Archimedes' Principle Calculator

Find the buoyant force on a submerged object from fluid density and displaced volume, then see its density and whether it floats or sinks.

Quick Facts

Formula
F_b = ρ_fluid × V_displaced × g
Buoyant force equals the weight of the fluid displaced by the submerged volume.

Your Results

Calculated
Buoyant Force
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Weight of fluid displaced
Object Density
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Mass ÷ volume
Net Force in Fluid
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Apparent weight if fully submerged
Submerged Fraction
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Portion of volume displaced

Ready

Enter fluid density, object volume, and mass, then press Calculate.

About Archimedes' Principle

Archimedes' Principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This single relationship explains why a steel ship floats, why a helium balloon rises, and why an object feels lighter when weighed underwater.

Understanding the formula

The buoyant force is F_b = ρfluid × Vdisplaced × g, where ρfluid is the fluid's density in kilograms per cubic meter, Vdisplaced is the submerged volume in cubic meters, and g is the local gravitational acceleration (9.81 m/s² on Earth). This calculator takes your volume in liters and converts it to cubic meters (1 L = 0.001 m³) before applying the formula.

Floating versus sinking

Compare the object's own density (mass divided by volume) with the fluid's density. If the object is less dense than the fluid, it floats, and only enough of its volume submerges for the buoyant force to match its weight. If the object is denser than the fluid, it sinks and stays fully submerged, with an apparent weight in the fluid equal to its true weight minus the full buoyant force.

Working with units

  • Fluid density is typically given in kg/m³: fresh water is about 1000 kg/m³, seawater about 1025 kg/m³, and air about 1.2 kg/m³.
  • Object volume is entered in liters; the calculator converts to cubic meters internally so the formula stays in consistent SI units.
  • Gravitational acceleration changes by location — switch the Gravity location input to see how the same object's buoyant force differs on the Moon or Mars.

Knowing the limits

This calculator assumes a fluid of uniform density and an object that does not dissolve in, absorb, or chemically react with the fluid. It computes the buoyant force and float-or-sink outcome at equilibrium, not the time it takes to settle, surface-tension effects on very small objects, or the added complexity of hollow or compressible shapes.

Frequently Asked Questions

What is Archimedes' Principle?
Archimedes' Principle states that the buoyant force on an object submerged in a fluid equals the weight of the fluid it displaces: F_b = fluid density × displaced volume × gravity. This is why objects feel lighter in water and why a steel ship can still float.
How do I know if an object will float or sink?
Compare densities: if the object's mass divided by its volume is less than the fluid's density, it floats with only part of its volume submerged. If the object's density is greater than the fluid's density, it sinks and stays fully submerged.
Why does gravity affect the buoyant force?
Buoyant force is the weight of displaced fluid, and weight depends on gravitational acceleration. The same object displaces the same volume of fluid on the Moon as on Earth, but because lunar gravity is about one sixth of Earth's, the resulting buoyant force in newtons is about one sixth as large too.

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