This buoyancy calculator applies Archimedes’ principle: the buoyant force on an object, whether it floats or sinks, and — if it floats — exactly how much of it sits below the waterline.
The “tip of the iceberg” is this math: ice at 917 kg/m³ in seawater at 1,025 floats with 89.5% submerged — roughly nine-tenths hidden, as advertised.
F = ρ_fluid × V_displaced × g
Archimedes: the buoyant force equals the weight of fluid displaced. Floating equilibrium is the elegant special case: an object settles until displaced weight equals its own weight, which happens when the submerged fraction = ρ_object ÷ ρ_fluid — shape doesn't enter it. Densities of everything else: our Density Calculator. Part of our Physics Calculators collection.
Worked Example (Verified)
- 0.5 m³ wooden block, 600 kg/m³, in fresh water (defaults): weight = 300 kg × 9.81 = 2,943 N; fully held under, buoyancy = 1,000 × 0.5 × 9.81 = 4,905 N — release it and it pops up until only 60% remains submerged, displacing exactly its weight
- Steel in water: 7,850 vs 1,000 — sinks at 7.85× overmatched; steel ships float because the hull's average density (steel + air volume) falls below 1,000 — form, not material, grants buoyancy
- Ice in fresh water: 91.7% submerged; in your drink (meltwater ≈ water) the level famously doesn't rise as the cube melts — displacement equals melt volume, Archimedes' party trick
- Hot-air balloons are this calculator in a gas: lift = (ρ_cold − ρ_hot) × V × g — a 2,800 m³ envelope with Δρ ≈ 0.25 lifts ~700 kg of balloon, basket and optimists
Where Buoyancy Runs the World
- Ship draft marks and Plimsoll lines: legally enforced free-floating fractions by water type and season.
- Submarines: neutral buoyancy by ballast trim — the rho-equals-rho boundary this calculator labels.
- Hydrometers (including the brewing kind on our ABV Calculator) are floating-fraction instruments: the submerged depth reads density directly.
- Life jackets are rated in newtons of buoyancy (ISO levels 50/100/150/275 N) — the F card's units, worn.
Related Tools
- Density Calculator — the ρ in every line here
- Pressure Calculator — buoyancy's hydrostatic sibling
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate buoyant force?
F = ρ_fluid × V_submerged × g — density of the fluid times the submerged volume times gravity: the weight of the displaced fluid. Half a cubic meter submerged in fresh water displaces 500 kg of water and feels 4,905 N of upward force.
How do I know if an object will float?
Compare densities: object density below fluid density floats; above, sinks; equal, it hovers neutrally. For composite objects (boats, bottles) use the average density — total mass divided by total external volume, air spaces included.
How much of a floating object is underwater?
Exactly the density ratio: submerged fraction = ρ_object ÷ ρ_fluid. Wood at 600 in fresh water rides 60% under; ice in seawater shows ~10.5% above the surface — the literal origin of "tip of the iceberg."
Why does a steel ship float when steel sinks?
Because the relevant density is the ship's average: a hull encloses enormous air volume, so mass ÷ total volume lands around 200–500 kg/m³ even fully loaded — comfortably floatable. Breach the hull, flood the air spaces, and the average density crosses 1,000: that's sinking, arithmetically.
Does buoyancy depend on depth?
Not for incompressible fluids and rigid objects — pressure grows with depth, but its difference across the object (which is what buoyancy is) stays constant. Compressible objects (a balloon, a diver's wetsuit) shrink with depth and do lose buoyancy — a real freediving and submarine-trim consideration.
Is this buoyancy calculator free?
Yes — free, instant, no sign-up.