Buoyancy Calculator (Archimedes)
Enter the mass and volume of an object and pick the fluid. You get the buoyant force, the verdict and how much of it is submerged.
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Formula
F_b = ρ_fluid × V_displaced × g
- If
ρ_object < ρ_fluidthe object floats: the buoyant force equals its weightm × gand the submerged fraction isρ_object / ρ_fluid. - If
ρ_object > ρ_fluidit sinks: the object is fully submerged,V_displaced = V, and the apparent weight ism × g − F_b. - g = 9.80665 m/s². Densities: fresh water 1000, sea water 1025, oil 900, mercury 13,595.1 kg/m³.
Worked example
A 5 kg object with a volume of 10 L (0.01 m³) in fresh water:
- Density = 5 / 0.01 = 500 kg/m³, less than 1000, so it floats.
- Submerged fraction = 500 / 1000 = 50%.
- Buoyant force = weight = 5 × 9.80665 = 49.03 N.
A 10 kg object of 5 L sinks (density 2000 kg/m³): F_b = 1000 × 0.005 × 9.80665 = 49.03 N, weight 98.07 N, apparent weight 49.03 N.
Frequently asked questions
What is Archimedes principle?
The buoyant force on an object equals the weight of the fluid it pushes aside: F = ρ(fluid) × V(displaced) × g. A fully submerged 5 L object in water displaces 5 kg of water, so F = 1000 × 0.005 × 9.80665 = 49.03 N.
How do I know if an object floats or sinks?
Compare densities. If the object is less dense than the fluid it floats; if it is denser it sinks. A 5 kg object of 10 L has a density of 500 kg/m³, below water at 1000, so it floats.
How much of a floating object is underwater?
The submerged fraction equals the object density divided by the fluid density. Ice at 917 kg/m³ in sea water at 1025 kg/m³ is 917 / 1025 = 89.5% submerged.
Why do ships made of steel float?
A hull encloses a lot of air, so the ship as a whole has an average density below water. Use the total enclosed volume of the vessel, not just the volume of steel, to see this.