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Pressure in Solids

Definition of pressure, how area affects pressure, and the formula P = F/A.

Last updated: 5 January 2026

★★☆☆☆ Level 2PressureForceAreapascal3 min read

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What is Pressure?

Pressure is the force applied per unit area. The same force spread over a larger area gives less pressure.

Pressure

P=FAP = \dfrac{F}{A}

P = pressure (Pa), F = force (N), A = area (m²)

Force

F=P⋅AF = P \cdot A

Area

A=FPA = \dfrac{F}{P}

Units: 1 Pascal (Pa) = 1 N/m²

A 600 N person stands on snow. Feet area = 0.03 m². Snowshoes area = 0.15 m².

Without snowshoes: P=6000.03=20 000 PaP = \dfrac{600}{0.03} = 20\,000 \text{ Pa}

With snowshoes: P=6000.15=4 000 PaP = \dfrac{600}{0.15} = 4\,000 \text{ Pa}

Snowshoes reduce pressure by 5 times → you don't sink as deep.

Why Sharp Objects Cut

A sharp knife has a tiny edge area → very high pressure → it cuts easily.

A stiletto heel vs. a flat heel (both 500 N)

Stiletto heel area: 0.001 m20.001 \text{ m}^2 → P=500 000 PaP = 500\,000 \text{ Pa}

Flat heel area: 0.05 m20.05 \text{ m}^2 → P=10 000 PaP = 10\,000 \text{ Pa}

Real world: Camel hooves on sand

A camel weighing 6000 N distributes its weight across four wide, flat hooves — each roughly 0.05 m² — giving a total contact area of 0.2 m².

P=60000.2=30 000 PaP = \frac{6000}{0.2} = 30\,000 \text{ Pa}

The wide hooves spread the weight over a large area, keeping pressure low enough not to sink into soft desert sand. Humans would sink deeper with smaller, narrower feet.

Real world: Cutting with a knife

A chef pressing a knife downward with a force of 20 N. A sharp knife edge has an area of about 0.00001 m² (1 cm²), while a blunt knife has an area of about 0.001 m²:

Psharp=200.00001=2,000,000 PaP_{\text{sharp}} = \frac{20}{0.00001} = 2{,}000{,}000 \text{ Pa} Pblunt=200.001=20,000 PaP_{\text{blunt}} = \frac{20}{0.001} = 20{,}000 \text{ Pa}

The sharp knife exerts 100× more pressure — which is why it cuts through food so easily.

Tip Where do you see this in real life? Drawing pins, hiking boot cleats, wide tyres on tractors, caterpillar tracks on tanks, and even the design of chairs and tables all involve thinking about pressure and contact area!

Practice Problems

A force of 200 N acts on an area of 0.5 m². Calculate the pressure.

Show answer
P = 200 ÷ 0.5 = 400 Pa.

The pressure on a surface is 1500 Pa and the area is 0.2 m². What force is acting?

Show answer
F = 1500 × 0.2 = 300 N.