Buoyancy calculator, Archimedes’ principle
Floats or sinks, submerged fraction, buoyant force on a volume and apparent weight under the fluid, with the usual fluids preset.
Result
89.463 %
- Calculation
- fraction = ρobject / ρfluid = 917 / 1025 = 0.89463
- Density ratio
- 0.89463
Notes (3)
The object floats, submerged to 89.463 % of its volume at equilibrium.
g is 9.80665 m/s², the conventional standard value, exact by definition.
In air, a one-cubic-metre balloon gains 1.2 kg of lift; precision weighing is corrected for this buoyancy.
Calculation, assumptions and sources
OverviewArchimedes’ principle in three questions.
Archimedes’ principle in three questions. Does the object float, and what fraction of its volume sits below the waterline? What force does the fluid exert on a submerged volume? How much does an object weigh on a scale under water? The usual fluids are preset (fresh water, sea water, oil, mercury, air).
Method & formulasF = ρ_fluid × g × V_submerged
The buoyant force is the weight of the displaced fluid. A floating body sinks until that weight equals its own, hence a submerged fraction equal to the density ratio, independent of g.
- Buoyant force
- the resultant of the fluid pressure forces on the body: vertical, upward, equal to the weight of the displaced fluid.
- Submerged fraction
- the share of the volume below the surface at equilibrium, ρ_object/ρ_fluid for a homogeneous floating body. Ice (917 kg/m³) in sea water (1025 kg/m³) sits 89% under water.
- Apparent weight
- what a scale reads under the fluid: the true weight minus the buoyant force. Hydrostatic weighing uses it to measure densities.
- Neutral buoyancy
- the indifferent equilibrium of a body with the same density as the fluid.
Validity domainThe calculation assumes a fluid at rest and, for the submerged fraction, a homogeneous object; it neglects air buoyancy on the emerged part (about 0.1% against water).
The calculation assumes a fluid at rest and, for the submerged fraction, a homogeneous object; it neglects air buoyancy on the emerged part (about 0.1% against water). The preset densities hold at ordinary conditions: sea water ranges from 1020 to 1029 kg/m³ with salinity and temperature. Surface tension, which floats a paper clip denser than water, is not taken into account.
Reading the resultFloating or sinking depends only on the density ratio.
Floating or sinking depends only on the density ratio. Buoyancy grows with volume. A human body, around 985 kg/m³, weighs almost nothing in water. Weighing an object in air then in water gives its density without measuring its volume.