Pressure is simply the amount of force applied over a certain area. Imagine trying to push a thumbtack into a bulletin board. You push on the flat, wide head, and the sharp, tiny point goes into the board easily. The force from your thumb is the same on both ends, but the effect is completely different. On the sharp end, that force is concentrated into a very small area, creating high pressure. On the flat end, the same force is spread out, creating low pressure that's comfortable for your thumb.

This relationship is described by a straightforward formula.

In this equation:

• $P$ is pressure.
• $F$ is the force acting perpendicular to the surface.
• $A$ is the area over which the force is applied.

From this, we can see that pressure is directly proportional to force and inversely proportional to area. If you increase the force, the pressure increases. If you increase the area, the pressure decreases.

The standard unit for pressure in the International System of Units (SI) is the pascal (Pa). One pascal is defined as one newton of force applied over an area of one square meter ($1 \text{ Pa} = 1 \text{ N/m}^2$).

A single pascal is a very small amount of pressure. The gentle pressure of a dollar bill resting flat on a table is about 1 Pa. Because it's so small, we often use kilopascals (kPa), where 1 kPa = 1,000 Pa. But the pascal isn't the only unit you'll encounter. Different fields use different units for convenience.

Here's how they relate:

• 1 atm ≈ 101,325 Pa
• 1 atm ≈ 14.7 psi

It's important to understand that pressure is a scalar quantity. This means it has a magnitude (a size or amount) but no direction. This might seem strange because the force that creates the pressure clearly has a direction. You push down on the thumbtack.

However, the pressure itself doesn't have a direction. Think of the air in a balloon. The air pressure pushes outwards on every part of the balloon's inner surface equally. It doesn't just push up or down. A force is a vector (magnitude and direction), while pressure is a scalar (magnitude only).

We can use the formula $P = F/A$. The force $F$ is his weight (800 N) and the area $A$ is 0.04 m².

So, he exerts a pressure of 20,000 pascals, or 20 kPa. Now, what if he stands on one foot, halving the area to 0.02 m²? His weight (the force) is the same, but the area changes.

By concentrating the same force over a smaller area, he doubles the pressure to 40 kPa. This core concept is the foundation for understanding how pressure works in any system.