Archimedes' principle states that the buoyant force on an object submerged in a fluid equals the weight of the fluid displaced by that object. Mathematically: Fₑ = ρ × V × g. This principle explains why ships float despite being made of heavy materials—the volume of water they displace creates an upward force equal to their weight. This ancient principle, discovered over 2,200 years ago, remains fundamental to physics and engineering.

The determining factor is the relative density of the object compared to the fluid. If the object's density is less than the fluid density (ρ_object < ρ_fluid), it will float. If the object's density exceeds the fluid density (ρ_object > ρ_fluid), it will sink. When densities are equal, the object achieves neutral buoyancy and remains suspended. For example, wood floats in water because its density (~700 kg/m³) is less than water's density (~1000 kg/m³).

Weight (W = m × g) is the gravitational downward force on an object. Buoyant force (Fₑ = ρ × V × g) is the upward force exerted by the fluid. The net force (Fₙₑₜ = Fₑ − W) determines motion: if buoyant force exceeds weight, the object accelerates upward and floats; if weight exceeds buoyant force, the object sinks.

Ships float because of their shape and structure, not the material itself. A ship's hull is hollow and contains air, which gives it an overall average density less than water. The large volume of the hull displaces a massive amount of water, creating a buoyant force that exceeds the ship's total weight. This is why designing ship hulls requires precise calculation of volume and weight distribution.

Yes, fluid density has a direct proportional effect on buoyant force. Higher fluid density increases buoyancy. For example, objects float much more easily in the Dead Sea (ρ ≈ 1240 kg/m³) than in fresh water (ρ ≈ 1000 kg/m³). Similarly, objects are more buoyant in seawater (ρ ≈ 1025 kg/m³) than in fresh water, which is why salt water supports greater buoyancy.

Yes, absolutely. Select "Custom Density" and enter air density at sea level (approximately 1.225 kg/m³). The physics is identical for gases and liquids. Hot air balloons float because hot air inside the balloon is less dense than the surrounding cooler air, creating a buoyant force. This calculator works for any fluid medium.

Gravitational acceleration appears in both the buoyant force formula (Fₑ = ρ × V × g) and the weight formula (W = m × g). On the Moon (g ≈ 1.62 m/s²), both forces are weaker than on Earth, but the ratio between them remains constant. You can enter custom g values to calculate buoyancy conditions on different celestial bodies or in unusual gravitational environments.

Partial submersion occurs when only part of an object is below the fluid surface, as with a floating log or ship. The buoyant force depends on the volume actually submerged, not the total volume. This calculator includes a "Submersion Percentage" field so you can calculate scenarios where objects are only partially underwater. Most floating objects achieve equilibrium with partial submersion.