By definition, **pressure** is the perpendicular or normal force applied per unit area to a surface. Typical symbols for pressure are P or p. The International Union of Pure and Applied Chemistry (IUPAC) recommends the lowercase letter, but you actually see the capital letter in most formulas in physics, chemistry, and engineering.

### Units of Pressure

Pressure is a derived unit of measurement. The SI unit of pressure is the pascal (Pa) which is newtons per square meter (N/m^{2}). Other common units include pounds per square inch (psi), atmospheres (atm), torr, and millimeters of mercury (mm Hg).

### Pressure Formula

The pressure formula is normal force per unit area.

**Pressure = Force / Area**

**P = F / A**

### Pressure Is a Scalar Quantity

Although the pressure formula includes force, which is a vector quantity, pressure is a scalar quantity. In other words, it has magnitude, but not direction. So, even though we think of pressure as having a direction, it really does not. This is because it’s based on the *normal* component of the force acting on a surface.

For example, if you think of the force of wind pressing against a wall, the pressure depends on the direction of the wind relative to the wall. If the wind strikes the wall straight-on (perpendicular or normal), it exerts a greater pressure than if it strikes the wall at an angle at the same speed. Only the normal component of the force factors into the equation, so it does not actually tell you the direction of the wind!

Another example is the pressure inside an inflated balloon. It does not matter where you measure pressure on the balloon, even though the gas particles within it move in all different directions. Pressure is the net effect of the gas particles colliding with the wall of the balloon.

Usually, pressure is a positive pressure, but negative pressure is also possible. Negative pressure indicates a partial vacuum, which is a measure of relative or gauge pressure. Pull on bulk liquids or solids also acts as negative pressure.

### Simple Pressure Example

A simple example of pressure is cutting fruit with a knife. If you press the flat part of the knife against the fruit, you may mash the fruit, but you won’t cut it. The force is spread out across a large area, so the pressure is low. On the other hand, if you press the blade of the knife against the fruit, it cuts. You exert the same force over a much smaller area, so the pressure is higher.

### Example Pressure Problem

For example, find the pressure acting on a 5 m^{2} surface when a force of 10 N acts upon it.

P = F/A

P = 10 N/5 m^{2}

P = 2 N/m^{2} = 2 Pa

### Gauge Pressure (Gage Pressure)

Gauge pressure is a pressure measurement against ambient air pressure. In other words, it is absolute pressure minute atmospheric pressure. Gauge pressure may be either positive or negative, but usually a positive or negative sign is omitted. Pressure lower than ambient pressure is vacuum pressure.

### References

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*Fluid Mechanics: With Engineering Applications*. New York: McGraw Hill, Inc. ISBN 978-0-07-243202-2. - Giancoli, Douglas G. (2004).
*Physics: Principles With Applications*. Upper Saddle River, N.J.: Pearson Education. ISBN 978-0-13-060620-4. - Imre, A. R. (2007). “How to generate and measure negative pressure in liquids?”.
*Soft Matter under Exogenic Impacts*. NATO Science Series II: Mathematics, Physics and Chemistry. 242. pp. 379–388. doi:10.1007/978-1-4020-5872-1_24 - Knight, Randall D. (2007). “Fluid Mechanics.”
*Physics for Scientists and Engineers: A Strategic Approach*(2nd ed.). San Francisco: Pearson Addison Wesley. ISBN 978-0-321-51671-8.