Buoyancy Force Calculator

Calculate buoyancy force and whether an object floats or sinks.

1 liter = 0.001 m³
Water=1000, Seawater=1025, Air=1.2
Wood≈600, Ice=917, Steel=7800
Please check your inputs and try again.

Archimedes' Principle and Floating Equilibrium

Buoyant force is the net upward pressure force created because fluid pressure is greater at the bottom of an immersed object than at the top. For a fluid of uniform density, that net force equals the weight of the displaced fluid: Fb=ρfgVdisp. The relevant volume is displaced or submerged volume, not automatically the entire object's volume.

Whether an object floats or sinks depends on comparing buoyant force with its weight. A fully submerged object with average density greater than the fluid has W>Fb and tends to sink. If its average density is lower, it can float by settling at a depth where the displaced-fluid weight exactly equals the object's weight. For a uniform floating object in a single fluid, the submerged fraction is approximately ρobject/ρfluid.

Fb = ρfluidgVdisplaced,   W = mg
SymbolMeaningWhy it appears / units
FbBuoyant forceN; upward resultant of pressure forces.
ρfluidFluid densitykg/m3; denser fluids give more buoyancy for the same volume.
VdisplacedDisplaced fluid volumem3; equals submerged volume for an impermeable object.
gGravitational accelerationm/s2; appears in both fluid weight and object weight.

Shape matters because it controls how much fluid can be displaced before an object is fully submerged. That is why a hollow steel ship can have an average density lower than water even though solid steel is much denser. For compressible fluids, large depth ranges, or rapidly accelerating flows, density and pressure may vary enough that the simple uniform-fluid model needs refinement.

Worked Examples

Example 1: Ice in water: V=0.001m³, ρ_ice=917, ρ_water=1000
Fb=9.81N, W=9.0N
Result: FLOATS — 91.7% submerged
Explains why icebergs float mostly underwater
Example 2: Steel ball in water: V=0.001m³, ρ=7800
Fb=9.81N, W=76.5N
Result: SINKS — net 66.7N downward
Steel is 7.8× denser than water
Example 3: Buoyant force in seawater
Vdisp=0.002m3, ρ=1025kg/m3 → Fb=1025×9.81×0.002
Result: Fb≈20.11 N
The same displaced volume receives slightly more buoyant force in seawater than in fresh water because seawater is denser.
Example 4: Fraction submerged for floating wood
ρwood=800kg/m3, ρwater=1000kg/m3 → Vsub/V=800/1000
Result: 80% submerged
At floating equilibrium, the displaced water weighs exactly as much as the object.

Common Mistakes

⚠️
Using total object volume when only part is submerged

Archimedes' principle uses displaced volume. For a floating object, that is generally less than the total object volume.

⚠️
Comparing material density instead of average object density

A hollow steel structure can float because its total mass divided by its overall displaced volume can be less than the fluid density.

⚠️
Adding buoyancy and weight in the same direction

Buoyant force acts upward while weight acts downward. The net vertical force is their difference, with direction determined by which is larger.

Frequently Asked Questions

What is Archimedes' principle?
A body immersed in fluid experiences an upward force equal to the weight of fluid displaced: Fb = ρ_fluid × g × V_submerged.
How do steel ships float?
Ships are mostly hollow — the average density of the ship+air system is less than water. A steel hull shaped to displace enough water equals the ship's weight.
Does buoyant force depend on the object's density?
For a specified displaced volume, buoyant force depends on fluid density, gravity, and displaced volume, not directly on object density. Object density matters because it determines the object's weight and, for a floating object, how much volume must submerge to reach equilibrium.
Why does an object feel lighter underwater?
The scale or support force only has to balance the object's weight minus the upward buoyant force. This reduced support force is called apparent weight. The true gravitational weight has not disappeared; the surrounding fluid is carrying part of the load through pressure forces.
Does buoyant force increase with depth in water?
For a fully submerged rigid object in an incompressible fluid of nearly constant density, the net buoyant force is essentially independent of depth even though absolute pressure increases. The pressure difference across the object's vertical extent remains tied to ρg and displaced volume.
What condition gives neutral buoyancy?
Neutral buoyancy occurs when the object's weight equals the buoyant force while it is fully submerged. For a uniform incompressible fluid and an object whose entire volume displaces fluid, this corresponds to the object's average density equaling the surrounding fluid density.

Formula Explorer connections

Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.

Capacitor Energy Calculator →Carnot Efficiency Calculator →Center of Mass Calculator →Physics Formula Explorer →