Work, Energy and Power Formulas
Work, energy and power explained: W = Fd, P = W/t, units like joules and watts, efficiency, and worked examples from lifting boxes to climbing stairs.
Key takeaways
- Work is force times distance moved in the direction of the force: W = Fd.
- Power is how fast work is done: P = W ÷ t, measured in watts.
- Efficiency = useful energy output ÷ total energy input.
On this page
In physics, “work” has a precise meaning: energy transferred when a force moves something. Power tells you how quickly that happens.
Work
W = F × d
- F = force (N)
- d = distance moved in the direction of the force (m)
- W in joules (J)
Holding a heavy bag still does no work in the physics sense, because nothing moves. If the force is at an angle, use W = F d cos θ.
Energy
Work transfers energy. Lifting a box gives it gravitational potential energy; pushing a cart gives it kinetic energy. See kinetic vs potential energy.
Power
P = W ÷ t
- P in watts (W); 1 W = 1 J/s
Two people climbing the same stairs do the same work, but the faster one is more powerful.
Worked example
A 60 kg person climbs 3 m of stairs in 4 s. Work = mgh = 60 × 9.81 × 3 ≈ 1,766 J. Power = 1,766 ÷ 4 ≈ 441 W.
Efficiency
Efficiency = useful output ÷ total input × 100%. No machine is 100% efficient; some energy becomes heat, often through friction.
Electrical power
In circuits, P = V × I; see our Ohm’s law calculator.
Summary
| Quantity | Formula | Unit |
|---|---|---|
| Work | W = Fd | Joule (J) |
| Power | P = W/t | Watt (W) |
| Efficiency | useful ÷ total | % |
Heating is another energy transfer; see specific heat capacity. Hydraulic machines trade force for distance, as explained in our guide to pressure.
Frequently asked questions
What is the difference between work and power?
Work is energy transferred; power is the rate of transfer.
What is a kilowatt-hour?
A unit of energy: 1 kW for one hour = 3.6 million joules, used on electricity bills.
Can work be negative?
Yes, when the force opposes the motion, like friction slowing an object.
Sources
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