Fluid Pressure at Depth Calculator
Calculate hydrostatic pressure at any depth in a fluid.
Supports seawater, fresh water, mercury, and custom densities.
Shows pressure in Pa, atm, bar, and PSI.
Fluid pressure at depth is the pressure exerted by the weight of fluid above a given point. It increases linearly with depth and is independent of the container’s shape or horizontal dimensions.
The Formula:
P = ρ × g × h
Where:
- P = gauge pressure at depth (Pascals, Pa)
- ρ = fluid density (kg/m³): water = 1,000, seawater = 1,025, mercury = 13,600
- g = gravitational acceleration = 9.81 m/s²
- h = depth below the surface (meters)
Absolute Pressure:
P_absolute = P_atmospheric + ρ × g × h
Standard atmospheric pressure = 101,325 Pa (≈ 101.3 kPa)
Worked Example:
A scuba diver is at 30 m depth in seawater (ρ = 1,025 kg/m³):
Gauge pressure = 1,025 × 9.81 × 30 = 301,657 Pa ≈ 3.0 atm
Absolute pressure = 101,325 + 301,657 = 402,982 Pa ≈ 4.0 atm
At this pressure, a diver’s air supply depletes 4× faster than at the surface.
Pressure Reference Table:
| Depth | Gauge Pressure (seawater) | Absolute Pressure |
|---|---|---|
| 0 m (surface) | 0 Pa | 1.0 atm |
| 10 m | ~1.0 atm | 2.0 atm |
| 30 m | ~3.0 atm | 4.0 atm |
| 100 m | ~10.0 atm | 11.0 atm |
| 11,000 m (Mariana Trench) | ~1,100 atm | ~1,101 atm |
Practical Applications:
- Dam engineering: pressure on walls increases with depth squared (for total force)
- Submarine hull design: must withstand hundreds of atmospheres
- Blood pressure measurement uses mmHg (1 mmHg = 133.3 Pa)
Practical Tips:
- Ear equalization in diving is necessary because pressure rises ~0.1 atm per meter
- Water pressure rule of thumb: every 10 m = 1 additional atmosphere in fresh water; 9.8 m in seawater