In science, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.

For example, when a ball is held above the ground and then dropped, the work done by the gravitational force on the ball as it falls is positive, and is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). If the ball is thrown upwards, the work done by the gravitational force is negative, and is equal to the weight multiplied by the displacement in the upwards direction.

Both force and displacement are vectors. The work done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the displacement s is also constant, then the work done is given by: $${\displaystyle W=\mathbf {F} \cdot \mathbf {s} =Fs\cos {\theta }}$$

If the force and/or displacement is variable, then work is given by the line integral:

$${\displaystyle {\begin{aligned}W&=\int \mathbf {F} \cdot d\mathbf {s} \\&=\int \mathbf {F} \cdot {\frac {d\mathbf {s} }{dt}}dt\\&=\int \mathbf {F} \cdot \mathbf {v} dt\end{aligned}}}$$

where ${\displaystyle d\mathbf {s} }$ is the infinitesimal change in displacement vector, ${\displaystyle dt}$ is the infinitesimal increment of time, and ${\displaystyle \mathbf {v} }$ represents the velocity vector. The first equation represents force as a function of the position and the second and third equations represent force as a function of time.

Work is a scalar quantity, so it has only magnitude and no direction. Work transfers energy from one place to another, or one form to another. The SI unit of work is the joule (J), the same unit as for energy.

The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche (On Mechanics), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create energy, only transform it.