Pressure calculator: p = F ÷ A with working

Example: a 600 N box rests on an area of 0.02 m². $p = 600 \div 0.02 = 30000$ Pa, or 30 kPa.

Area conversions use the square of the length conversion:

• 1 m² = 100 × 100 = 10,000 cm², so divide cm² by 10,000.
• 1 m² = 1,000 × 1,000 = 1,000,000 mm², so divide mm² by 1,000,000.

Example: a force of 50 N on 2 cm². $2 \text{ cm}^2 = 0.0002 \text{ m}^2$, so $p = 50 \div 0.0002 = 250000$ Pa. Dividing by 100 instead of 10,000 is the classic slip.

For the same force, halving the area doubles the pressure. That's why knives are sharp (tiny area, huge pressure), drawing pins push in easily, and snowshoes and tractor tyres are wide (large area, low pressure, so they don't sink).

In a liquid, pressure increases with depth: $p = h\rho g$, where $h$ is the depth in m, $\rho$ the density of the liquid in kg/m³ and $g$ the gravitational field strength. At 10 m deep in water ($\rho = 1000$ kg/m³, $g = 9.8$ N/kg), the pressure from the water is $10 \times 1000 \times 9.8 = 98000$ Pa. Dams are thicker at the bottom for this reason. Our density calculator helps with the $\rho$ part.

• Converting area like length (cm² ÷ 100 instead of ÷ 10,000).
• Using a force that isn't at right angles to the surface.
• Mixing up kPa and Pa: 1 kPa = 1,000 Pa.

Practise with our pressure questions.

• Convert the area before dividing: most lost marks come from cm² and mm².
• If the question gives a mass, change it to a weight first: $W = mg$.
• For a solid block, the pressure depends on which face it rests on: the smallest face gives the biggest pressure.
• Atmospheric pressure is about 100,000 Pa (100 kPa) at sea level, a useful check on gas pressure answers.