Buoyancy Force
Compute buoyant force from fluid density, displaced volume, and gravity using Archimedes principle. Free online calculator with formulas and step-by-step solutions.
Key formula
Fb = ρ V g
How do you calculate buoyant force?
Use Archimedes’ principle: Fb = ρ V g. Multiply fluid density by the displaced volume and by g. The result is an upward force in newtons. An object floats when Fb equals its weight, and sinks when its weight is larger than Fb for full submersion.
About this tool
Buoyant force is the upward push a fluid exerts on a submerged or floating object. Archimedes’ principle says it equals the weight of the displaced fluid: Fb = ρ V g. This page keeps that formula visible so float/sink homework stays consistent on density and volume units.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: 0.020 m³ in fresh water
ρ = 1000 kg/m³, V = 0.020 m³, g = 9.81. Fb = (1000)(0.020)(9.81) = 196.2 N. Displaced fluid mass = ρV = 20 kg.
Example 2: same volume in seawater
ρ ≈ 1025 kg/m³, V = 0.020 m³, g = 9.81. Fb = (1025)(0.020)(9.81) = 201.105 N — a bit more lift than fresh water.
Example 3: will a 15 kg block float?
Weight W = mg = (15)(9.81) = 147.15 N. If fully submerged volume is 0.020 m³ in fresh water, Fb = 196.2 N > W, so it floats (only part submerged at equilibrium).
Frequently asked questions
What is the buoyant force formula?
Fb = ρ V g, where ρ is fluid density, V is the volume of fluid displaced, and g is gravitational acceleration. Fb points upward.
What is Archimedes’ principle?
The buoyant force on an object equals the weight of the fluid it displaces. That is the same statement as Fb = ρ V g.
What density should I use for water?
Fresh water is often taken as 1000 kg/m³ (or 997 near room temperature). Seawater is often about 1025 kg/m³. Use the value given on the paper when it differs.
Is displaced volume the same as the object’s volume?
Only when the object is fully submerged. A floating object displaces a volume whose fluid weight equals the object’s weight, which is usually less than the object’s full volume.
How do I know if something sinks or floats?
Compare weight W = mg to the maximum buoyant force when fully submerged (ρ V_object g). If W is larger, it sinks. If W is smaller, it floats with part of its volume above the surface.