Result

Archimedes' principle

F_{B} = ρ_{fluid} g V_{displaced}

Statement

The buoyant force on a submerged or floating object equals the weight of the fluid it displaces.

Symbols and units

$F_{B}$	buoyant force	N
$ρ_{fluid}$	fluid density	kg/m³
$V_{displaced}$	volume of fluid displaced	m³
$g$	gravitational acceleration	9.8 m/s²

When it applies

Any object fully or partially submerged in a fluid at rest.

Don't use when

Only for an object at rest (or moving at constant velocity) in the fluid — an accelerating object requires including the fluid's added-mass and drag effects.

Derivation

The pressure difference between the top and bottom of a submerged object, times its cross-sectional area, gives the net upward force:

F_{B} = (P_{bottom} - P_{top}) A = ρ g Δ h A

Since Δh·A is exactly the volume of fluid displaced:

F_{B} = ρ_{fluid} g V_{displaced}

Worked examples

Does an object float?

A 2.0 kg block of volume 0.0030 m³, fully submerged in water:

F_{B} = ρ_{w} g V = (1000) (9.8) (0.0030) \approx 29.4 N

Compare to weight:

m g = (2.0) (9.8) = 19.6 N

F_B > mg, so the block floats, submerging only partially until the displaced weight matches its own.

Watch out for

Buoyant force depends on the volume of fluid displaced, not on the object's own weight or material — a solid steel block and a hollow steel shell of the same submerged volume feel the same buoyant force.

Connects to

Hydrostatic pressure