Working back to the force
The formula does not work in one direction only. Given the pressure and the area, it can be rearranged to find the force.
Rearranging the formula
force = pressure × area
Obtained by multiplying both sides of pressure = force ÷ area by the area.
The problem
A heap of soil collected over an area of 8 square metres of ground produces a pressure of 150 Pa on the ground. What is the force exerted on the ground by the heap of soil?
The solution
pressure = 150 Pa = 150 N m−2
area = 8 m2
force = 150 N m−2 × 8 m2 = 1200 N
Checking with the units
Multiplying N m−2 by m2 cancels the m−2 against the m2 and leaves N alone. The answer comes out as a force, so the units themselves confirm the working.
The formula three ways
- pressure = force ÷ area
- force = pressure × area
- area = force ÷ pressure