How to use this calculator
- Enter or choose fluid density.
- Enter or choose density unit.
- Enter or choose submerged volume.
- Enter or choose volume unit.
- Enter or choose object mass (optional).
- The buoyant force updates as you type. Use Copy result or Share to keep it.
Method
F_b = ρ_fluid × g × V; W = m g; net = F_b − W; fraction submerged when floating = W ÷ F_b(full volume)
- F_b
- buoyant force in N
- ρ_fluid
- fluid density in kg/m³
- V
- volume of fluid displaced in m³
- m
- object mass in kg
Worked example
- V = 2 L = 0.002 m³; displaced water = 1,000 × 0.002 = 2 kg.
- F_b = 2 kg × 9.80665 = 19.6133 N.
- Weight = 1.5 × 9.80665 = 14.71 N, less than F_b, so it floats with 1.5 ÷ 2 = 75% of its volume under water.
A 2-litre object fully under water feels 19.6 N of upthrust; at 1.5 kg it floats, riding 75% submerged.
What the result means
An object floats if its average density is below the fluid’s. Ships float despite steel hulls because the hull encloses air, lowering the average density. The net force tells you how much ballast (if negative) or buoyancy aid (if positive) is needed for neutral buoyancy.
Assumptions and limits
- Fluid of uniform density at rest.
- For the float check, the volume entered is the object’s whole volume.
- Ignores surface tension, which matters only for very small objects.
Questions
Why do objects float higher in seawater?
Seawater is denser than fresh water, so less volume needs to be submerged to displace the object’s weight.
Does depth change the buoyant force?
Not for an incompressible object in a uniform liquid. Compressible things such as divers’ wetsuits lose volume, and buoyancy, as they go deeper.