Work Formula — W = Fd

The work formula W = Fd explained: when a force counts as doing work, the angle factor, units, and a worked example.

W = Fd

Work equals force times distance moved in the direction of the force.

What it means

Work is energy transferred by a force acting through a distance. No motion, no work — pushing with all your might against a wall that does not move does zero mechanical work, however tired you get. Only the force component along the displacement counts, which is why carrying a heavy bag horizontally at constant height does (ideally) no work against gravity. The joule, the unit of work, is the same as the unit of energy — because work and energy are two sides of one transaction.

Variables

Symbol	Name	Unit	Meaning
$W$	Work	J	Energy transferred by the force
$F$	Force	N	Magnitude of the constant force along the displacement
$d$	Distance	m	Distance moved in the direction of the force

Assumptions

Force is constant along the displacement
Force acts parallel to the displacement (otherwise use W = Fd cosθ)
Object treated as a point mass

Derivation

Work is defined as the line integral of force along a path: $W = \int \vec{F}\cdot d\vec{x}$ . For a constant force parallel to a straight displacement, the integral collapses to the product $Fd$ .

Worked example

Problem

You push a box across the floor with a steady horizontal force of 50 N, and it moves 4 m. How much work do you do?

Given:

F = 50 N (horizontal)
d = 4 m (horizontal)

Write the formula: $W = Fd$
Substitute: $W = 50 \times 4$
Multiply: $W = 200\ \mathrm{J}$

200 J of work done on the box

The push transferred 200 joules of energy to the box. If the box speeds up, that energy appears as kinetic energy; if it slides at constant speed against friction, it becomes heat.