Pressure

2026 Syllabus Objectives

Core:

  1. Define pressure as force per unit area; recall and use the equation p = F/A
  2. Describe how pressure varies with force and area in the context of everyday examples
  3. Describe, qualitatively, how the pressure beneath the surface of a liquid changes with depth and density of the liquid

Supplement: 4. Recall and use the equation for the change in pressure beneath the surface of a liquid Δp = ρgΔh

What is Pressure?

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Pressure is the force acting on each square metre (or square centimetre) of a surface. In other words, it tells us how spread out or concentrated a force is over an area.

Definition: Pressure is the force per unit area.

Think of it this way: if you press your hand flat on a table, the force from your hand is spread over a large area. But if you poke the table with your fingertip, the same force is concentrated on a tiny area—that's why it feels more intense.

The Pressure Equation

The relationship between pressure, force, and area is given by:

p = F/A

Where:

  • p = pressure, measured in pascals (Pa) or newtons per metre squared (N/m²)
  • F = force, measured in newtons (N)
  • A = area, measured in metres squared (m²)

Important: 1 pascal (Pa) = 1 newton per metre squared (N/m²)

Pressure is a scalar quantity, which means it only has size (magnitude) but no direction.

Rearranging the Equation

You can rearrange the pressure equation to find force or area:

  • To find force: F = p × A
  • To find area: A = F/p

Tip: You can use a formula triangle to help remember these rearrangements. Put F at the top, and p and A at the bottom.

How Pressure Varies with Force and Area

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The pressure equation tells us two important things:

  1. If a force is spread over a large area, it produces a small pressure

    • Example: A wide, flat object creates low pressure

  2. If the same force is concentrated on a small area, it produces a large pressure

    • Example: A sharp, pointed object creates high pressure

In formula terms:

  • Pressure is directly proportional to force (p ∝ F) — if force increases, pressure increases
  • Pressure is inversely proportional to area (p ∝ 1/A) — if area decreases, pressure increases

Everyday Examples of Pressure

Example 1: Tractors

  • Tractors have large, wide tyres
  • This spreads the weight (force) of the heavy tractor over a large area
  • This creates low pressure on the ground
  • Result: The tractor doesn't sink into soft mud or soil

Example 2: Drawing Pins (Thumbtacks)

  • Drawing pins have a sharp, pointed end with a very small area
  • The force you apply with your thumb is concentrated on this tiny area
  • This creates very high pressure at the point
  • Result: The pin easily pushes into a wall or board
  • The flat head of the pin has a large area, so the pressure on your thumb is low and doesn't hurt

Example 3: High Heels vs Flat Shoes

  • High heels have a small, narrow heel with a small area

  • The person's weight (force) is concentrated on this small area

  • This creates high pressure on the ground

  • Result: High heels sink into soft surfaces like grass or carpet

  • Flat shoes spread the same weight over a much larger area

  • This creates lower pressure on the ground

  • Result: Flat shoes don't sink into soft surfaces as easily

Example 4: Knives

  • A sharp knife has a very thin blade edge (small area)
  • When you push down, the force is concentrated on this small area
  • This creates high pressure, allowing the knife to cut through food easily
  • A blunt knife has a thicker edge (larger area), creating lower pressure and making cutting harder

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