Hydrostatic Pressure Calculator

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid column above a point. For an incompressible fluid with constant density ρ, the gauge pressure at vertical depth h below a free surface is P = ρgh, where g ≈ 9.81 m/s². This is one of the most fundamental results in fluid statics, derived from balancing vertical forces on a fluid element: dP = ρg dh.

Gauge pressure is measured relative to the local atmospheric pressure P_atm ≈ 101.325 kPa (14.7 psi, 1 bar). Absolute pressure includes atmospheric head: P_abs = P_atm + ρgh for a tank open to the atmosphere. In a continuous static fluid, pressure is the same at every point on the same horizontal level — this explains why water seeks a common level in connected vessels (communicating vessels).

Numerical reference (water, ρ = 1000 kg/m³): P ≈ 9.81 kPa per meter of depth (~98 kPa at 10 m, ~1 bar). Scuba divers feel ~2 atm absolute at 10 m depth (1 atm water + 1 atm air). Mercury barometers use ρ_Hg ≈ 13,600 kg/m³ so 760 mm Hg ≈ 1 atm in a compact column. Oil (ρ ≈ 850 kg/m³) gives lower pressure than water at the same depth.

The hydrostatic paradox demonstrates that pressure at a point depends on vertical depth h, not on the shape or total volume of fluid above — a narrow tall column and a wide shallow basin at the same water level exert the same pressure at the bottom. This is essential for dam, tank, and submarine hull design.

Pressure increases linearly with h, so the force on a vertical wall is found by integrating the triangular pressure distribution (see Hydrostatic Force calculator). For large vertical extents of gas, density varies with height and the isothermal barometric formula P = P₀ exp(−Mgh/RT) replaces ρgh.

Engineering conversions: 1 Pa = 1 N/m²; 1 kPa = 1000 Pa; 1 bar = 10⁵ Pa; 1 psi ≈ 6895 Pa. Blood pressure in mmHg is a direct hydrostatic column tradition (133.3 Pa per mmHg).