Buoyant Force Calculator

Buoyant force is the upward push a fluid exerts on anything placed in it, and Archimedes worked out the rule more than two thousand years ago: the force equals the weight of the fluid the object pushes out of the way. In symbols, buoyant force is the fluid density times gravity times the submerged volume. Nothing about the object’s own material enters the formula, only how much fluid it displaces.

That is why a steel ship floats while a steel bolt sinks. The ship is shaped to displace a huge volume of water before it is fully under, so the buoyant force grows large enough to match its weight. The bolt displaces only its own small volume, so the water can never push up hard enough. Whether something floats comes down to a comparison: if the buoyant force at full submersion beats the object’s weight, it floats; if not, it sinks and feels lighter underwater by exactly the buoyant force.

Fluid choice matters more than people expect. Seawater is about 2.5 percent denser than fresh water, which is the small edge that lets you float a little higher in the ocean than in a lake. This calculator carries densities for fresh water, seawater, and oil, and takes a custom value for anything else.

Enter the submerged volume and, if you like, the object’s mass. You get the buoyant force in newtons, kilograms-force, and pounds-force, a float-or-sink verdict, and a chart of how the force grows as more of the object goes under. The volume here is the part actually below the surface, which for a fully submerged object is just its total volume.