Calculate kinetic energy from mass and velocity, potential energy from mass and height, or both at once.
Kinetic energy is the energy of motion: Eₖ = ½mv², where m is mass in kilograms and v is velocity in metres per second. A 1,000 kg car at 100 km/h (27.8 m/s) carries about 386 kJ of kinetic energy — enough to understand why braking distance grows with the square of the speed.
Potential energy (gravitational) is the energy of position: Eₚ = mgh, where h is the height above a reference point and g is gravitational acceleration. A 70 kg person standing on a 10 m diving board has about 6,867 J of potential energy relative to the water. At the point of impact, all of it has become kinetic energy (in the absence of air resistance).
The total mechanical energy is the sum of the two: E = Eₖ + Eₚ. In a system without friction or air resistance, mechanical energy is conserved — what is lost in potential energy is gained in kinetic energy, and vice versa. This is the principle behind pendulums, roller coasters and orbital mechanics.
Eₖ = ½mv² (joules). Eₚ = mgh (joules). E_total = Eₖ + Eₚ. 1 kJ = 1,000 J.
The SI unit of energy. One joule is the energy needed to move a force of one newton through one metre. A food calorie is about 4,184 joules.
Because the work needed to accelerate an object is proportional to the distance over which the force acts, and that distance grows with velocity. Doubling the speed quadruples the kinetic energy and the braking distance.
Any height you choose — only differences in potential energy are physically meaningful. This calculator uses the height you type as the height above whatever reference you have in mind.
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