Fluid Pressure at Depth Calculator

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:

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