Buoyancy Experiment Calculator

Find the buoyant force, displaced volume, and density of an object using Archimedes' principle: weigh it in air, then weigh it again fully submerged in a fluid.

Quick Facts

Principle
Archimedes' principle
Buoyant force = weight of fluid displaced: F₌ = ρ_fluid × V × g.
Reference
Water = 1000 kg/m³
Specific gravity compares object density to this standard water reference.

Your Results

Calculated
Buoyant force
-
Weight of fluid displaced
Displaced volume
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Volume of object submerged
Object density
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Mass in air ÷ displaced volume
Specific gravity
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Density relative to water (1000 kg/m³)

Ready

Enter the mass in air and submerged, then press Calculate.

Understanding the Buoyancy Experiment

This tool implements the classic hydrostatic-weighing experiment used to teach and apply Archimedes' principle: any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Weigh an object in air, then weigh it again while fully submerged in a fluid (usually water) using a hanging scale or a balance and a thread — the object always appears lighter underwater, and that apparent loss of mass is exactly the mass of the fluid it pushed out of the way.

The formulas

Let m_air and m_fluid be the mass readings in air and submerged (in kilograms), ρ_fluid the fluid's density, and g the local gravitational acceleration:

  • Mass of displaced fluid: Δm = m_air − m_fluid
  • Buoyant force: F₌ = Δm × g (Newtons) — equivalently F₌ = ρ_fluid × V × g
  • Displaced volume: V = Δm / ρ_fluid (this equals the object's own volume, since it is fully submerged)
  • Object density: ρ_object = m_air / V
  • Specific gravity: SG = ρ_object / 1000 kg/m³ (density relative to pure water)

Notice that gravity cancels out of the density calculation entirely — V = Δm / ρ_fluid does not contain g. That is why this method works the same on a lab bench regardless of the local value of g; the gravity field only affects how much force the scale itself reads in Newtons, not the density result.

Common reference densities

  • Water (4°C): 1000 kg/m³ — the standard specific-gravity reference.
  • Seawater: about 1025 kg/m³.
  • Aluminum: about 2700 kg/m³.
  • Steel/iron: about 7750–8050 kg/m³.
  • Gold (pure, 24k): about 19,300 kg/m³.

Why it works

A submerged object pushes fluid out of the space it occupies. That displaced fluid "wants" to return to its original position and the surrounding fluid pressure resists the object, producing an upward force equal to the weight of the fluid displaced. Because the scale can only report the net downward force, the reading in fluid is smaller than in air by exactly that buoyant force — a mass-equivalent drop of Δm. Since Δm/ρ_fluid gives volume regardless of the object's shape, this method finds the density of oddly shaped objects (rocks, castings, jewelry) without ever measuring their dimensions directly.

Frequently Asked Questions

What is Archimedes' principle?
Archimedes' principle states that a fully or partially submerged object experiences an upward buoyant force equal to the weight of the fluid it displaces. In a two-weighing experiment, that force also equals the mass an object appears to lose when weighed submerged compared to weighed in air, multiplied by gravity.
Why does the object need to be fully submerged?
The formulas here assume the displaced volume equals the object's total volume, which is only true when it is completely underwater with no part breaking the surface and no trapped air bubbles clinging to it. A partially submerged (floating) object displaces less than its own volume, so the density calculation would be wrong.
Can this calculator find a fluid's density instead of an object's?
Not directly — it solves for the object's density given a known fluid density. To find an unknown fluid's density instead, you would need an object of known volume and density and solve the same Archimedes equation for the fluid term.
What if the apparent mass in fluid is not less than the mass in air?
For a fully submerged object hanging from a scale, the apparent mass in fluid must be less than the mass in air, since buoyancy always reduces the reading. If your submerged reading is equal to or greater than the air reading, check for a scale error, an object touching the container, or trapped air pushing the reading around.

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