What Is the Formula Relating Pressure, Force and Area?

Pressure is calculated as force per unit area. The formula is written as pressure equals force divided by surface area. The unit for pressure, Pascal, can also be written as newtons per square meter based on this relationship.

The pressure exerted by an object is directly proportional to the force being applied by the object, but inversely proportional to the surface area that the force is being applied to. Decreasing the surface area over which the force needs to be applied results in a smaller amount of force being exerted to do the same amount of work as applying a large force over a large surface area.

For example, the effectiveness of a knife depends on how sharp the blade is because the sharpness of the blade is determined by how small the contact surface area of the knife is. A small contact surface area will require the use of less force to slice through an object. A dull knife has a bigger surface area that is in contact with the object that needs to be sliced and therefore requires more force to achieve the same result as a sharp knife.This is a less efficient use of energy compared to the sharp knife.

Similarly, when giving an injection, the sharpness of the needle determines how much force needs to be applied in order to penetrate the skin. A sharper needle has a smaller surface area that comes in contact with the skin, which means that less force is required for penetration of the needle through the skin. A dull needle results in a more painful injection because greater force is required for the needle to penetrate the skin.