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Buoyant Force Calculator

Find the upward buoyant force on an object immersed in a fluid.

How it is calculated

The tool uses Archimedes' principle: the upward force equals the weight of the fluid displaced. First the displaced mass m = ρ × V, then the force F = m × g. Here ρ is the fluid density in kg/m³, V is the displaced volume in m³ (the submerged part of the object, not the whole object if it floats), g is gravitational acceleration in m/s², and F comes out in newtons.

Only the volume is required and it must be greater than zero. If the density is left empty or is zero or negative, the tool assumes 1000 kg/m³ (fresh water); if g is empty or not positive, it uses 9.81 m/s². The tool does not compare the force with the object's weight, so you need to do that yourself to know whether the object floats.

Worked example

A hull displaces 0.5 m³ of seawater with a density of 1025 kg/m³, with g = 9.81. Displaced mass: 1025 × 0.5 = 512.50 kg. Buoyant force: 512.5 × 9.81 = 5,027.63 N. If the object weighs less than about 5,028 N it can float with that volume under water; if it weighs more, it sinks further or goes down.

Try this example →

Common mistakes

  • Entering the volume of the whole object for a floating body; only the part below the waterline displaces fluid.
  • Using litres or cubic centimetres for the volume; the tool expects m³, so 500 litres must be typed as 0.5.
  • Leaving the density empty for salt water or oil and not noticing that the tool silently used 1000 kg/m³.
  • Entering density in g/cm³ (1.025) instead of kg/m³ (1025); the force then comes out 1000 times too small.
  • Treating the buoyant force as the object's weight; the object floats only if its own weight is no more than this force.

About this calculator

This calculator finds the buoyant force on a submerged or floating object using Archimedes' principle: F = ρ·g·V, where ρ is the fluid's density, g is gravitational acceleration, and V is the volume of fluid displaced. The result equals the weight of the fluid the object pushes out of the way, which is also the mass of fluid displaced multiplied by g.

Naval architects, engineers, and physics students use this to size ballast tanks, check whether a hull or hot-air balloon will float, and to solve textbook problems on floating versus sinking objects.

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Comments (1)

  • Editorial team

    For a floating object the useful question is how deep it sits. The submerged fraction equals the object's density divided by the fluid's density, so wood at 600 kg/m³ sits about 60 percent under in fresh water, a little less in seawater. The tool takes the displaced volume, so work out that fraction first, then enter the submerged part. What object are you floating, and in which fluid?

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