring is PE = ½kx², where k is the spring constant and x is displacement from equilibrium. Other forms include chemical and electrical potential energy.

The law of conservation of energy says that energy cannot be created or destroyed, only converted from one form to another. In an isolated (closed) system with no external work or heat, the total energy—kinetic, potential, thermal, and any other forms—stays constant. For example, a roller coaster converts gravitational potential energy into kinetic energy as it descends, and some energy may be lost to friction as heat. In physics problems, tracking these conversions and losses helps you solve for speed, height, work, or power.

Inputs are SI. KE = ½mv², gravitational PE = mgh with the g you enter, work = ½m(v₂² − v₁²), energy from power = Pt, thermal energy = mcΔT, electrical energy = VIt, and spring energy = ½kx². A metric result of at least 3,600,000 J is shown as kWh. The BTU result divides joules by 1,055.05585262, the international table BTU. Calories are not a result unit. The joule is the SI unit of energy (BIPM).