Archimedes’ buoyancy
F = ρ_fluid × g × V_submerged
Archimedes’ principle in three questions: does the object float, and sitting how deep? 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) and the verdict is physical: an object exactly as dense as the fluid floats mid-water, an object lighter than the displaced fluid rises instead of weighing. The submerged fraction of sea ice, 89%, comes out of the density ratio.
89.463 %
- Calculation
- fraction = ρ_object / ρ_fluid = 917 / 1025 = 0.89463
- Density ratio
- 0.89463
The object floats, submerged to 89.463 % of its volume at equilibrium.
The submerged fraction is the ratio of the densities: a floating body sinks until the displaced fluid weighs exactly its own weight. Ice (917 kg/m³) in sea water (1025) sits 89% under: the iceberg is not an image, it is this quotient.
g is 9.80665 m/s², the conventional standard value: exact by definition, not measured. The floats-or-sinks verdict does not even depend on g: only the density ratio matters.
Buoyancy exists in every fluid, air included: a one-cubic-metre balloon gains 1.2 kg of lift there. It is also why precision weighing is corrected for the air buoyancy on the weighed object.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasF = ρ_fluid × g × V_submerged
F = ρ_fluid × g × V_submerged
submerged fraction = ρ_object / ρ_fluid
apparent weight = W − F = (m − ρ_fluid·V)·g
The buoyant force is the weight of the displaced fluid: that is the whole principle. A floating body sinks until that displaced weight equals its own, hence the submerged fraction as a plain density ratio, with no 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. It equals ρ_object/ρ_fluid for a homogeneous floating body.
- Apparent weight
- · what a scale reads under the fluid: the true weight minus the buoyant force. This is hydrostatic weighing, the historical method for measuring densities.
- Neutral buoyancy
- · the indifferent equilibrium of a body exactly as dense as the fluid: it neither rises nor sinks. It is the trim of a submarine or a diver’s float.
Validity domainThe tool assumes a fluid at rest, a homogeneous object for the submerged fraction, and neglects the air buoyancy on the emerged part (about 0.
The tool assumes a fluid at rest, a homogeneous object for the submerged fraction, and neglects the air buoyancy on the emerged part (about 0.1% against water). The preset densities are ordinary-condition values: sea water ranges from 1020 to 1029 kg/m³ with salinity and temperature. Surface tension, which floats a paper clip denser than water, is another phenomenon: here only buoyancy counts.
Reading the resultThe floats-or-sinks verdict depends only on the density ratio, not on size: a grain of sand sinks just as a mountain of sand would.
The floats-or-sinks verdict depends only on the density ratio, not on size: a grain of sand sinks just as a mountain of sand would. What size changes is the force: buoyancy grows with volume. The apparent weight explains the lightness felt in water, a human body at 985 kg/m³ weighs almost nothing there, and hydrostatic weighing turns it into an instrument: weighing an object in air then in water gives its density without measuring its volume.