What is Archimedes principle?

Archimedes principle states that the upward buoyant force on a submerged or floating object equals the weight of the fluid it displaces. That is the basis of the F = ρ·V·g formula used here.

How does the float-or-sink test work?

The calculator compares the object weight (mass × g) with the maximum buoyant force when fully submerged. If the buoyant force is greater than or equal to the weight it floats; if the weight is larger it sinks.

What density should I use for the fluid?

Use about 1000 kg/m³ for fresh water and roughly 1025 kg/m³ for seawater. Denser fluids produce a larger buoyant force for the same displaced volume, which is why objects float higher in salt water.

Why does displaced volume matter more than shape?

Buoyant force depends only on the volume of fluid pushed aside, not the object shape. A hollow hull floats because its large displaced volume creates enough buoyant force to support its relatively small mass.

Buoyancy Calculator

Fluid Density ρ (kg/m³)

Displaced Volume V (m³)

Gravity g (m/s²)

Object Mass (kg, optional for float test)

Buoyant Force (N)981.0000

Displaced Mass (kg)100.0000

Object Weight (N)490.5000

Float or SinkFloats

The Buoyancy Calculator applies Archimedes principle: any object immersed in a fluid feels an upward buoyant force equal to the weight of the fluid it displaces, F = ρ·V·g. Enter the fluid density, the displaced volume, and gravity to get the buoyant force and the mass of displaced fluid. Add the object mass and the calculator compares its weight to the buoyant force to tell you whether it floats or sinks.

Formula

F_b = ρ × V × g

F_b: Buoyant (upward) force (newtons)
ρ: Density of the displaced fluid (kg/m³)
V: Volume of fluid displaced by the object (m³)
g: Gravitational acceleration (m/s²)

How it works

Enter the fluid density ρ (1000 kg/m³ for fresh water by default) and the displaced volume V in cubic metres.
Set gravity g (9.81 m/s² on Earth); the calculator multiplies ρ × V × g to get the buoyant force.
Optionally enter the object mass: its weight (mass × g) is compared with the buoyant force to decide float versus sink when fully submerged.

Worked example

A 0.1 m³ object fully submerged in fresh water.

F_b = ρ × V × g = 1000 × 0.1 × 9.81.
F_b = 981 N (displaced mass = 100 kg).
A 50 kg object weighs 50 × 9.81 = 490.5 N < 981 N, so it floats.

Buoyant force = 981 N; a 50 kg object floats.

Frequently asked questions

What is Archimedes principle?: Archimedes principle states that the upward buoyant force on a submerged or floating object equals the weight of the fluid it displaces. That is the basis of the F = ρ·V·g formula used here.
How does the float-or-sink test work?: The calculator compares the object weight (mass × g) with the maximum buoyant force when fully submerged. If the buoyant force is greater than or equal to the weight it floats; if the weight is larger it sinks.
What density should I use for the fluid?: Use about 1000 kg/m³ for fresh water and roughly 1025 kg/m³ for seawater. Denser fluids produce a larger buoyant force for the same displaced volume, which is why objects float higher in salt water.
Why does displaced volume matter more than shape?: Buoyant force depends only on the volume of fluid pushed aside, not the object shape. A hollow hull floats because its large displaced volume creates enough buoyant force to support its relatively small mass.

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