Buoyancy and Archimedes’ principle, explained.
A fluid exerts an upward buoyant force equal to the weight of displaced fluid. A floating object settles where buoyancy equals its weight. Its submerged volume fraction then equals object density divided by fluid density, provided the object is less dense than the fluid.
The relationship to remember
Key formulas
- Buoyant force (Archimedes’ principle)
- Fᵦ = ρfluid g Vsubmerged
- Weight of the displaced fluid
- Weight of the object
- W = ρobject g V
- Mass × g
- Floating fraction
- Vsubmerged / V = ρobject / ρfluid
- Only when ρobject < ρfluid
- Apparent weight underwater
- Wapparent = W − Fᵦ
- What a spring scale reads
Worked example
Problem. A 2 L block of wood with density 600 kg/m³ is placed in fresh water (1,000 kg/m³). Find its weight, the buoyant force if it were held fully underwater, and how much of it is submerged when it floats.
- Volume: V = 2 L = 0.002 m³. Weight: W = 600 × 9.81 × 0.002 = 11.77 N.
- Fully submerged: Fᵦ = 1,000 × 9.81 × 0.002 = 19.62 N. This exceeds the weight, so the block rises when released.
- Floating: Fᵦ = W, so Vsubmerged = W / (ρfluid g) = 11.77 / (1,000 × 9.81) = 0.0012 m³ = 1.2 L.
- Check: the floating fraction is 600 / 1,000 = 60% of the volume.
Answer. The block weighs 11.77 N, would feel 19.62 N of buoyancy fully underwater, and floats with 1.2 L (60%) submerged.
A quick check
A 2 L object with density 500 kg/m³ weighs 9.81 N. In water of density 1,000 kg/m³, it floats with 1 L submerged: half its volume.
Inside the default experiment
- Volume = 2 L = 0.002 m³. Submerged volume = 0.001 m³.
- Buoyancy = ρfluid g Vsubmerged = 9.81 N. Weight = ρobject g V = 9.81 N.
- At equilibrium, submerged fraction = ρobject/ρfluid = 50%.
When this model applies
Uniform fluid and object. Submerged fraction is set by the control. Only gravity and buoyancy are shown; drag and any external force holding the object are excluded. g = 9.81 m/s².
Make a prediction. Then test it.
Submerge a wooden block completely. Which way does the net force point?
Try it: Buoyancy & floating simulator ↗Frequently asked questions
Wondering about the why? Start here.
Why does a dense object sink?
If its density exceeds the fluid density, even full immersion cannot displace enough fluid for buoyancy to balance its weight. The net force is downward.
What happens if object and fluid densities are equal?
When fully submerged, weight and buoyancy balance. This is neutral buoyancy in the ideal uniform-fluid model.