Buoyant force calculator
Archimedes' force, the body's weight, and whether it floats.
Fill in the fields and the result will appear here automatically.
Buoyancy depends on displaced fluid volume and fluid density. Comparing it with weight gives the vertical net of those two forces at the specified immersion. A body already floating at rest displaces its own mass; its larger fully submerged volume describes buoyancy reserve, not its actual equilibrium displacement.
How it works
Formula and logic
F = ρ · g · V with g = 9.80665; the net force is F − m · g.
Example
A 15 kg body of 20 litres in water gets 196.13 N against a weight of 147.1 N — it floats.
Fields and units
- Body volume — m³
- Fluid density — kg/m³
- Body mass — kg
How to use
- — Fluid density: fresh water 1000, sea water about 1025, diesel about 840, mercury 13 546 kg/m³.
- — A positive net force floats the body, a negative one sinks it, zero holds it mid-water.
- — Enter the volume actually excluded from the fluid. A sealed dry cavity contributes its outer displaced volume; an openly flooded cavity does not. 1 L=0.001 m³.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: displaced-fluid weight
- Limitation
- Static homogeneous fluid, specified displaced volume and constant g=9.80665 m/s². Drag, supports, surface tension and changing immersion are omitted.
FAQ
Why does a heavy ship not sink?
A dense hull material can enclose a large watertight volume containing air. While a ship floats at rest, displaced water mass equals total ship mass. Flooding adds mass and can remove available dry volume; a force calculation does not check stability or watertightness.
What does neutral buoyancy give you?
Equal displaced and body masses give a zero sum of weight and buoyancy. A body initially at rest with no other forces has no vertical acceleration; existing velocity and fluid drag are separate matters.
Why is floating easier in the sea?
At the same displaced volume, force is proportional to density. Illustrative values of 1025 and 1000 kg/m³ give 2.5% more force, but actual density depends on temperature and salinity. This is not a guarantee of a person’s safety in water.
Do I need the body's own density?
No — volume and mass are enough, and their ratio is the density. The calculation deliberately takes what is easier to measure: mass on a scale, volume by displaced water.