// physics › Buoyancy
Find the buoyant force on a submerged object, or solve for fluid density or displaced volume.
F_b = ρ V g
A mind behind this: Archimedes c. 287 – c. 212 BC
When you put something in water, it pushes some water out of the way. The water pushes back up on the object with a force equal to the weight of the water that got shoved aside. That upward push is called buoyancy — it is what makes things feel lighter in water.
It is all about how much water you push aside. A ship is hollow and wide, so it shoves aside a massive amount of water — enough that the upward push equals the ship's weight, so it floats. Squash that steel into a nail and it pushes aside almost no water, so it sinks.
Say an object pushes aside 0.001 cubic metres of water (density 1000 kg/m³), with gravity g = 9.81. Buoyant force = density × volume × g = 1000 × 0.001 × 9.81 = 9.81. So the water pushes up with 9.81 newtons.
It is just the amount of fluid the object pushes out of the way. If the object is fully underwater, the displaced volume equals the object's own volume. If it floats, only the underwater part counts.
Because the water is pushing up on you with a buoyant force, holding up a lot of your weight. You still weigh the same, but the upward push from the water means your legs have to support much less, so you feel light and can even float.
No. It works in any fluid — including air and other liquids. A helium balloon rises because the air around it pushes up with more force than the balloon's weight. Denser fluids give a bigger upward push, which is why it is easier to float in very salty sea water.