Force-displacement graph

A force-displacement graph measures:

• The force applied in newtons, , on the y-axis
• The displacement in metres, , on the x-axis

Area under the graph

The area under a force-displacement graph gives the work done, in joules, .

That’s because , and the area under the graph is just the force multiplied by the distance (because the two axis multiply when finding the area).

Units of the area

To find the area under the graph, we multiply the force (in newtons, ) by the displacement (in metres, ).

That gives us newton-metres, .

If we look at the SI units of newton-metres:

One joule is defined as .

So the units are the same! That shows us that the area under the graph must be in joules, , so represents the work done (or energy transferred).