🛟 Buoyancy Calculator (Archimedes)
Enter the fluid density and displaced volume to get the buoyant force, add the object's mass to see whether it floats or sinks.
Buoyant force
490.33 N
Object weight 392.27 N →
Floats ⬆
Archimedes' principle: the upward buoyant force equals the weight of the displaced fluid, F = ρ·V·g. An object floats when that force is at least its own weight (i.e. its average density is below the fluid's). 🔒 In your browser.
How the buoyancy calculator (archimedes) works
Archimedes' principle says the upward buoyant force on an object equals the weight of the fluid it displaces: F = ρ_fluid × V × g, where ρ is the fluid's density, V the displaced volume and g gravity (9.81 m/s²). If you also enter the object's mass, the tool compares its weight (m × g) to the buoyant force: it floats when the buoyant force from its fully submerged volume is at least its weight, equivalently, when its average density is less than the fluid's.
Density presets are built in (fresh water 1000, seawater 1025, oil ~900, mercury 13534 kg/m³). A ship of steel floats because its shape displaces a large volume of water, its average density, including the air inside, is below water's. The same steel as a solid block sinks.
Frequently asked questions
What is Archimedes' principle?
The buoyant (upward) force on a body in a fluid equals the weight of the fluid it displaces: F = ρ·V·g. It explains why objects feel lighter in water and why some float.
How do I calculate buoyant force?
Multiply the fluid's density by the displaced volume and by g: F = ρ × V × 9.81. One cubic metre submerged in water (1000 kg/m³) experiences about 9,807 N of buoyancy.
Will an object float or sink?
It floats if its average density is less than the fluid's, equivalently, if the buoyant force when fully submerged is at least its weight. Enter the object's mass and the tool tells you which.
Why does a steel ship float but a steel bar sinks?
A ship's hull encloses a large volume of air, so it displaces a lot of water for its weight, its average density is below water's. A solid steel bar displaces only its own small volume, so it sinks.
Does buoyancy work in air?
Yes, air (density ~1.2 kg/m³) exerts a small buoyant force, which is why helium and hot-air balloons rise. Set the fluid density to air to explore it, though the forces are much smaller than in water.