Work, energy and power calculator

Five closely related formulas that students mix up constantly. Pick what you are calculating, leave the unknown blank, and the working shows which formula applies and why.

What are you working out?

How these five fit together

Work and energy are the same quantity measured the same way, both in joules. Doing work on something is how you transfer energy to it. Push a box across a floor and the work you do becomes kinetic energy, or heat if friction takes it.

Power is different in kind: it is energy per second, not an amount of energy. A small motor and a large one can do exactly the same work, but the powerful one does it faster. That is the whole distinction, and it is where marks are most often lost.

Quantity	Formula	Unit
Work done	W = F × d	joule (J)
Kinetic energy	Eₖ = ½mv²	joule (J)
Potential energy	Eₚ = mgh	joule (J)
Power	P = E ÷ t	watt (W)
Efficiency	useful ÷ total × 100	percent

Two traps worth knowing. In kinetic energy the v is squared but the ½ is not, so doubling speed quadruples the energy, which is why stopping distances grow so fast. And in work, the distance must be measured along the direction of the force. Carrying a bag horizontally does no work against gravity at all, because the force is vertical and the movement is not.

Common questions

Why is a joule the same for work and energy?: Because they measure the same thing. Work is energy being transferred, so the amount transferred is an amount of energy. One joule is the work done when a force of one newton moves something one metre.
Is this the same as working out my electricity bill?: No, though the physics is the same. This tool works in joules and watts for exam questions. For household energy in kilowatt-hours and appliance costs, use the power, energy and time calculator instead.
What is the difference between a watt and a joule?: A joule is an amount of energy. A watt is one joule per second, so it is a rate. A 60 W bulb uses 60 joules every second it is on.
Can efficiency ever reach 100%?: Not in any real device. Some energy always ends up as heat through friction or resistance. Efficiency above 100% is impossible and always signals a measurement or arithmetic error, since energy cannot be created.
Does height in mgh mean height above the ground?: It means height above whatever reference level the question chooses, which is usually the ground or the lowest point of the motion. What matters is the change in height, so pick a level and stay consistent.