Buoyancy Force Calculator
Calculate buoyant force from Archimedes' principle using fluid density and displaced volume, and check whether an object floats or sinks.
Buoyancy Force Calculator
Calculator
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Formula: F_b = ρ_fluid × V_displaced × g
Worked example — 4905 N
Formula
F_b = ρ_fluid × V_displaced × g
Archimedes principle: buoyant force equals the weight of displaced fluid.
Worked Examples
Example 1: Wooden block
Problem:ρ=1000 kg/m³, V=0.5 m³
Solution:Fb=1000×0.5×9.81=4905 N
Result:4905 N
Frequently Asked Questions
What is buoyancy force?
Buoyancy force (F_b) is the upward force exerted by a fluid on a submerged or floating object. It equals the weight of the displaced fluid: F_b = ρ_fluid × V_displaced × g, where ρ is density (kg/m³), V is volume (m³), and g = 9.81 m/s².
How do you calculate buoyancy force?
Apply Archimedes' principle: F_b = ρ_fluid × V_displaced × g. For example, a 0.5 m³ object submerged in water (ρ = 1000 kg/m³): F_b = 1000 × 0.5 × 9.81 = 4905 N upward.
What units does the buoyancy calculator use?
Fluid density is entered in kg/m³ (water ≈ 1000, seawater ≈ 1025, air ≈ 1.225). Displaced volume is in m³. The resulting buoyant force is in Newtons (N). Object mass is in kg, and weight is calculated as mg in Newtons.
What is a real-world example of buoyancy?
A steel ship floats because its hollow hull displaces a large volume of water. A ship of mass 50,000,000 kg must displace 50,000,000 / 1025 ≈ 48,780 m³ of seawater to generate enough buoyant force (about 490 MN) to balance its weight.
When does an object float and when does it sink?
Compare the average density of the object with that of the fluid. If the object is less dense it floats, settling until the displaced volume weighs exactly as much as the object, which means the submerged fraction equals the ratio of the two densities. If it is denser the buoyant force cannot balance the weight and it sinks. Equal densities give neutral buoyancy, as divers aim for with a weight belt.
Why does a submerged object feel lighter, and how do I compute its apparent weight?
Apparent weight is the true weight minus the buoyant force. A 10 kg block weighing about 98.1 N in air and occupying 0.004 m3 displaces water weighing 1000 x 0.004 x 9.81, that is 39.2 N, so a scale reads only about 58.9 N when it hangs submerged. The object has not lost mass; the fluid simply pushes upward on it.
How much does fluid density change the buoyant force?
Buoyant force scales directly with the density of the fluid. Seawater at roughly 1025 kg/m3 is about 2.5 per cent denser than fresh water, so the same hull sits slightly higher in the sea than in a river and must displace a correspondingly smaller volume. Ships carry load line markings precisely because permissible draught depends on the water they are floating in.
What fraction of an iceberg is submerged, and how does buoyancy set it?
A floating body displaces its own weight of fluid, so the submerged fraction is the ratio of ice density to seawater density. With ice near 917 kg/m3 and seawater near 1025 kg/m3 that ratio is about 0.89: roughly nine tenths of the volume sits underwater and only about a tenth shows above. The same buoyancy argument fixes the draught of any freely floating body from its average density.
How can Archimedes' principle be used to measure the density of an irregular object?
Weigh the object in air, then weigh it while fully submerged. The difference between the two readings is the buoyant force, so the volume equals that difference divided by the fluid density and by g. Dividing the mass by that volume gives the density without any need to measure the shape. This hydrostatic weighing method works for castings, gemstones and porous samples alike.
What is the difference between buoyancy and the stability of a floating body?
Buoyancy is the magnitude of the upward force, acting through the centre of buoyancy at the centroid of the displaced volume. Stability is about what happens when the body heels: it rights itself only if the metacentre lies above the centre of gravity. A vessel can satisfy the buoyancy condition perfectly and still capsize if its load is stowed too high.
Background & Theory
Buoyancy and Density, by Fluid
Whether an object floats depends entirely on comparing its average density to the fluid's density — an object less dense than the fluid it's placed in floats with part of its volume above the surface, while a denser object sinks. This calculator applies Archimedes' principle directly: the buoyant force always equals the weight of the fluid displaced, regardless of the submerged object's own weight or shape.
| Fluid | Density (kg/m³) |
|---|---|
| Fresh water (4°C) | 1,000 |
| Seawater | 1,020-1,030 |
| Air (sea level, 20°C) | ~1.2 |
| Vegetable oil | ~920 |
| Mercury | 13,534 |
A steel ship floats not because steel is less dense than water (it isn't — steel is about 7,850 kg/m³) but because the hull's hollow shape means the ship's overall AVERAGE density, hull plus air-filled interior, is less than water. That's also why a solid steel block sinks instantly while a steel ship, carrying the same mass spread over a much larger displaced volume, stays afloat.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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