MotionLab

Buoyancy Calculator

The upward force a fluid exerts on anything submerged in it, from rubber ducks to cargo ships.

Fluid density (kg/m³)

Displaced volume (m³)

Gravity (m/s²)

Buoyant force (N)

490.5

F = ρ · V · g (Archimedes' principle)

What you entered

Fluid density (kg/m³): 1000Displaced volume (m³): 0.05Gravity (m/s²): 9.81

1
F = ρ × V × g
1000 × 0.05 × 9.81= 490.5 N

Result

Buoyant force (N): 490.5

Displacing 0.05 m³ of fluid at 1000 kg/m³ gives 490.5 N of buoyant force.

Buoyant force on submerged volumes in water

Archimedes' principle: the upward force equals the weight of fluid displaced, which is fluid density times volume times g. These use 9.81 m/s2.

Fluid density (kg/m3)	Volume displaced (m3)	Buoyant force (N)	Fluid
1000	0.001	9.810	Fresh water, 1 litre
1000	0.01	98.100	Fresh water, 10 litres
1000	1	9810.000	Fresh water, 1 cubic metre
1025	0.05	502.763	Seawater, 50 litres
1.225	1000	12017.250	Air, 1000 cubic metres

The force depends on the fluid displaced, not on what the object is made of - a kilogram of lead and a kilogram of cork displacing the same volume feel the same upward push, and only their weights differ. That is why an object floats when its average density is below the fluid's. The last row is why airships work: a thousand cubic metres of displaced air produces over 12 kilonewtons of lift, enough to hold up about 1.2 tonnes. Seawater at 1025 kg/m3 is denser than fresh, which is why swimmers float more easily in the sea.

Why some things float and others sink

An object floats if the buoyant force from its displaced fluid exceeds its weight — a steel ship floats not because steel is light, but because its hollow shape displaces enough water that the buoyant force outweighs the ship's actual weight.

It's about displaced volume, not the object's own density alone

This calculator computes buoyant force purely from how much fluid is displaced — whether that force is enough to float the object depends on comparing it to the object's actual weight, a separate calculation.

Frequently asked questions

A 500 cm³ block is submerged in water. What buoyant force acts on it?

F_b = ρ_fluid × V × g = 1000 × 0.0005 × 9.81 = 4.905 N. If the block weighs less than 4.905 N (mass < 500 g), it floats. If more, it sinks. Equal = neutral buoyancy.

Why does a steel ship float when a steel ball sinks?

A solid steel ball displaces very little water relative to its weight. A hollow steel hull displaces enormous amounts of water — the buoyant force from all that displaced water exceeds the ship's total weight. It's about shape and volume, not just material. See the density calculator.

A helium balloon rises. Is that buoyancy?

Yes — Archimedes' principle works in any fluid, including air. Air density ≈ 1.225 kg/m³, helium ≈ 0.164 kg/m³. A balloon displaces air heavier than itself, creating a net upward buoyant force — the same principle that floats ships, just in a different fluid.

How is this different from the buoyant force calculator?

Both use Archimedes' principle (F = ρVg). This calculator focuses on whether an object floats or sinks by comparing buoyant force to weight. The buoyant force calculator focuses on computing the upward force itself. Same physics, different emphasis.

How deep do I need to submerge something for buoyancy to work?

Any submersion creates buoyancy — the force equals the weight of fluid displaced, regardless of depth. A half-submerged object gets half the buoyant force of full submersion. Total submersion at 1 m or 100 m gives the same buoyant force (for incompressible fluids).