Hydrostatic Force and Center of Pressure Calculator

Calculate hydrostatic force and center-of-pressure depth on a vertical rectangular surface.

F = ρgAyc; ycp = yc + IG/(Ayc)

Fluid density ρ (kg/m³)

Gravity g (m/s²)

Plate width b (m)

Plate height h (m)

Top-edge depth y0 (m)

Enter valid values in all required fields.

What this formula means

Hydrostatic pressure increases linearly with depth. Integrating that pressure over a plane surface gives the resultant force, while the center of pressure locates its line of action below the area centroid.

Use the result for gates, tank walls, dams, submerged panels, aquarium windows, and retaining structures. The result should be interpreted with consistent units and with the assumptions of the underlying model in mind.

Worked example

A 2 m × 3 m plate with its top 1 m below water has F ≈ 147.2 kN and center-of-pressure depth 2.8 m.

Applications

Use the result for gates, tank walls, dams, submerged panels, aquarium windows, and retaining structures. It is also useful as an independent check when comparing hand calculations, laboratory measurements, simulations, or preliminary engineering estimates.

Assumptions and common mistakes

Important: All depths must be measured from the same free surface, and the formula here assumes a vertical rectangular plane.

Use SI units unless the field label states otherwise. Keep significant figures appropriate to the accuracy of the inputs, and do not treat a simplified calculator as a replacement for codes, detailed design standards, or professional review.

Frequently asked questions

What equation does this calculator use?F = ρgAyc; ycp = yc + IG/(Ayc). The calculator evaluates the displayed relationship using the values entered above.

Are the results unit-sensitive?Yes. The input labels use SI units so the displayed output follows the corresponding SI unit.

Can I use this for engineering design?Use it for learning and preliminary checks. Final designs require validated data, applicable standards, safety factors, and professional judgment.