Fluid Mechanics
Buoyancy Calculator
Calculate buoyant force using Archimedes' principle. Determine if an object floats or sinks. Fluid presets included.
Buoyant Force
F₂ = ρVg (Archimedes)
Float/Sink
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Net Force
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Step-by-Step Solution
What is Buoyancy?
Buoyancy is the upward force exerted by a fluid on any object submerged (fully or partially) in it. Archimedes' principle states that this force equals the weight of fluid displaced by the object. If the buoyant force exceeds the object's weight, it floats; if not, it sinks.
F₂ = ρVg
ρ = fluid density (kg/m³) | V = volume of fluid displaced (m³) | g = 9.81 m/s²
💡 An object floats when its average density is less than the fluid. A steel ship floats because its hollow hull displaces a volume of water whose weight exceeds the ship's total weight.
Real-World Applications
Ship Design
Steel ships float because their hull shape displaces enough water to exceed the ship's weight.
Hot Air Balloons
Warm air inside is less dense than cool air outside — buoyancy lifts the balloon.
Fish Swim Bladders
Fish control their depth by adjusting the gas in their swim bladder, changing their average density.
Density Measurement
Archimedes' method — measuring displaced water — is used to find the density of irregular objects.
Frequently Asked Questions
Why does a heavy ship float but a small stone sinks?
The ship's hull encloses a large volume of air, making its average density less than water. The stone is solid metal with density much greater than water. Floating depends on average density, not mass alone.
What is the Archimedes principle?
Archimedes' principle states: the buoyant force on an object equals the weight of fluid it displaces. F_b = ρ_fluid × V_displaced × g. This was discovered by Archimedes in ~250 BC.
How do submarines submerge and surface?
Submarines have ballast tanks. Filling them with water increases average density above seawater, causing submersion. Blowing compressed air back in reduces density, causing the submarine to rise.