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Physics

Calculate the Buoyant Force

Updated · Standard formula, shown below

Buoyant force 19.61 N
Buoyant force
4.41 lbf
Result
Mass of fluid displaced
2.00 kg
Result
Fluid density
1000 kg/m³
You entered

This calculator applies Archimedes’ principle: the upward buoyant force equals the weight of the fluid an object pushes aside. Enter the fluid density and the volume displaced and you get the force in newtons and pounds-force.

Formula

Fb = ρ × V × g.

  • ρ: fluid density in kg/m³ (fresh water about 1000, sea water about 1025)
  • V: displaced volume in m³; litres ÷ 1000 = m³
  • g: standard gravity, 9.80665 m/s²
  • 1 lbf = 4.4482216 N

Worked Example

A 2 L object fully under fresh water (ρ = 1000 kg/m³).

  1. V = 2 ÷ 1000 = 0.002 m³
  2. Fb = 1000 × 0.002 × 9.80665 = 19.61 N
  3. In pounds-force: 19.6133 ÷ 4.44822 = 4.41 lbf
  4. Mass of water displaced = 1000 × 0.002 = 2.00 kg

Limits and common mistakes

  • For a floating object, V is only the part below the surface, not the whole object.
  • The object floats if the buoyant force at full submersion is more than its weight (mass × g).
  • Mixing litres and cubic metres is the common error: 1 m³ = 1000 L. One US gallon is 3.785 L.
  • The same force acts in any fluid, including air: a 2 L object in air (about 1.2 kg/m³) gets only about 0.024 N of lift.
Formula used
in rho | Fluid density | kg/m³ | 1000 | 0
in v | Volume of fluid displaced | L | 2 | 0
out fb | Buoyant force | N | rho * (v / 1000) * 9.80665 | 2
out lbf | Buoyant force | lbf | fb / 4.4482216152605 | 2
out mass | Mass of fluid displaced | kg | rho * v / 1000 | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.