What this calculator does
Archimedes' principle says the upward force on a submerged object equals the weight of the fluid it displaces. Whether something floats comes down to a straight comparison: if that buoyant force is at least as large as the object's weight, it floats.
This is why a steel ship floats while a steel bar sinks. The bar displaces only its own small volume; the ship's hull encloses a great deal of air, so it displaces far more water and receives a far larger upward force.
The formula
Multiply the fluid density by gravity and by the volume displaced to get the buoyant force in newtons. Comparing that against the object's weight, which is its mass times gravity, determines whether it floats and what it appears to weigh when submerged.
| Term | Meaning |
|---|---|
| Buoyant force | The upward force from displaced fluid, equal to the weight of that fluid. |
| Displacement | The volume of fluid pushed aside by the object. |
| Apparent weight | What an object seems to weigh while submerged: its real weight minus the buoyant force. |
The inputs explained
| Field | What to enter |
|---|---|
| Fluid density (water = 1000) (kg/m³) | The density of the fluid in kilograms per cubic metre. Fresh water is 1,000; seawater about 1,025. |
| Volume displaced (m³) | The volume of fluid displaced, in cubic metres. For a fully submerged object this is its own volume. |
| Mass of the object (kg) | The mass of the object in kilograms, used to work out its weight for comparison. |
When to use it
Checking whether something will float
Comparing buoyant force against weight settles the question before anything gets wet.
Working out how much ballast is needed
The difference between buoyant force and weight is the margin available, which determines how much extra load can be carried.
Understanding apparent weight underwater
Lifting something submerged is easier than lifting it in air by exactly the buoyant force, which is why salvage work is done underwater where possible.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
At what mass does a 0.02 m³ object stop floating?
The same displaced volume for objects of increasing mass.
| Object mass | Buoyant force | Weight of object |
|---|---|---|
| 10 kg | 196.13 N | 98.07 N |
| 15 kg | 196.13 N | 147.10 N |
| 25 kg | 196.13 N | 245.17 N |
| 30 kg | 196.13 N | 294.20 N |
Questions
Why does a steel ship float?
Because what matters is average density, not the density of the material. A hull encloses a large volume of air, so the ship as a whole is less dense than water even though steel is around eight times denser.
Does an object float higher in seawater?
Yes, slightly. Seawater is about 2.5 per cent denser than fresh water, so it provides more buoyant force for the same displaced volume. Ships genuinely ride lower when they move from sea into fresh water.
What does neutral buoyancy mean?
That the buoyant force exactly balances the weight, so the object neither rises nor sinks. Divers achieve it by fine-tuning weights and the air in a buoyancy device.
Does depth change the buoyant force?
For a rigid object in a liquid, essentially no, since liquids barely compress and the displaced volume stays the same. For anything containing gas it very much does, because the gas compresses with depth, reducing displacement.
For the density comparison behind all of this, see the density calculator. For pressure at depth, see the pressure calculator.