What Is Buoyancy and How Does This Calculator Work?
Buoyancy is the upward force a fluid exerts on an object submerged or floating in it, caused by pressure increasing with depth. It is governed by Archimedes' principle: an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces, regardless of the object's own weight or material.
The buoyancy formula — attributed to the Greek mathematician Archimedes of Syracuse around 250 BC — is: Fb = ρ_fluid × V_submerged × g, where Fb is the buoyant force, ρ_fluid is the density of the fluid, V_submerged is the volume of fluid displaced by the submerged part of the object, and g is standard gravity (9.80665 m/s²). This calculator compares that buoyant force to the object's weight (mass × g) to determine whether it floats, sinks, or hovers at neutral buoyancy.
According to Archimedes' principle, an object floats when its average density is lower than the fluid's density, sinks when it is higher, and remains suspended at any depth when the two densities are exactly equal — a state called neutral buoyancy that submarines and scuba divers actively control with ballast.
How to Use This Buoyancy Calculator
Enter the object's density and volume, plus the fluid it is placed in, and the calculator updates instantly. Here is what each field means:
- Object Material: Pick a common material preset — ice, wood, aluminum, steel, gold — or choose "Custom Material" to type any density.
- Object Density: Mass per unit volume of the object itself (kg/m³ or lb/ft³), independent of what it floats in.
- Object Volume: The total volume of the object, in m³ (metric) or ft³ (US customary).
- Fluid: Pick a preset — air, gasoline, fresh water, seawater, honey, mercury — or enter a custom fluid density.
This calculator works in both metric (kg/m³, m³, newtons) and US customary units (lb/ft³, ft³, pounds-force), and the underlying physics is identical for liquids and gases — the same formula explains why a ship floats on water and why a helium balloon rises through air.
What Your Buoyancy Result Means
When an object floats, it sinks only until the buoyant force from its submerged volume exactly equals its weight — the fraction submerged is simply its own density divided by the fluid's density. When it sinks, the full volume displaces fluid, and the "apparent weight submerged" (weight minus buoyant force) is what a scale would read if you weighed the object while it hung underwater, a trick Archimedes reportedly used to prove a goldsmith's crown was not solid gold.
| Fluid | Density (kg/m³) | What Floats In It |
|---|---|---|
| Air (sea level) | 1.225 | Helium, hot air, hydrogen |
| Gasoline | 720 | Ice, wood, most plastics |
| Fresh Water | 1,000 | Ice, wood, cork, the human body |
| Seawater | 1,025 | Same as fresh water, plus slightly denser objects |
| Honey | 1,420 | Fruit, ice, many woods and plastics |
| Mercury | 13,534 | Iron, steel, aluminum, lead |
Frequently Asked Questions
What is the formula for buoyant force?
Buoyant force is Fb = ρ_fluid × V_submerged × g, where ρ_fluid is the fluid's density, V_submerged is the volume of fluid displaced, and g is gravity (9.80665 m/s²). This is Archimedes' principle: the buoyant force equals the weight of the fluid displaced by the object, not the object's own weight.
How do you know if an object floats or sinks?
Compare average densities: an object floats if its density is lower than the fluid's, it sinks if its density is higher, and it hovers at neutral buoyancy if the two densities are equal — this is true whether the fluid is water, oil, or air, and it does not depend on the object's total mass or shape.
Why do steel ships float if steel sinks in water?
Solid steel has a density of about 7,850 kg/m³, nearly eight times denser than water, so a solid block sinks. A ship's hull, however, is hollow and shaped to enclose a large volume of air, which lowers the vessel's average density — hull, cargo, and trapped air combined — below that of water, so it displaces enough water to float.
How accurate is this buoyancy calculator?
The calculation is exact given the densities and volume entered, since it applies Archimedes' principle directly with no approximations. Accuracy in practice depends on knowing the true density of the object and fluid — the preset values are representative averages at typical temperatures, and real materials (like wood or seawater) vary somewhat with moisture, temperature, and salinity.