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MasterMath

Buoyancy Calculator

Archimedes' principle: the upward force equals the weight of the fluid displaced. It is what decides whether anything floats.

Result

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How this was worked out

    The formula

    E = ρ · g · V

    SymbolQuantityUnit
    EBuoyant forceN
    pDensity of the fluidkg/m³
    VSubmerged volumem³

    What it means

    A submerged object pushes fluid out of the way, and the fluid pushes back with a force equal to the weight of what was displaced. Float or sink depends entirely on how that compares with the object's own weight.

    How to work it out by hand

    1. Take the density of the fluid
    2. Multiply by gravity and by the submerged volume
    3. The result is the upward force in newtons

    What is worth knowing

    This is why a steel ship floats: what matters is the average density of the whole hull including the air inside, not the density of steel. Breach the hull, let water replace the air, and the average density rises past water's — which is precisely how ships sink. The principle also gives the neatest density measurement there is: weigh an object in air and again submerged, and the difference is the buoyant force, from which the volume and hence the density follow. Archimedes is said to have worked this out in the bath, though the shouting is probably later embellishment.

    Frequently asked questions

    Why does a steel ship float?

    Because its average density, hull and enclosed air together, is less than water's. Steel alone would sink.

    What decides whether something floats?

    Whether the buoyant force matches its weight. Equivalently, whether its average density is below the fluid's.

    Does buoyancy depend on depth?

    Not for an incompressible fluid: the displaced volume is the same at any depth. It does for gases, whose density falls with altitude.

    How can I measure density with this?

    Weigh the object in air and submerged. The difference gives the buoyant force, and from that the volume.