Pressure under water
The deeper you go, the more water is stacked above you, and the higher the pressure. This hydrostatic pressure depends only on the depth and the density of the liquid, not on the shape or size of the body of water. Divers feel it in their ears after a few feet, and engineers must account for it when designing dams, tanks, pools and submarines.
The formulas
- Gauge pressure = fluid density × g × depth (P = ρgh)
- Absolute pressure = gauge pressure + pressure at the surface
- Air volume at depth = surface pressure ÷ absolute pressure (Boyle’s law)
Gauge pressure is what a pressure gauge or a dive computer reads relative to the air; absolute pressure is the total felt by your body or a sealed container.
Worked example
A diver descends to 33 ft in seawater (1,025 kg/m³), with 14.7 psi at the surface.
- 33 ft = 10.06 m.
- Gauge pressure = 1,025 × 9.81 × 10.06 = 14.66 psi, about 1 bar.
- Absolute pressure = 14.66 + 14.7 = 29.4 psi, or 2.00 atmospheres.
- A balloon filled at the surface would shrink to 50% of its volume.
Every 33 ft (10 m) of seawater adds one more atmosphere.
Pressure at common depths in seawater
| Depth | Gauge pressure | Absolute pressure |
|---|---|---|
| 10 ft | 4.4 psi | 19.1 psi |
| 33 ft | 14.7 psi | 29.4 psi |
| 66 ft | 29.3 psi | 44.0 psi |
| 100 ft | 44.4 psi | 59.1 psi |
| 130 ft (recreational limit) | 57.8 psi | 72.5 psi |
Why it matters for divers
Because gas volume halves between the surface and 33 ft, the biggest volume changes happen close to the surface. Divers must equalize their ears early and must never hold their breath while ascending, since the air in their lungs expands as pressure drops. Depth also increases the amount of nitrogen absorbed by the body, which is why dive tables limit time at depth.
The hydrostatic paradox
A narrow tube filled with 33 ft of water exerts the same pressure at its base as a lake 33 ft deep: pressure depends on height, not volume. The total force on the bottom, however, is pressure times area, so a large tank wall must be far stronger than a narrow pipe.
Other liquids and pressure units
Select fresh water, the Dead Sea, oil or mercury, or enter any density. Mercury is 13.6 times denser than water, which is why barometers use a column of only 760 mm of mercury to balance the atmosphere, against more than 10 m for a water barometer. The calculator can show results in psi, bar, kPa, hPa, atmospheres or millimeters of mercury.