How To Calculate Work

Work in physics is done when a force moves an object through a distance. The formula is force multiplied by distance, so pushing with two hundred and fifty newtons for twelve metres does three thousand joules of work.

Both ingredients are essential. A force with no movement does no work at all, which is why holding a heavy box still is exhausting but physically zero work. Conversely, movement with no force, such as a body drifting in space, also counts as no work.

The distance must be measured along the direction of the force. If you push at an angle, only the component of the force along the direction of travel does work. Pushing a trolley downwards as well as forwards does no useful work with the downward part.

This is why carrying a suitcase along a level corridor does no work on the suitcase in the physics sense. The force you exert is upward, the motion is horizontal, and the two are at right angles, so the component of force along the motion is zero.

Work is measured in joules, the same unit as energy. That is not a coincidence: work is energy being transferred. Doing three thousand joules of work on an object gives it three thousand joules of energy, whether as motion, height or heat.

The joule is a small unit. One joule is roughly the energy needed to lift an apple by a metre. Lifting a twenty kilogram suitcase onto a shelf two metres high takes about four hundred joules, so everyday tasks run to hundreds rather than millions.

Power is work divided by time, which is why the same work can be done slowly with little power or quickly with a lot. Pushing a car a hundred metres in a minute needs far more power than doing it over ten minutes, though the work is identical.

Negative work is meaningful and useful. Friction does negative work on a sliding object, removing kinetic energy and turning it into heat. A brake does negative work, which is exactly what braking is for.

Work and kinetic energy are linked by the work energy theorem: the net work done on an object equals its change in kinetic energy. That single statement solves many problems without ever writing down a time variable.

Lifting is the cleanest example. Raising a mass against gravity requires a force equal to its weight, so the work is mass times gravity times the height gained. This is also the potential energy the object gains, which is why the two formulas look identical.

Finally, be careful with units. Force in newtons times distance in metres gives joules. If the distance is in centimetres, convert it, or the answer will be out by a factor of a hundred, and that kind of slip is invisible in the final number.