Archimedes Principle Calculator

Calculate the buoyant force on an object submerged in a fluid based on displaced volume and fluid density.

BUOYANT FORCE
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Buoyant Force
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Object Weight
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Net Force
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Floats?
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Archimedes Principle Explained

Archimedes Principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle, discovered by the ancient Greek mathematician Archimedes around 250 BC, explains why objects float or sink and is fundamental to naval architecture, submarine design, and fluid mechanics.

The principle applies to all fluids including liquids and gases. Hot air balloons float because the heated air inside is less dense than the surrounding cooler air, so the weight of displaced air exceeds the weight of the balloon. Ships float because their hull displaces a volume of water whose weight exceeds the ship total weight.

Buoyancy Formula

Fb = ρfluid × g × Vdisplaced
Object floats if Fb ≥ Wobject

Where Fb is the buoyant force, rho is fluid density, g is gravitational acceleration (9.81 m/s²), and V is the volume of fluid displaced by the object.

Common Fluid Densities

FluidDensity (kg/m³)
Air (sea level)1.225
Freshwater1,000
Seawater1,025
Mercury13,534
Olive oil911
Gasoline737

FAQ

Why do ships made of steel float?

Although steel is denser than water (7,800 vs 1,000 kg/m³), a ship hull is mostly hollow air space. The total weight of the ship is less than the weight of water displaced by its hull volume. If you crumpled a ship into a solid steel ball, it would indeed sink.

Why is it easier to float in the Dead Sea?

The Dead Sea has a salinity of about 34%, making its water density approximately 1,240 kg/m³ compared to normal seawater at 1,025. The greater density means the buoyant force on your body is about 21% greater, so you float higher with less effort.

How did Archimedes use this principle?

Legend says King Hiero asked Archimedes to determine if a crown was pure gold without damaging it. Archimedes realized he could compare the crown volume (by water displacement) to its weight. If the density matched pure gold (19,300 kg/m³), it was genuine. A less dense alloy would displace more water for the same weight.