HesapHanem

Hydrostatic Pressure Force

Total force on a submerged flat surface

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.

Worked example

A flat gate with area 2 m² has its centre 3 m under fresh water (ρ = 1000 kg/m³, g = 9.81 m/s²). Step 1: p = 1000 × 9.81 × 3 = 29,430 Pa. Step 2: F = 29,430 × 2 = 58,860 N. The tool shows a pressure of 29,430.00 Pa and a total force of 58,860.00 N, which is about 5.9 tonnes-force pushing on the gate.

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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.

About this calculator

Hydrostatic force on a flat submerged surface is F = ρ × g × h̄ × A, where ρ is fluid density, g is gravitational acceleration, h̄ is the depth of the surface's centroid below the fluid surface, and A is the surface area — it works because pressure increases linearly with depth, so the centroid depth gives the correct average pressure across the whole surface.

Civil and structural engineers use this exact calculation to size dam walls, tank sides, retaining walls and submerged gates, since getting the total force wrong on something holding back water has serious consequences — a swimming pool wall and a small dam are sized using the identical physics, just at very different scales.

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Comments (1)

  • Editorial team

    For a vertical wall that holds water up to its full height, the force grows with the square of the depth. Take a wall 10 m wide with 3 m of water: enter a centroid depth of 1.5 m and an area of 30 m² to get 441,450 N. Fill it to 6 m and the force is four times that, not double. That is why a small rise in water level matters so much. What structure are you checking?

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