Calculate hydrostatic force from fluid density, area and depth, or hydrostatic pressure at depth with optional surface pressure inputs.

Force from fluid weight on a fully submerged plane area.

Static fluid with constant density; g = 9.81 m/s². Force uses the plane area’s centroid depth and excludes surface-pressure force. Net force requires pressures on both sides.

Approximate presets; density varies with temperature and composition. You can edit the value.

Hydrostatic Force Formula

The following formula calculates the resultant force from fluid weight on a fully submerged plane area, using its vertical centroid depth. A horizontal surface at uniform depth is a special case. The model assumes constant density and g ≈ 9.81 m/s².

Hf = ρ × g × h × A
  • Where Hf is the hydrostatic force (N, newtons)
  • ρ is the density of the fluid (kg/m³)
  • g is the acceleration due to gravity (≈9.81 m/s²)
  • h is the vertical depth of the submerged area’s centroid below the free surface (m), not the center of pressure
  • A is the area of the surface the pressure acts on (m²)

Multiply density, gravity, centroid depth and submerged plane area for the force due to fluid weight. Point pressure uses p = psurface + ρgh with the point’s depth: blank surface pressure gives only the increment; a supplied surface pressure sets the result’s gauge or absolute reference. One-sided force including surface pressure is Hf = pcentroidA; net force also requires pressure on the opposite side. Fluid presets are approximate and vary with temperature and composition.

What is Hydrostatic Force?

Definition:

Hydrostatic force is the resultant force a fluid at rest exerts on a submerged surface due to hydrostatic pressure, which increases with depth. It is not generally the same as buoyant force; buoyant force is the net upward force on a fully or partially submerged body and equals the weight of the displaced fluid (Archimedes’ principle).

How to calculate hydrostatic force?

Example:

The following example outlines the steps needed to calculate a hydrostatic force.

First, determine the density of the fluid. We are assuming freshwater for this example so the density is approximately 1000 kg/m³.

Next, determine the submerged plane area’s centroid depth. In this example it is 100 meters below the free surface.

Next, determine the surface area of the object. In this problem, the surface area is calculated to be 10 m².

Finally, calculate the hydrostatic force using the formula above (gauge):

Hf =  ρ * g * h * A

Hf =  1000 * 9.81 * 100 * 10

Hf =  9,810,000 N