Buoyancy Calculator
Buoyancy is the upward force a fluid exerts on a submerged or floating object, equal to the weight of the fluid it displaces. Pick a fluid or enter a custom density, give the displaced volume, and get the buoyant force in newtons with Archimedes’ principle F = ρ·V·g. Add the object’s mass to see its apparent (immersed) weight, whether it floats or sinks, and how much of it sits below the surface.
Formula
Worked example
A 7 kg block displacing 0.01 m³ of fresh water (ρ = 1000 kg/m³) on Earth (g = 9.81 m/s²): F = 1000 × 0.01 × 9.81 = 98.1 N up. Its weight is 7 × 9.81 = 68.7 N, so buoyancy wins and it floats; fraction submerged = 700 ÷ 1000 = 70%. Fully held under, its apparent weight would be 68.7 − 98.1, a net 29.4 N push upward.
What buoyancy is and how it works
Buoyancy is the upward force a fluid exerts on any object placed within it, and it arises because pressure in a fluid increases with depth. The bottom of a submerged object sits deeper than its top, so the fluid pushes up on the underside harder than it pushes down on the top, and the difference is a net upward force. Archimedes’ principle states this force exactly: it equals the weight of the fluid the object displaces, written F = ρ·V·g, where ρ is the fluid density, V is the displaced (submerged) volume, and g is gravitational acceleration. The force does not depend on the object’s own weight or material, only on how much fluid it pushes aside and how dense that fluid is. Pick a fluid preset to load its density automatically, or choose Custom to type any value, and switch the volume between cubic metres, litres, cubic feet or US gallons to match your figures.
Apparent weight, floating, sinking and fraction submerged
Turn on the object option and add a mass to go further than the bare force. The calculator works out the object’s real weight (mass times gravity) and its apparent or immersed weight, which is the real weight minus the buoyant force, the lighter value a scale reads when the object hangs underwater. Comparing the two forces decides the outcome: if buoyancy is larger the object floats, if weight is larger it sinks, and if they are equal it is neutrally buoyant and hovers at any depth, the balance submarines and scuba divers hold. For a floating object the calculator also reports the fraction submerged, equal to the object’s average density divided by the fluid’s density. That single ratio explains why roughly nine tenths of an iceberg hides below the waterline and why a ship rides higher in dense seawater than in fresh water.
Gravity, units and worked steps
Because the force scales directly with gravity, you can switch from Earth to the Moon, Mars or Jupiter, or enter a custom value, to see how the same displaced volume lifts differently off-planet. The unit switch reports the force in newtons or pounds-force to suit physics homework or engineering rules of thumb alike. Every result comes with a show-your-work panel that substitutes your actual numbers into F = ρ·V·g and then into the apparent-weight and fraction-submerged steps, so you can follow the arithmetic rather than trust a black box. These are idealised figures that assume a single uniform fluid and ignore surface tension and compressibility, which is accurate for everyday liquids and gases but not for extreme pressures.
Typical fluid densities for buoyancy calculations
| Fluid | Density (kg/m³) | Buoyant force on 0.01 m³ (N) |
|---|---|---|
| Air (sea level) | 1.225 | 0.12 |
| Gasoline | 740 | 72.6 |
| Ethanol | 789 | 77.4 |
| Olive oil | 915 | 89.8 |
| Fresh water | 1000 | 98.1 |
| Seawater | 1025 | 100.5 |
| Mercury | 13534 | 1327.7 |
Buoyant force scales directly with fluid density (F = ρ·V·g), so denser fluids lift harder.
Frequently asked questions
What is the formula for buoyant force?
The buoyant force is F = ρ·V·g, where ρ is the density of the fluid in kilograms per cubic metre, V is the volume of fluid displaced in cubic metres, and g is gravitational acceleration (9.81 m/s² on Earth). The result is in newtons and always acts upward, equal to the weight of the displaced fluid.
What is apparent or immersed weight?
Apparent weight is what a scale reads when an object hangs submerged in a fluid: its real weight minus the buoyant force pushing up. A 10 N rock that experiences 3 N of buoyancy underwater has an apparent weight of 7 N. If the buoyant force exceeds the weight the apparent weight is negative, which simply means the object is being pushed upward and will float.
How do I know whether an object floats or sinks?
Compare the buoyant force from the fully submerged volume with the object’s weight. If buoyancy is greater it floats, if weight is greater it sinks, and if they are equal it is neutrally buoyant. Equivalently, an object floats when its average density is less than the fluid’s. A steel ship floats because its hull encloses air, lowering its average density below that of water.
How much of a floating object sits below the surface?
For a floating object the submerged fraction equals its average density divided by the fluid’s density. Ice at about 920 kg/m³ in seawater at 1025 kg/m³ floats with roughly 90% of its volume underwater, which is why only the tip of an iceberg shows. The calculator reports this fraction whenever you add an object mass and it floats.
Does buoyant force depend on how deep the object is?
No. As long as the object stays fully submerged, the buoyant force is the same at any depth, because it depends only on the displaced volume, the fluid density and gravity, not on depth. Pressure does increase with depth, but the difference between the pressure on the top and bottom of the object stays constant, so the net upward force does not change.