Archimedes gave the magnitude of buoyant force acting on a solid object immersed in a liquid. It was given by his famous principle commonly known as Archimedes principle which stated that

The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced.