Calculate buoyant force on a submerged object from fluid density and displaced volume using Archimedes' principle F_b = ρgV, with float/sink determination.
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Buoyant force
9,806.65 N
Buoyant force (N)
9806.65
Fluid density (kg/m³)
1000.0
Also in Physics
Science — Physics
Archimedes' principle states that a submerged object experiences an upward buoyant force equal to the weight of the fluid it displaces: F_b = ρ_fluid × V_displaced × g. This force determines whether objects float or sink, and governs ship design, submarine depth control, and hot-air ballooning.
A 1 m³ object fully submerged in fresh water (ρ = 1000 kg/m³) at standard gravity experiences a buoyant force of 1000 × 1 × 9.80665 ≈ 9807 N. If the object weighs more than 9807 N (mass > 1000 kg), it sinks; if less, it floats. Salt water (ρ ≈ 1025 kg/m³) provides about 2.5% more buoyancy than fresh water, which is why ships sit slightly higher in rivers than in the ocean.
The calculator solves for any of the three variables: buoyant force, displaced volume, or fluid density. "Displaced volume" is the submerged portion of an object — for a partially floating object this is less than the total object volume. Knowing the buoyant force and fluid density allows back-calculating the submerged volume, useful for estimating cargo loads or checking tank ballast requirements.
Frequently asked questions
A steel ship displaces a large volume of water because its hull is hollow. The total mass of the ship (steel + contents + air) divided by the total volume of the hull gives an effective density less than water. As long as the average density of the entire vessel is below the water's density, it floats.
Neutral buoyancy occurs when the buoyant force exactly equals the object's weight, so it neither sinks nor rises. Submarines achieve neutral buoyancy by adjusting ballast tanks. Divers use buoyancy compensators (BCDs) to control depth.
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