Buoyancy Calculator

Buoyancy is the upward force a fluid exerts on any object placed within it, and Archimedes' principle gives the exact formula: the buoyant force equals the weight of the fluid displaced by the object. Written as F = ρgV, where ρ is the fluid density in kg/m3, g is gravitational acceleration, and V is the volume of fluid displaced in m3, this single equation explains why ships float, why hot air balloons rise, why objects feel lighter underwater, and why submarines can dive and surface at will. The key insight is that buoyancy depends on the volume of fluid displaced, not the volume or mass of the object itself. A hollow steel hull displaces far more water than a solid steel ball of the same mass, so the hull floats while the ball sinks. Whether an object floats or sinks comes down to whether the buoyant force equals or exceeds the object's weight: if the maximum buoyant force when fully submerged is greater than the weight, the object floats; if the weight exceeds even full submersion buoyancy, it sinks. This calculator finds the buoyant force from the fluid density and the submerged volume, both of which you enter. It also shows the mass of fluid displaced and, if you enter the object's mass, a float or sink indicator and the net upward or downward force. The default example uses V = 0.1 m3 submerged in water (1,000 kg/m3), giving F = 981 N and displaced mass = 100 kg. Results update as you type. Use this for physics homework, ship design, diving, and fluid mechanics.

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Archimedes: F = rho x g x V. The object floats if buoyant force is greater than or equal to its weight. Water is 1,000 kg/m³, seawater ~1,025 kg/m³. Rounded for display.