Buoyancy Calculator
Find the buoyant force on a submerged object.
Results update as you type.
How it works
Buoyancy is the upward force a fluid exerts on any object placed in it, and this calculator finds that force using Archimedes' principle. You enter the density of the fluid and the volume of fluid the object displaces, with gravity defaulting to Earth's value, and it returns the buoyant force in newtons. Archimedes' principle, discovered over two thousand years ago, states that the buoyant force equals the weight of the displaced fluid, which is why a dense fluid like seawater lifts objects more strongly than fresh water, and why the same object floats higher in salt water. Whether an object floats or sinks depends on comparing this buoyant force to the object's weight: if the buoyant force is greater, it floats; if less, it sinks; if equal, it hovers in place. This principle explains how ships made of steel float by displacing a large volume of water, how submarines dive and surface by adjusting their displacement, how hot-air and helium balloons rise through air, and how a hydrometer measures liquid density. Engineers designing vessels and physicists analysing fluids use it constantly. Enter the fluid density and displaced volume to compute the upward force, and compare it with the object's weight to predict whether it floats.
F = ρ · g · V
Archimedes' principle states that the upward buoyant force on an object equals the weight of the fluid it displaces. That weight is the fluid's density multiplied by the displaced volume to get the mass, then multiplied by gravitational acceleration to get the force. So the buoyant force is density times gravity times volume, acting upward, independent of the object's own weight or what it is made of.
Source:Fluid mechanics (Archimedes' principle)
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Worked example
How to use this calculator
- 1
Enter your values
Enter fluid density (ρ) and displaced volume (v).
- 2
Adjust the options
Adjust gravity (optional) if they apply — sensible defaults are already set.
- 3
Read your result
Buoyant force updates instantly as you type — no button to press.
Frequently asked questions
What is buoyancy?
Buoyancy is the upward force that a fluid exerts on an object immersed in it, opposing the object's weight. It arises because pressure in a fluid increases with depth, so the upward pressure on the bottom of an object exceeds the downward pressure on its top. The net result is an upward push equal to the weight of the fluid the object displaces.
What is Archimedes' principle?
Archimedes' principle states that the buoyant force on a submerged or floating object equals the weight of the fluid it displaces. This elegant rule means you do not need to analyse complex pressure distributions; you simply calculate the weight of the displaced fluid. It applies to any fluid, liquid or gas, and to fully or partially submerged objects alike.
Why do some objects float and others sink?
An object floats if the buoyant force pushing it up is at least equal to its weight pulling it down, which happens when the object is less dense than the fluid overall. A steel ship floats because its hollow shape displaces enough water to generate a large buoyant force, even though steel itself is denser than water. A solid steel block sinks because it displaces too little.
Does buoyancy depend on the fluid?
Yes. The buoyant force is proportional to the fluid's density, so denser fluids produce stronger buoyancy for the same displaced volume. This is why you float more easily in salty seawater than in fresh water, and why the Dead Sea, with its very high salt content, makes swimmers bob on the surface. Air, being far less dense, provides only tiny buoyancy.
What is the displaced volume?
The displaced volume is the volume of fluid pushed aside by the object, which for a fully submerged object equals the object's own volume. For a floating object, only the submerged part displaces fluid, so the displaced volume is less than the total volume. Enter the volume of fluid actually pushed out of the way to get the correct buoyant force.