Pressure is the force pressing on each square metre of a surface. For a solid, use P = F ÷ A. For a liquid, use P = ρgh.
This lesson is part of SPM Physics pressure. Once you can calculate pressure, continue with comparing pressure at different depths.
How do I find the pressure a solid exerts?
Find the force pressing on the surface, find the area in contact with it, then divide. For a block resting on a table, the force is its weight, W = mg.
Take g = 10 N kg⁻¹ unless your paper says otherwise. The same block exerts different pressures when placed on different faces, because the contact area changes.
Worked example: one block, two faces
An original block has mass 20 kg and measures 0.50 m × 0.40 m × 0.25 m.
Weight = 20 × 10 = 200 N. Lying on its largest face (0.50 m × 0.40 m = 0.20 m²), the pressure is 200 ÷ 0.20 = 1000 Pa.
Standing on its smallest face (0.40 m × 0.25 m = 0.10 m²), the pressure is 200 ÷ 0.10 = 2000 Pa. The force stays at 200 N, but the area is half as big, so the pressure doubles.
The mistake that costs marks
The usual slip is to divide by an area that is still in cm². Take a narrow heel of area 4 cm² that carries a force of 500 N.
| Step | Wrong | Right |
|---|---|---|
| Area used | 4 | 4 cm² = 4 × 10⁻⁴ m² |
| Calculation | 500 ÷ 4 | 500 ÷ (4 × 10⁻⁴) |
| Answer | 125 Pa | 1.25 × 10⁶ Pa |
The fix: 1 m² is 10 000 cm², so divide any area in cm² by 10 000. Convert before you substitute, every time.
How do I find the pressure in a liquid?
Use P = ρgh, where ρ is the density of the liquid, g is 10 N kg⁻¹ and h is the depth below the surface. This pressure comes from the weight of the liquid above the point.
For water in an original tank 0.60 m deep, use ρ = 1000 kg m⁻³. The pressure at the bottom is 1000 × 10 × 0.60 = 6000 Pa. The shape of the tank does not matter. Only depth and density do.
Which formula should I choose?
| Situation | Formula | Quantities needed |
|---|---|---|
| Block on a table | P = F/A | Weight and contact area |
| Point under water | P = ρgh | Density and depth |
| Force on the flat base of a tank | P = ρgh, then F = PA | Depth, density and base area |
A question that asks for the force on a flat base under liquid uses both formulas in turn. Find the pressure first, then multiply by the area.
Check yourself
A force of 60 N presses on an area of 30 cm². Find the pressure in pascals, then find the depth of oil (density 800 kg m⁻³) that would give the same pressure.
Answer
Convert the area: 30 cm² = 30 ÷ 10 000 = 0.0030 m².
P = F ÷ A = 60 ÷ 0.0030 = 20 000 Pa.
For the oil, h = P ÷ (ρg) = 20 000 ÷ (800 × 10) = 2.5 m.
What to study next
Pressure in a liquid changes with depth, and the next lesson shows how to compare it. Go to comparing pressure at different depths, then test yourself with the pressure practice set.
If you want a teacher to watch your working on these questions, see online one-to-one Physics tuition.