Library / Fluid Mechanics / FLU-08

Fluid Mechanics

Buoyant force

Upward force on a body from the fluid it displaces.

Ref: FLU-08
Rev: v1
Field: Fluid Mechanics
Result: F_B [N]

F_{B} = ρ_{f} g V_{displaced}

Buoyancy acts upward in a uniform-density stationary fluid and equals the weight of the fluid displaced. A body floats when it displaces a weight of fluid equal to its own weight.

A body in a fluid is pushed up by a force equal to the weight of the fluid it pushes aside.

Calculator

Solve for

F_BBuoyant forceComputed

ρ_fFluid density

kg/m³

7001,500

VDisplaced volume

m³

0.001100

Mass of fluid displaced51.25 kg
Buoyancy per litre displaced10.05 N/L

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Buoyant force (N) current value 502.6 N

VDisplaced volumeKey driver

10.11,010,000

ρ_fFluid density

343735

A fully submerged 50-litre body in seawater feels a buoyant force of about 503 N.
Seawater gives about 2.5% more buoyancy per litre than fresh water.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (N)	Local step	Change in result
V Displaced volume	0.001 to 100 m³	10.05	1,005,000	1,005,000	+10%	+10 %
ρ_f Fluid density	700 to 1,500 kg/m³	343.2	735.5	392.3	+10%	+10 %

Sweep of Displaced volume

Displaced volume (m³)	Buoyant force (N)
0.001	10.05
0.004217	42.39
0.01778	178.7
0.07499	753.8
0.3162	3,179
1.334	13,400
5.623	56,530
23.71	238,400
100	1,005,000

Sweep one variable

Vary

Buoyant force (N)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

F_B

Buoyant force

Result · N

What the equation gives you. Everything else feeds it.

ρ_f

Fluid density

kg/m³ · typical 700 to 1,500

Density of the fluid (seawater 1025). Directly proportional.

Displaced volume

m³ · typical 0.001 to 100

Volume of fluid displaced. Directly proportional.

Worked example with the values above

Mass displaced: ρV = 1,025 × 0.05 = 51.25 kg.
Weight: 51.25 × 9.807.
F_B = 502.6 N.

Assumptions and limits

Stationary fluid of uniform density.
Body fully or partly submerged with V the submerged volume.

Common mistakes

Using the body’s total volume for a floating body.
Using the body’s density in place of the fluid’s.

Statistics and uncertainty

Density changes with temperature and salinity by about 1–3%, which carries directly into the buoyant force.

Where it is used

Flotation and ballast design.
Underwater vehicle trim.

Maths you need

Density: ρ = m/V
Weight: W = mg

Related formulas

Practise this formula