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KE = ½mv² · PE = mgh · W = Fd

Kinetic and potential energy calculator

Pick the formula you need — ½mv², mgh or Fd — and the page returns joules, kilojoules and kilocalories with the substituted expression.

Short answer: 2 kg moving at 3 m/s has 9 J of kinetic energy. 10 kg lifted 5 m gains 490.3 J of potential energy, and a 100 N force acting over 2.5 m does 250 J of work.

Which formula to pick

Use ½mv² for anything already moving, mgh for anything raised against gravity, and Fd when you know the force and the distance but not the mass or the speed. The three are interchangeable in mechanics problems — a rollercoaster converts mgh into ½mv² as it descends.

Worked example

A 1,000 kg car at 20 m/s: KE = ½ × 1,000 × 400 = 200,000 J, or 200 kJ. Braking doubles the speed to 40 m/s and the energy becomes 800 kJ — the squared term, and the reason brake fade is a safety issue rather than an inconvenience.

Energy questions

What are the three formulas?

Kinetic energy KE = ½mv², gravitational potential energy PE = mgh and work W = Fd. All three come out in joules when the inputs are kilograms, metres, seconds and newtons.

Why does velocity get squared in kinetic energy?

Because doubling speed quadruples the energy. That is the physics behind braking distances growing far faster than speed, and why a car at 80 km/h needs four times the distance of one at 40 km/h to stop.

What does the height need to be measured from?

Any reference level you choose — the floor, a bench or sea level. Only the difference between two heights matters, so the choice of reference cancels out of any comparison.

How do joules compare with calories?

One thermochemical calorie is 4.184 J, so a 250 kcal snack is about 1,046,000 J. The page shows both, because joules are correct for physics and kilocalories are how food is labelled.

Related tools

Force calculatorF = ma and weight from mass.Unit converterJoules, calories and kilowatt-hours.Speed, distance and time calculatorWhere the velocity in ½mv² comes from.