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Buoyancy Calculator (Archimedes' Principle)

Find out whether an object floats or sinks in a fluid, the buoyant force and net force involved, and — if it floats — what fraction of it stays submerged.

Result
Floats
Weight
4.905 N
Buoyant force (if fully submerged)
9.81 N
Object density
500 kg/m³ (50% of fluid density)
Submerged fraction at rest
50%

Where this falls

50 falls in the "Floats low (mostly submerged)" range.

How it works

Archimedes' principle: an object fully submerged in a fluid displaces a volume of fluid equal to its own volume, and feels an upward buoyant force equal to the weight of that displaced fluid — F_buoyancy = fluid density × volume × g. Its own weight is F_weight = mass × g. Comparing the two when fully submerged decides the outcome: buoyancy greater than weight means it floats (a net upward force pushes it toward the surface), weight greater than buoyancy means it sinks, and the two being equal means it's neutrally buoyant.

If it floats, the fraction of its volume that stays submerged once it settles follows from balancing weight against buoyancy at equilibrium: mass × g = fluid density × (submerged volume) × g, which simplifies to submerged fraction = object density ÷ fluid density — an object half as dense as the fluid floats exactly half-submerged.

Fluid density is left as a plain, un-toggled kg/m³ input (default 1000 for fresh water, editable for seawater, oil, or anything else) since kg/m³ is the standard unit used worldwide for density; mass, volume, and gravity get this page's metric/imperial toggle and are converted internally before the formula runs.

FAQ

Why does gravity not actually matter for whether something floats or sinks?

Because both the buoyant force and the object's weight scale by the same factor of g, so g cancels out of the comparison between them — whether an object floats or sinks, and what fraction of it stays submerged, depends only on the ratio of its density to the fluid's density, not on how strong gravity is. Changing gravity (e.g. to model another planet) rescales both forces equally and changes the reported newtons, but never flips the floats/sinks result.

What if I only know the object's density, not its mass and volume separately?

Enter any volume you like (1 works fine) along with a mass equal to that volume times the known density, since only their ratio — the object's density — actually determines whether it floats or sinks and what fraction is submerged; the absolute size only scales the reported force values.

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