Math
Buoyancy Calculator
Apply Archimedes' principle: compute buoyant force, decide whether an object floats or sinks, and find what percent sits below the surface. Includes fluid presets.
Buoyancy Calculator
Given fluid density, displaced volume, and gravity, compute the buoyant force (Archimedes' principle).
Densities are in kg/m³ at standard conditions.
Must be greater than zero. Water is 1000, sea water 1025.
1 liter = 0.001 m³. 1 US gallon ~ 0.003785 m³.
Standard gravity is 9.80665. Use 1.62 for the Moon, 3.71 for Mars.
Buoyant force
9,806.65 N
Fluid density
1,000 kg/m³
Gravity
9.80665 m/s²
Frequently Asked Questions about the Buoyancy Calculator
What is Archimedes' principle?
Archimedes' principle states that the upward buoyant force on an object equals the weight of the fluid it displaces. In formula form: F_b = rho_fluid x V_displaced x g, where rho_fluid is the fluid density in kg/m^3, V_displaced is the displaced volume in m^3, and g is gravity in m/s^2.
How do I know if an object will float or sink?
Compare the average density of the object (mass / volume) to the density of the fluid. If the object is less dense than the fluid it floats; if it is denser it sinks. A 1 kg block that takes up 1.5 L has an average density of 667 kg/m^3, which is lower than fresh water at 1000 kg/m^3, so it floats.
What percent of an iceberg is below water?
About 90 percent. Ice has a density near 917 kg/m^3 and sea water sits around 1025 kg/m^3. The submerged fraction equals rho_ice / rho_sea_water = 917 / 1025, which is about 0.895, so roughly 89.5 percent of an iceberg's volume sits below the surface.
Can iron float on mercury?
Yes. Iron has a density of about 7874 kg/m^3, while mercury is 13534 kg/m^3. Because iron is the lighter material, an iron block floats in mercury with about 7874 / 13534 = 58.2 percent of its volume submerged.
Why is the buoyant force on a floating object less than the maximum?
A floating object only sinks until the displaced fluid weighs the same as the object. At that point the buoyant force equals the object's weight in air, not the larger force you would get if the object were fully submerged. The calculator reports both numbers: buoyant force is the equilibrium value, and net force shows how much push or pull the object would feel if fully submerged.