How to use this calculator
Pick the fluid (or type its density), then enter the object’s total volume and mass. The calculator finds the buoyant force when the object is fully submerged and compares it with the weight. If the object floats, it shows how much of its volume is below the surface; if it sinks, it shows what a scale would read with the object hanging underwater.
Formulas
The buoyant force is the net result of fluid pressure on the object: pressure grows with depth (p = ρgh), so the bottom of an object is pushed up harder than the top is pushed down. Adding up that difference over the whole surface gives exactly the weight of the displaced fluid.
Worked example
A 20 L, 12 kg block in fresh water (the default)
- Fully submerged: FB = 998.2 × 9.807 × 0.020 = 195.8 N.
- Weight: W = 12 × 9.807 = 117.7 N, so it would push up with 78.1 N if held under.
- Its density is 12/0.020 = 600 kg/m³, less than water, so it floats.
- Fraction below the surface: 600/998.2 = 60.1%, the same as a block of pine.
Where engineers use buoyancy
Naval architects size hulls so the displaced water carries the ship, cargo and a safety margin. Civil engineers check that empty underground tanks and pipelines won’t float out of saturated soil. Divers and submarines adjust their average density with ballast to hover at a chosen depth. Weighing an object in air and again in water is also the classic way to measure its volume and density, the trick Archimedes reportedly used on the king’s crown.
Assumptions and limits
- The fluid is at rest and its density is uniform. Seawater density changes a little with depth and temperature.
- Uses standard gravity, g = 9.80665 m/s².
- The volume is the object’s outer volume, including any sealed air inside. A hollow steel ball can float even though steel cannot.
- Floating stability (whether it tips over) depends on the shape and the position of the center of gravity, which this calculator doesn’t cover.
Frequently asked questions
Does the buoyant force increase with depth?
No. Once an object is fully submerged, the pressure on the top and bottom both grow with depth, and their difference stays the same. Only a compressible object, such as a diver’s wetsuit, loses buoyancy as it is squeezed smaller.
Why does a steel ship float?
Its average density, counting all the air inside the hull, is less than water. It sinks only until the displaced water weighs as much as the ship.
Is there buoyancy in air?
Yes, about 1.2 kg/m³ times the volume. It is why helium balloons rise and why precise scales correct for air buoyancy.