Buoyancy Calculator
Work out the upward buoyant force on an object in a fluid using Archimedes’ principle, F = ρ·V·g — from the fluid’s density, the volume it displaces and gravity.
Buoyant force
980.665 N
- Mass of displaced fluid
- 100.000 kg
- Buoyant force (kilogram-force)
- 100.000 kgf
- Buoyant force (pound-force)
- 220.462 lbf
Archimedes’ principle: the buoyant force equals the weight of the displaced fluid, F = ρ·V·g.
How to use this calculator
Enter three values in SI units: the density of the fluid in kilograms per cubic metre (kg/m³), the volume of fluid the object displaces in cubic metres (m³), and the local gravitational acceleration in metres per second squared (m/s²). The displaced volume is simply the volume of the submerged part of the object — for a fully submerged object it is the object’s whole volume; for a floating object it is only the part below the waterline. Freshwater has a density of about 1000 kg/m³, seawater about 1025 kg/m³, air about 1.225 kg/m³ and mercury about 13 534 kg/m³. Leave gravity at the default 9.806 65 m/s² (standard gravity) unless you are working on another planet or need a local value. The primary result is the buoyant force in newtons, with the mass of displaced fluid and the force in kilogram-force and pound-force shown below. Remember 1 m³ = 1000 litres, so a 2-litre bottle displaces 0.002 m³.
How the calculation works
Archimedes’ principle, discovered by the Greek mathematician Archimedes in the 3rd century BC, states that the upward buoyant force on a body immersed in a fluid is equal to the weight of the fluid the body displaces. In modern notation the buoyant force is F = ρ·V·g, where ρ (rho) is the density of the fluid, V is the volume of fluid displaced (the submerged volume of the object), and g is the gravitational acceleration. The mass of the displaced fluid is ρ·V, and multiplying that mass by g gives its weight — which is exactly the buoyant force. Crucially, the buoyant force depends on the density of the *fluid*, not the object: a steel cube and a foam cube of the same size submerged in the same water feel the same buoyant force, even though they behave very differently because their own weights differ. An object floats when it can displace enough fluid for the buoyant force to equal its weight, which happens when the object’s average density is less than the fluid’s. It sinks when its average density is greater. This is why a solid steel ball sinks but a steel ship — mostly hollow, so its average density is low — floats. The calculator uses standard gravity g₀ = 9.806 65 m/s² by default, the value fixed by the General Conference on Weights and Measures.
Worked example
A sealed plastic drum with an external volume of 0.2 m³ (200 litres) is pushed fully underwater in freshwater (ρ = 1000 kg/m³). It displaces 0.2 m³ of water, so the mass of displaced water is ρ·V = 1000 × 0.2 = 200 kg. The buoyant force is F = ρ·V·g = 200 × 9.806 65 ≈ 1961 N, about 200 kgf or 441 lbf pushing upward. If the drum and its contents weigh less than 1961 N (about 200 kg), the drum floats; if they weigh more, it sinks. Switching the fluid to seawater (ρ = 1025 kg/m³) raises the buoyant force to 1025 × 0.2 × 9.806 65 ≈ 2010 N — roughly 2.5 % more lift, which is why the same object floats a little higher in the sea than in a freshwater lake.
Frequently asked questions
What is Archimedes’ principle?
Archimedes’ principle states that any object wholly or partly immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces. It was described by Archimedes of Syracuse around 250 BC. In equation form the buoyant force is F = ρ·V·g, where ρ is the fluid density, V is the displaced volume and g is gravitational acceleration. The principle explains floating, sinking and why objects feel lighter underwater.
Does the buoyant force depend on the object’s density or the fluid’s?
Only on the fluid’s density (and on how much volume the object displaces). Two objects of identical shape and size displace the same volume and therefore feel the same buoyant force, regardless of what they are made of. What differs is their own weight: the object sinks if its weight exceeds the buoyant force and floats if it does not. So a foam cube and a lead cube of equal size feel equal buoyancy, but the lead cube sinks because it weighs far more than the water it displaces.
How do I know if an object will float or sink?
Compare average densities. If the object’s average density (its total mass divided by its total volume) is less than the fluid’s density, it floats; if greater, it sinks; if exactly equal, it hovers (neutral buoyancy). Equivalently, compare the object’s weight with the maximum buoyant force it could generate when fully submerged, F = ρ_fluid·V_object·g. If that force exceeds the object’s weight, it floats. A steel ship floats because its overall shape encloses a lot of air, dropping its average density below that of water.
What density should I use for water, seawater and air?
Freshwater is about 1000 kg/m³ at 4 °C (its maximum density) and around 998 kg/m³ at 20 °C. Seawater averages about 1025 kg/m³ because of dissolved salts. Air at sea level and 15 °C is about 1.225 kg/m³, so buoyancy in air is tiny but not zero — it is why helium balloons rise. Mercury is about 13 534 kg/m³. Use the fluid at your working temperature; density falls slightly as most fluids warm up.
Why does an object feel lighter in water?
Because the buoyant force pushes upward against gravity. The object’s apparent weight in the fluid is its true weight minus the buoyant force. For example, a 100 N rock that displaces 4 litres of water experiences an upward buoyant force of about 39 N, so it feels like it weighs only about 61 N while submerged. This apparent-weight loss is exactly the weight of the displaced fluid — another way of stating Archimedes’ principle.
Does buoyancy change with gravity?
Yes. The buoyant force is proportional to g, so it scales with local gravity. On the Moon, where g is about 1.62 m/s², the same displaced volume of a given fluid produces roughly one-sixth of the buoyant force it would on Earth — but the object’s weight is reduced by the same factor, so whether it floats or sinks does not change. Floating depends on the ratio of densities, which is independent of g. Change the gravity field in the calculator to model other planets.