Buoyancy Calculator (Archimedes' Principle)
By Santaji GadepatilinUpdated October 27, 2026
Any object in a fluid is pushed upward by a force equal to the weight of fluid it displaces — Archimedes' principle. It explains why ships float, why balloons rise and why things feel lighter underwater. This free buoyancy calculator solves for whichever value you leave blank and shows the formula and steps.
How to use the buoyancy calculator
Enter the volume of the object under the fluid, the fluid density and the object’s mass. You get the buoyant force, the object’s weight and its apparent weight while submerged. A negative apparent weight means the object would rise and float.
Buoyancy formula
Fb = ρfluid × g × Vsubmerged
Fluid densities
| Fluid | Density (kg/m³) |
|---|---|
| Fresh water | 1,000 |
| Seawater | 1,025 |
| Dead Sea water | about 1,240 |
| Olive oil | 910 |
| Mercury | 13,534 |
| Air (20 °C) | 1.2 |
Example
A 10 L object weighing 8 kg, fully submerged in fresh water:
- Buoyant force = 1,000 × 9.81 × 0.01 = 98.1 N
- Weight = 8 × 9.81 = 78.5 N
- Apparent weight = −19.6 N → it floats, with 80% of its volume underwater.
Weighing in water
Apparent weight lets you find density without measuring volume: density = ρwater × weight in air ÷ (weight in air − weight in water). Archimedes is said to have used this to test whether a crown was pure gold.
Hot-air balloons
Balloons float in air for the same reason. Heating the air inside lowers its density; the difference in density times the balloon volume gives the lift.
Frequently asked questions
What is Archimedes' principle?
An object immersed in a fluid is pushed up by a force equal to the weight of fluid it displaces.
How do I know if something will float?
If its average density is less than the fluid’s, it floats. In the calculator, a negative apparent weight when fully submerged means it will float up.
How much of a floating object is underwater?
The fraction submerged equals object density ÷ fluid density. Ice (917 kg/m³) floats with about 90% underwater in seawater.
Why do ships made of steel float?
Their hollow hulls displace a large volume of water, so their average density is less than water.