Pressure in fluids: p = hρg explained
By Engr. Mehmood Kakar · Updated
Quick answer
The pressure from a column of liquid is p = h × ρ × g: height (depth) × density × gravitational field strength. It rises with depth and with density because there is more weight of liquid above. The pressure difference between the top and bottom of a submerged object causes upthrust.
What pressure in a fluid is
A fluid is a liquid or a gas. Its particles collide with any surface they touch, and these collisions push on the surface. Pressure in a fluid acts at right angles (normal) to every surface, in all directions.
Pressure is force per unit area: p = F ÷ A, measured in pascals (1 Pa = 1 N/m²).
Pressure and depth: p = hρg
In a liquid, the pressure at a point depends on the weight of liquid above it. That gives the equation p = h × ρ × g:
- h: height of the column of liquid above the point (the depth), in metres
- ρ: density of the liquid, in kg/m³
- g: gravitational field strength, 9.8 N/kg on Earth
So pressure increases with depth and with density. It does not depend on the width or shape of the container. This is why dams are built thicker at the bottom, and why water spurts further from a hole low down in a tank (try the liquid pressure simulation).
Worked questions
Calculate the pressure due to the water at a depth of 5.0 m in a swimming pool. (ρ = 1000 kg/m³, g = 9.8 N/kg)
- p = h × ρ × g = 5.0 × 1000 × 9.8
- p = 49 000 Pa (49 kPa)
That is the pressure from the water only. The atmosphere presses on the surface too, adding about 100 000 Pa, so the total pressure at that depth is about 149 000 Pa.
A diver measures a water pressure of 30 000 Pa in sea water of density 1030 kg/m³. How deep is she?
- Rearrange: h = p ÷ (ρ × g)
- h = 30 000 ÷ (1030 × 9.8) = 30 000 ÷ 10 094
- h = 2.97 m (3 s.f.)
How much greater is the water pressure at 8.0 m than at 3.0 m? (ρ = 1000 kg/m³)
- Difference in depth: Δh = 8.0 − 3.0 = 5.0 m
- Δp = Δh × ρ × g = 5.0 × 1000 × 9.8
- Δp = 49 000 Pa
Upthrust and floating
A submerged object has its bottom deeper than its top, so the pressure on the bottom is bigger. The difference gives a resultant upward force called upthrust.
A cube with sides 0.10 m is held under water with its top face 0.20 m below the surface. Calculate the upthrust on it.
- Pressure on top: 0.20 × 1000 × 9.8 = 1960 Pa
- Pressure on bottom: 0.30 × 1000 × 9.8 = 2940 Pa
- Pressure difference: 2940 − 1960 = 980 Pa
- Upthrust = pressure difference × area = 980 × (0.10 × 0.10) = 980 × 0.010
- Upthrust = 9.8 N
The upthrust equals the weight of the water the object pushes aside (here 0.001 m³ of water, mass 1 kg, weight 9.8 N). An object floats when the upthrust can balance its weight before it is fully submerged. A dense object displaces too little water for that, so it sinks.
Atmospheric pressure
The atmosphere is a thin layer of air around the Earth. Air molecules collide with surfaces and create atmospheric pressure, about 100 000 Pa at sea level. (AQA: GCSE Physics only.)
Atmospheric pressure decreases with height: higher up there is less air above, so less weight of air, and the air is less dense, with fewer collisions. That is why your ears pop in a plane or a lift in a tall building.
Common mistakes
- Depth in centimetres. Convert to metres: 50 cm = 0.50 m.
- Density in g/cm³. Multiply by 1000 for kg/m³: water is 1.0 g/cm³ = 1000 kg/m³.
- Using the depth of the object, not the point. h is the depth of the point you want the pressure at.
- Thinking the container shape matters. Only depth, density and g affect the liquid pressure.
Practice
1. Calculate the pressure due to water at a depth of 12 m. (ρ = 1000 kg/m³, g = 9.8 N/kg)
p = h × ρ × g = 12 × 1000 × 9.8 → p = 117 600 Pa (118 kPa, 3 s.f.)
2. Oil has a density of 800 kg/m³. What is the pressure due to the oil 2.5 m below its surface?
p = 2.5 × 800 × 9.8 → p = 19 600 Pa
3. At what depth in fresh water is the water pressure 98 000 Pa?
h = p ÷ (ρ × g) = 98 000 ÷ (1000 × 9.8) → h = 10 m
4. Explain why a submarine’s hull must be stronger the deeper it is designed to go.
Pressure increases with depth (p = hρg) because there is a greater weight of water above, so the force on each square metre of the hull is larger.
Frequently asked questions
What is the equation for pressure in a liquid?
Pressure due to a column of liquid = height of the column × density of the liquid × gravitational field strength, p = h ρ g. It is on the AQA equation sheet and is Higher tier, GCSE Physics only.
Why does pressure increase with depth?
The deeper you go, the taller the column of liquid above you, so the greater the weight of liquid pressing down on each square metre.
What causes upthrust?
The bottom of a submerged object is deeper than its top, so the pressure on the bottom is greater. This pressure difference gives a resultant upward force: the upthrust.
Why does atmospheric pressure decrease with height?
Higher up, there is less air above you, so less weight of air pressing down. The air is also less dense, with fewer molecules colliding with surfaces.
Written by Engr. Mehmood Kakar
Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)
Checked against the AQA GCSE Physics (8463) specification on 15 November 2026.