Pressure is force divided by area
Pressure is the amount of force pushing on a surface, spread across that surface. The formula is straightforward: pressure equals force divided by area. If you push with 100 pounds of force on a surface that is 10 square inches, the pressure is 10 pounds per square inch (PSI). The same force spread over a larger area creates less pressure; the same force on a smaller area creates more pressure.
The units you use depend on what you are measuring. In the United States, pressure is often measured in PSI (pounds per square inch) or atmospheres. In science and most other countries, the standard unit is the pascal (Pa), where one pascal equals one newton of force per square meter. You will also see bars, millibars, and kilopascals in weather reports and industrial settings.
Understanding which unit to use matters because a number without a unit is meaningless. Saying "the pressure is 14.7" tells you nothing until you add "PSI" or "pascals" or "atmospheres".
Key Takeaways
- Pressure equals force divided by area: P = F ÷ A, and the result depends entirely on what units you use for force and area.
- PSI (pounds per square inch) is common in the United States; pascals are the scientific standard; atmospheres and bars appear in weather and industrial work.
- The same force on a smaller area always produces higher pressure, which is why a knife cuts better than a flat hand.
- Gauge pressure measures the difference between absolute pressure and atmospheric pressure, while absolute pressure includes the weight of the air above.
The basic pressure formula and how to use it
The formula for pressure is P = F ÷ A, where P is pressure, F is force, and A is area. To use it, you need two pieces of information: the force being applied and the area over which it is applied. Both must be in matching units.
If you are working in metric, measure force in newtons and area in square meters. One newton is the force needed to accelerate one kilogram at one meter per second squared. If you are working in pounds and inches, measure force in pounds and area in square inches. The result will be PSI.
Example: A 150-pound person stands on a floor wearing shoes with a total contact area of 50 square inches. The pressure on the floor is 150 ÷ 50 = 3 PSI. If that same person stands on one foot (25 square inches), the pressure doubles to 6 PSI, even though the force has not changed.
Converting between pressure units
Once you have calculated pressure in one unit, you may need to convert it to another. The most common conversions are between PSI, pascals, bars, and atmospheres.
| From | To | Multiply by |
|---|---|---|
| PSI | Pascals | 6,894.76 |
| Pascals | PSI | 0.000145 |
| Atmospheres | PSI | 14.696 |
| PSI | Atmospheres | 0.068046 |
| Bars | PSI | 14.504 |
| PSI | Bars | 0.068948 |
Standard atmospheric pressure at sea level is 14.696 PSI, 101,325 pascals, 1 atmosphere, or 1.01325 bars. These are all the same pressure, just expressed in different units. Knowing this reference point helps you check whether your answer makes sense.
Absolute pressure versus gauge pressure
Absolute pressure is the total pressure exerted by a gas or liquid, including the weight of the atmosphere above it. Gauge pressure is the difference between absolute pressure and atmospheric pressure. Most pressure gauges on everyday equipment (tire gauges, water pressure gauges) read gauge pressure, not absolute pressure.
If a tire gauge reads 32 PSI, that is gauge pressure. The absolute pressure inside the tire is 32 + 14.7 = 46.7 PSI (assuming sea level). The 14.7 PSI is the atmospheric pressure pushing on the outside of the tire. When you see a pressure reading without the word "absolute" or "gauge," it is usually gauge pressure in practical settings and absolute pressure in scientific contexts.
This distinction matters when you are calculating pressure in closed systems or working with gases. In most everyday situations — checking tire pressure, measuring water pressure in a home — you are working with gauge pressure and do not need to add atmospheric pressure.
Pressure in liquids and gases
Pressure in a liquid increases with depth because the weight of the liquid above pushes down. The formula is P = ρgh, where ρ (rho) is the density of the liquid, g is the acceleration due to gravity (9.81 meters per second squared), and h is the depth in meters. The result is in pascals.
For water, which has a density of 1,000 kilograms per cubic meter, the pressure at 10 meters deep is 1,000 × 9.81 × 10 = 98,100 pascals, or about 0.97 atmospheres. At 100 meters deep, the pressure is 981,000 pascals, or about 9.7 atmospheres. This is why deep-sea diving requires special equipment and training.
Gas pressure works differently. In a sealed container, gas pressure depends on the number of gas molecules, the temperature, and the volume of the container. This relationship is described by the ideal gas law: PV = nRT. For most practical purposes, you do not need to calculate gas pressure from first principles; you measure it with a gauge.
Real-world examples of pressure calculations
A hydraulic jack lifts a car by explore force to a small piston, which creates high pressure in oil, which pushes a larger piston underneath the car. If the small piston has an area of 1 square inch and you push with 100 pounds of force, the pressure in the oil is 100 PSI. If the large piston has an area of 10 square inches, the force it exerts is 100 × 10 = 1,000 pounds. You have traded distance (the small piston moves farther) for force (the large piston moves less but pushes harder).
A bicycle tire pump compresses air into a smaller and smaller space as you push the handle down. The force you explore (your arm strength) is divided by the shrinking area of the air inside the pump, creating higher and higher pressure until the pressure inside the pump exceeds the pressure inside the tire, and air flows into the tire.
A weather report might say atmospheric pressure is 1,013 millibars. This is the weight of all the air above a given point, spread across the surface. High pressure systems (above 1,013 millibars) usually bring clear weather; low pressure systems (below 1,013 millibars) usually bring clouds and rain.
Common mistakes when calculating pressure
The most common mistake is forgetting to match units. If you measure force in pounds but area in square centimeters, your answer will be meaningless. Always convert to matching units before dividing. Write down the units at every step so you can catch errors.
The second mistake is confusing gauge pressure with absolute pressure. If a problem asks for absolute pressure and you forget to add atmospheric pressure, your answer will be off by 14.7 PSI (or 101,325 pascals). Read the problem carefully to see which one is being asked for.
The third mistake is using the wrong formula for the situation. Pressure from a point force (P = F ÷ A) is different from pressure in a liquid column (P = ρgh) or pressure from a gas (PV = nRT). Identify what you are measuring before you choose a formula.
Frequently Asked Questions
What is the difference between force and pressure?
Force is a push or pull measured in newtons or pounds. Pressure is that force spread over an area, measured in pascals or PSI. The same force creates different pressures depending on the area. A 100-pound force on 1 square inch creates 100 PSI; the same 100-pound force on 10 square inches creates only 10 PSI.
Why does a sharp knife cut better than a dull one?
A sharp knife has a thinner edge, so the same downward force is concentrated on a smaller area, creating higher pressure at the blade. Higher pressure cuts through material more easily. A dull knife spreads the force over a larger area, creating lower pressure and requiring more effort to cut.
How do I measure pressure if I do not have a gauge?
You cannot measure pressure directly without a gauge or sensor. However, you can calculate it if you know the force and area. For liquids, you can calculate pressure from depth using P = ρgh. For gases in a sealed container, you would need to know temperature and volume to use the ideal gas law.
What does PSI stand for?
PSI stands for pounds per square inch. It is the pressure created by one pound of force applied to one square inch of area. It is the most common pressure unit in the United States for tires, water systems, and industrial equipment.
Is atmospheric pressure the same everywhere?
Atmospheric pressure changes with altitude and weather. At sea level, it is about 14.7 PSI. At higher elevations, it is lower because there is less air above. Weather systems also change atmospheric pressure; low pressure systems have pressure below 14.7 PSI, and high pressure systems have pressure above it.