Buoyant Force Calculator — Archimedes' Principle

Archimedes' principle states that any object immersed in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. The formula is F_b = ρ_fluid × V_submerged × g. For 0.5 m³ submerged in freshwater: F_b = 1000 × 0.5 × 9.81 = 4,905 N — that upward push equals the weight of 500 kg of water, regardless of the object's own material.

NIST defines standard gravitational acceleration as 9.80665 m/s² (commonly rounded to 9.81 m/s²). On the Moon, g ≈ 1.62 m/s², which drastically reduces buoyant force even in the same fluid. For Earth-based engineering calculations, use 9.80665 m/s² for precision work, or 9.81 m/s² for general physics — never round to 10 m/s² in safety-critical design.

Freshwater at 20 °C has a density of approximately 998.2 kg/m³, while average ocean seawater (3.5% salinity) is about 1025 kg/m³ — roughly 2.7% denser. For a 1 m³ submerged volume, that difference equals 263 N of extra buoyant force. In the Dead Sea (~33% salinity, ~1240 kg/m³), buoyancy is so strong that it is nearly impossible for a person to submerge voluntarily.

For a freely floating object, the submerged fraction equals the ratio of object density to fluid density: fraction_submerged = ρ_object / ρ_fluid. Ice (917 kg/m³) floating in seawater (1025 kg/m³) submerges 917/1025 ≈ 89.5%, leaving 10.5% above the surface. A piece of oak (~700 kg/m³) floating in freshwater submerges 70%, with 30% above water.

Yes — buoyancy works in any fluid, including gases. A helium-filled balloon in air experiences an upward buoyant force because helium (0.1786 kg/m³) is far less dense than air (1.225 kg/m³ at sea level). The net lift per cubic meter of helium is (1.225 − 0.1786) × 9.81 ≈ 10.27 N/m³. Hot-air balloons work by reducing the air density inside the envelope below ambient levels.

An object is neutrally buoyant when its average density exactly equals the surrounding fluid density, so F_b = W_object and the net force is zero. Submarines achieve this by flooding or pumping ballast tanks to adjust their average density. Scuba divers aim for neutral buoyancy (average human body density ≈ 985 kg/m³, very close to freshwater) by adjusting their buoyancy compensator (BCD) and weight belts.

For most practical purposes with liquids, buoyancy depends only on the volume of fluid displaced and the fluid density at that location — not on the depth per se. However, seawater density increases slightly with depth due to compression (from ~1025 kg/m³ at the surface to ~1050 kg/m³ at 10,000 m). This means submarines experience marginally greater buoyancy at extreme depths, a factor that must be accounted for in deep-sea vehicle design.

Apparent weight is the measured weight of a submerged object: W_apparent = W_actual − F_b. A steel block weighing 500 N in air, submerged in freshwater with V = 0.004 m³, experiences F_b = 1000 × 0.004 × 9.81 = 39.24 N, giving an apparent weight of 500 − 39.24 = 460.76 N. This principle underlies hydrostatic weighing, a gold-standard body composition assessment technique.

A ship floats because its average density — total mass divided by total enclosed volume (including air spaces) — is less than water. A typical ocean freighter might have a hull steel mass of 20,000 tonnes, but its total enclosed volume is large enough that the average density falls below 1025 kg/m³. The buoyant force equals the weight of seawater displaced by the entire hull volume below the waterline.

When an object floats, only part of its volume is submerged, and buoyancy exactly equals its weight (equilibrium). The submerged fraction = ρ_object / ρ_fluid. When fully submerged, the buoyant force is fixed at ρ_fluid × V_total × g regardless of depth. If F_b > weight, the object rises; if F_b < weight, it sinks. The calculator uses the submerged volume you enter — for floating objects, enter only the submerged fraction of the total volume.