Archimedes Principle Calculator

Archimedes' principle states that a body wholly or partly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. The force is calculated by multiplying fluid density, displaced volume, and gravitational acceleration. This simple relationship explains why ships float, balloons rise, submerged objects feel lighter, and density can be measured through apparent weight. Displaced volume is the portion of an object's volume below the fluid surface. A fully submerged solid displaces its complete external volume, provided fluid does not enter internal cavities. A floating object settles until buoyant force equals its weight. For an object of uniform density, the equilibrium submerged fraction is object density divided by fluid density. A wooden block with density 600 kilograms per cubic meter in fresh water therefore rests with about 60 percent of its volume submerged. The calculator also compares the buoyant force for the entered displaced volume with the weight of an equal volume of the object. A positive upward net force means a fully submerged object tends to rise; a negative value means it tends to sink. Equal densities produce neutral buoyancy. The calculation assumes uniform densities and uses the entered local gravitational acceleration for both forces. Because gravity appears in both, it cancels from the density ratio that determines basic floating behavior. Fluid density depends on composition, salinity, pressure, and temperature. Fresh water is often approximated as 1000 kilograms per cubic meter, but its exact density changes with temperature. Seawater is denser, commonly near 1025 kilograms per cubic meter. Air is much less dense and varies strongly with altitude and weather. Object density should represent total mass divided by external volume, including sealed empty spaces when analyzing boats, floats, or hollow structures. This ideal model does not include surface tension, hydrodynamic lift, trapped bubbles, fluid acceleration, compressibility, or contact with a container. Stability is also separate from the vertical force balance: an object may have enough buoyancy to float yet overturn if its center of gravity and center of buoyancy produce an unstable moment. Use the result for education and preliminary fluid-mechanics estimates. Marine, lifting, diving, and pressure-vessel designs require appropriate safety factors, accurate geometry, load cases, free-surface effects, and engineering standards.