Buoyancy CalculatorArchimedes’ principle · Fb = ρgV
The buoyant force equals the weight of fluid an object displaces: Fb = ρfluid g Vsubmerged. If the object is less dense than the fluid it floats, with a fraction ρobject ÷ ρfluid underwater. Enter a volume and densities to see the buoyant force, whether it floats, how deep it sits and its apparent weight. Or find the volume a boat must displace to carry a load.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Object & fluid
Fresh water 1,000 kg/m³ · seawater 1,025 · olive oil ≈ 910 · mercury 13,534
Step-by-step working
What is buoyancy?
Buoyancy is the upward force a fluid exerts on any object placed in it. It arises because fluid pressure is greater at the bottom of the object than at the top.
Archimedes is said to have worked this out in his bath around 250 BC: the upthrust equals the weight of the fluid pushed aside. It explains why ships, icebergs, hot-air balloons and swimmers float, and why stones sink.
Quick answers
How do you calculate buoyant force?
Multiply fluid density, g and the submerged volume: Fb = ρgV. A fully submerged 2 L bottle in water feels 1,000 × 9.81 × 0.002 = 19.6 N of upthrust.
How do I know if an object will float?
Compare densities. If the object’s average density is less than the fluid’s, it floats. Work out density first with the density calculator if you only know the mass and size.
How much of an iceberg is underwater?
About 89–90% in seawater (917 ÷ 1,025 ≈ 0.895). Load the iceberg preset to see it.
Why does a steel ship float?
Its hull encloses a large volume of air, so the ship’s average density is far below that of water. It sinks only until it has displaced its own weight of water.
Buoyancy formula (Archimedes’ principle)
An object floats if its average density is lower than the fluid’s. Hollow steel ships float because their average density, hull plus air, is low.
| Symbol | Meaning | SI unit |
|---|---|---|
| Fb | Buoyant force | N |
| ρf | Fluid density | kg/m³ |
| ρo | Object (average) density | kg/m³ |
| Vsub | Submerged volume | m³ |
| g | Gravitational acceleration | m/s² |
| W | Weight of the object | N |
How to calculate buoyant force
- Find the submerged volume, in m³ (1 L = 0.001 m³).
- Multiply by the fluid density to get the mass of fluid displaced.
- Multiply by g for the buoyant force in newtons.
- Compare it with the weight: bigger means it floats, smaller means it sinks.
Worked example: a 10-litre block of pine
A 10 L block of pine (ρ = 500 kg/m³) is placed in fresh water.
Weight = 500 × 9.807 × 0.01 = 49.03 N
It floats with 500 ÷ 1,000 = 50% submerged
Swap in ice (917 kg/m³) and seawater (1,025 kg/m³) and 89.5% sits below the surface, the real “tip of the iceberg”.
Densities of common materials and fluids
Compare with the fluid: lower floats, higher sinks.
| Material | Density (kg/m³) | In fresh water |
|---|---|---|
| Cork | ≈ 240 | Floats (24% under) |
| Pine wood | ≈ 500 | Floats (50% under) |
| Ice | 917 | Floats (92% under) |
| Human body (lungs full) | ≈ 985 | Just floats |
| Seawater | 1,025 | — |
| Aluminium | 2,700 | Sinks |
| Steel | 7,850 | Sinks |
| Gold | 19,300 | Sinks |
Common mistakes to avoid
- Using the object’s total volume for a floating object. Only the submerged part displaces fluid.
- Forgetting that seawater is denser. Ships ride higher in the sea than in a river.
- Thinking heavy things always sink. Average density decides it, which is why a 100,000-tonne ship floats.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who became a full-time tech geek, and I’ve spent 13+ years designing and coding web tools. Density and specific gravity are everyday tools in pharmaceutics, from compounding liquids to checking formulation weights, so the floating-and-sinking maths behind this calculator is part of my professional background.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Buoyancy Calculator: frequently asked questions
Any object wholly or partly immersed in a fluid feels an upward buoyant force equal to the weight of the fluid it displaces.
Fb = ρfluid × g × Vsubmerged.
Not for an incompressible fluid and a rigid object. Once fully submerged, the buoyant force stays the same at any depth.
Seawater is about 2.5% denser than fresh water, and the Dead Sea about 24% denser, so the same displaced volume gives more upthrust.
The weight an object seems to have in a fluid: true weight minus buoyant force. It is what a spring scale reads underwater.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 14.4, Archimedes’ Principle and Buoyancy
- HyperPhysics, Georgia State University — buoyancy
- NOAA — Why is the ocean salty / seawater density — seawater composition
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.