# What Is the Formula to Calculate Buoyant Forces?

By Staff WriterLast Updated Apr 9, 2020 7:21:38 AM ET ZeroOne/CC-BY-SA 2.0

The formula to calculate buoyant force (FB) states that the upward force exerted on an immersed object is equal to the density (ρ ) of the fluid multiplied by both the fluid’s displaced volume (V) and the gravitational acceleration (g), or FB = ρ x V x g. Buoyant forces are the reasons why objects either sink or float in a fluid.

However, to derive this formula, it is necessary to know Archimedes’ law of buoyancy, which states that the buoyant force (FB) is equal to the weight (W) of the displaced fluid, or FB = W. To find the formula given above, one also must know two other physics formulas.

The first formula is that the weight of the fluid W = m x g, where (m) represents the mass of the fluid and (g) is already given above. So that FB= W = m x g. The second formula is that density (ρ) multiplied by the volume (V) is equal to the mass (m), or ρ x V = m. If one substitutes this for the mass (m) in FB = W = m x g, then one finds that FB= W = ρ x V x g.