Buoyancy Calculator
The upward force on a submerged or floating object, whether it floats, and how much of it sits below the surface.
Archimedes' principle: the upward force equals the weight of the fluid displaced.
How the buoyancy calculator works
Archimedes' principle: the upward force equals the weight of the fluid displaced. So an object floats when its average density is less than the fluid's, and the fraction submerged is exactly the ratio of the two densities — which is why about 90% of an iceberg is underwater, ice being roughly 917 kg/m³ against seawater's 1,025.
It is the *average* density that matters, not the material. A steel hull floats because most of its volume is air; crush it into a block and the same steel sinks.
Formula: upthrust = ρ_fluid × g × displaced volume; fraction submerged = ρ_object ÷ ρ_fluid
Worked examples
| Inputs | Buoyant force | Note |
|---|---|---|
| A liter of oak in fresh water | 6.8647 N | floats with 70% submerged |
| Ice in seawater | 8,992.6981 N | 89.5% below — the iceberg figure |
| A steel block | 9.8067 N | sinks |
FAQFrequently asked questions
What is Archimedes' principle?
The upward force on a submerged object equals the weight of the fluid it displaces.
Why do things float?
Because their average density is less than the fluid's. The fraction below the surface is exactly the ratio of the two densities.
Why is most of an iceberg underwater?
Ice is about 917 kg/m³ and seawater 1,025, so 917 ÷ 1,025 — about 89% — sits below.
How does a steel ship float?
Its average density counts, not the steel's. A hull is mostly air, so the average is well under water's.
Does salt water change things?
Yes — seawater is about 2.5% denser, so you float slightly higher in the sea than in a pool.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.