Work done calculator: W = Fs with working

Example: you push a box with a force of 50 N for 3 m. $W = 50 \times 3 = 150$ J.

• Lifting: lifting a 20 N bag up 1.5 m does $20 \times 1.5 = 30$ J of work against gravity, the same as the gravitational potential energy it gains.
• Braking: a car's brakes do 300,000 J of work over 50 m. The braking force is $300000 \div 50 = 6000$ N.
• Distance in cm: a 12 N force moves an object 40 cm. Convert first: 0.4 m, so $W = 12 \times 0.4 = 4.8$ J.

If the object doesn't move, no work is done, however hard you push: holding a heavy box still involves effort but zero distance. Work is also zero when the force is at right angles to the motion, like the upward force on a bag you carry along a level corridor.

Work done against friction warms the surfaces (energy is dissipated as heat). Dividing work done by the time taken gives power: our power calculator does that. For lifting, the work done equals the gain in gravitational potential energy, which our GPE calculator works out from mass and height.

• Using the total distance when the force only acts for part of it.
• Using mass (kg) instead of weight (N) when lifting: multiply by $g$ first.
• Leaving distance in cm or km.

Practise with our work done questions.

• State the equation, substitute, then give the answer with its unit (J).
• When a force acts against motion (friction, braking), the work done is the energy dissipated.
• For lifting, $W = Fs$ with $F$ the weight gives the same answer as $E_p = mgh$: use whichever fits the data.
• Keep track of kJ: 1 kJ = 1,000 J. A car's brakes typically do hundreds of thousands of joules of work.