Hydrostatic Pressure Force

How it is calculated

The tool first finds the gauge pressure at the surface centroid, p = ρ × g × h, then the total force, F = p × A. Inputs are SI: density ρ in kg/m³, depth h of the centroid below the free surface in m, area A in m² and gravity g in m/s². All four fields are required, including g (9.81 on Earth). Density, area and g must be above zero, and depth may be zero but not negative. Pressure is in Pa and force in N, each rounded to two decimals. The pressure excludes the atmosphere above the liquid, and the force acts at the centre of pressure, which is somewhat deeper than the centroid; the tool does not locate that point.

Common mistakes

• Using the depth of the top or bottom edge instead of the centroid depth; for a vertical rectangle the centroid is halfway down its height.
• Using centimetres or litres: depth must be in metres, area in square metres and density in kg/m³ (water 1000, not 1).
• Adding atmospheric pressure to the answer, or expecting it included; here only the fluid's own weight is counted, which is right when air presses on both sides.
• Assuming the force acts at the centroid; the line of action is lower, which matters for moment calculations.
• Leaving out g; the field is required, and 9.81 should be typed.