How to Calculate Buoyant Force (Fb = ρVg): Archimedes' Principle

Calculate buoyant force with Fb = ρVg, compare weight to decide float or sink, and check worked examples with a free buoyancy calculator.

What Buoyant Force Asks

Buoyant force is the upward push a fluid exerts on an object that is submerged or floating. Archimedes’ principle says that push equals the weight of the fluid the object displaces.

In symbols: Fb = ρ V g. ρ is the fluid density, V is the displaced volume, and g is gravity. The force points up; weight points down.

If you already have ρ, V, and g and only need a checked Fb, open the free buoyancy force calculator first, then return here for float-vs-sink checks and unit traps.

The Formula

  • Fb = ρ V g — buoyant force in newtons.
  • Displaced fluid mass = ρ V (kg when SI units are used).
  • Object weight for comparison: W = mg.

    • V is the volume of fluid pushed aside. Fully submerged: V equals the object’s volume. Floating: V is only the submerged part.

    Float or Sink

    Find the maximum buoyant force if the object were fully submerged: Fb,max = ρ V_object g. Compare to weight W = mg.

  • If W < Fb,max, the object floats (only partly submerged at equilibrium).
  • If W > Fb,max, the object sinks.
  • If W = Fb,max, it is neutrally buoyant when fully submerged.

    • Weight uses W = mg — refresh that with the weight calculator. Density for ρ comes from the density calculator.

    Open the density calculator when you need ρ = m / V first.

    Units

  • ρ → kg/m³ (fresh water often 1000; seawater often ≈ 1025).
  • V → m³ (1 L = 0.001 m³; convert cm³ carefully).
  • g → m/s² (9.8 or 9.81).
  • Fb → N.

    • Worked Examples

    Example 1: 0.020 m³ in fresh water

    ρ = 1000 kg/m³, V = 0.020 m³, g = 9.81. Fb = 196.2 N. Displaced mass = 20 kg.

    Example 2: same volume in seawater

    ρ = 1025 kg/m³. Fb = 201.105 N — more lift than fresh water.

    Example 3: 15 kg block, V = 0.020 m³

    W = 15 × 9.81 = 147.15 N. Fresh-water Fb,max = 196.2 N > W, so it floats.

    Common Mistakes

  • Putting object density into Fb = ρ V g instead of fluid density.
  • Leaving V in liters or cm³ without converting to m³.
  • Using full object volume for a floating object that is only partly submerged.
  • Comparing Fb (newtons) directly to mass (kilograms).

    • Check It on the Calculator

    Buoyancy force calculator.

    Density calculator.

    Weight calculator.

    Pressure calculator.

    Learn Fb = ρVg and check every float/sink homework number.

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