Archimedes' Buoyancy Force Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
Archimedes' buoyant force is calculated with Fb = fluid density × g × submerged volume. An object displacing 2 liters of fresh water (0.002 m³) experiences a buoyant force of about 19.62 N, directed upward.
Explanation
Archimedes' principle states that any object submerged, partly or fully, in a fluid experiences an upward force (the buoyant force), whose magnitude exactly equals the weight of the volume of fluid the object displaces. This force depends on neither the weight nor the nature of the submerged object itself: it depends only on the volume it displaces and the density of the fluid it's in. An object floats, sinks, or stays suspended between two depths of water depending on how this buoyant force compares to its own weight: if the buoyant force exceeds the weight (the object is less dense than the fluid, like wood in water), the object floats, with only part of its volume staying submerged until the displaced volume produces a buoyant force exactly equal to its weight; if the weight exceeds the maximum possible buoyant force (even fully submerged), the object sinks. It's this same principle that lets a massive steel ship float: it's not the density of the metal that matters, but the average density of the whole ship (hollow hull included), which stays lower than that of water thanks to all the air volume it displaces. Fluid density plays a direct, proportional role: the same object floats higher in seawater (denser, about 1,025 kg/m³) than in fresh water, which is why a ship's buoyancy is calibrated differently depending on the waters it sails. This same force directly opposes the object's weight, calculated by our weight calculator using the same constant g.
Example: an object displacing 2 liters of fresh water
Inputs
Fluid density (fresh water): 1,000 kg/m³. Submerged volume: 0.002 m³ (2 liters).
Calculation
Fb = 1,000 × 9.81 × 0.002 = 19.62 N.
Result
This object experiences a buoyant force of about 19.62 newtons, directed upward.
Frequently asked questions
Why does a massive steel ship float, when steel sinks?
Because it's not the density of the material alone that determines floating, but the average density of the whole object, hollow hull and interior air included. A ship displaces a volume of water far larger than the volume of metal it's actually made of, thanks to its hollow shape: its overall average density therefore stays lower than that of water, even though the metal of its hull, taken alone, is much denser than water and would sink by itself.
Does the buoyant force depend on how deep an object is submerged?
No, as long as the object stays fully submerged and the displaced volume doesn't change, the buoyant force stays constant regardless of depth — unlike pressure, which does increase with depth (see our hydrostatic pressure calculator). Buoyant force depends only on the displaced volume and the fluid's density, not on how deep the object is.
Does this principle also apply in air, not just in a liquid?
Yes, the same principle applies in any fluid, including a gas like air, which explains why a helium-filled balloon (less dense than air) rises: the buoyant force from the displaced air exceeds the weight of the balloon and its contents. The effect is simply much more subtle in air for most everyday objects, since air's density is about 800 times lower than water's.