TheoremProved

Archimedes' principle

Statement

$F_A = \rho_{\text{fluid}}\, g\, V_{\text{submerged}}$ — the buoyant force on an object immersed in a fluid equals the weight of the fluid it displaces.

Why is it true?

An object floats when the Archimedes buoyant force balances its weight (its average density is less than the fluid's); it sinks otherwise.

Drop objects of different densities into a water tank: they float, hover or sink by the ratio ρ_object/ρ_water; buoyancy equals the weight of displaced fluid.

Stated by

stated -250Archimedes of Syracuse

Topics that use this theorem

Archimedes’ principle

Step-by-step proofs

Proving Archimedes' principle from the fluid pressure gradient

PhysicLabs, 2026

References

Archimedes (-250). On Floating Bodies