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: the pressure on the wall rises linearly with depth, but the total force on the wall rises with depth squared, because you are multiplying a growing pressure by a growing wetted area. That is why dams are thin at the crest and thick at the base.
• 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 about 0.1 atm per metre of seawater, so the first 10 m doubles the pressure on your eardrum. That first 10 m is the single biggest proportional jump of the whole dive.
• The rule of thumb, stated properly: 10 m of seawater adds almost exactly 1 bar (100,553 Pa, so 1.005 bar). In fresh water it takes 10.2 m for the same bar, because fresh water is 2.5% less dense.
• If you want a full atmosphere rather than a bar, the numbers are 10.08 m of seawater and 10.33 m of fresh water. Bar and atmosphere differ by 1.3%, which is small enough that divers use them interchangeably and precise enough to matter in engineering.

Gauge versus absolute, the distinction that causes the most confusion

A pressure gauge on a scuba tank or a car tyre reads gauge pressure: the amount above the surrounding atmosphere. It reads zero at the surface even though the real pressure there is 101,325 Pa. Absolute pressure is gauge plus atmospheric, and it is the one that matters for anything involving gas volume or dissolved gas, because Boyle’s law and Henry’s law both work in absolute terms.

This is exactly why a diver’s air lasts a quarter as long at 30 m. Gauge pressure there is 3 atm, but absolute is 4 atm, and it is the 4 that sets how much gas each breath consumes. Reading the gauge figure instead would predict a third and leave you short.