Buoyant Force Calculator (Archimedes)
Compute the upward buoyant force on a submerged or floating object from Archimedes’ principle, plus its apparent weight and whether it floats or sinks.
How it works
F_b = ρ_fluid · V_displaced · g · Apparent weight = m·g − F_b
Archimedes’ principle states that the upward buoyant force on a body equals the weight of the fluid it displaces: F_b = ρ·V·g. An object floats when it can displace its own weight of fluid before being fully submerged — that is, when its average density is less than the fluid’s. If its density is greater, the buoyant force is smaller than its weight and it sinks, weighing an "apparent weight" of m·g − F_b while under the surface.
Worked example
An object displacing 0.01 m³ (10 litres) of fresh water (ρ = 1000 kg/m³): F_b = 1000 × 0.01 × 9.81 = 98.1 N. If the object’s mass is 12 kg its weight is 117.7 N, so it sinks and its apparent weight underwater is 117.7 − 98.1 = 19.6 N.
Sources: Archimedes’ principle — Wikipedia
Frequently asked questions
Why do some objects float and others sink?
An object floats if its average density is less than the fluid’s, because it only needs to displace part of its volume to displace its own weight of fluid. If it is denser, even fully submerged it cannot displace enough, so the buoyant force is less than its weight and it sinks.
Does a heavier fluid give more buoyant force?
Yes. Buoyant force is proportional to fluid density, so the same volume displaces more weight in seawater (≈1025 kg/m³) than in fresh water — which is why you float more easily in the ocean than in a lake.
What is apparent weight?
It is how heavy a submerged object seems when weighed in the fluid: its true weight minus the buoyant force. A rock that weighs 117.7 N in air might register only about 20 N on a scale underwater.
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This calculator is for educational purposes. Double-check important results before acting on them.