About the Buoyancy Calculator
This buoyancy calculator applies Archimedes’ principle: an object in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. Enter the object’s volume and mass and choose the fluid, and it returns the buoyant force if fully submerged, the object’s weight, the net force, and whether it will float or sink.
It is useful for physics students, model boat and ROV builders, divers working out weighting, and anyone wondering whether something will float in fresh water, seawater, oil or even air (for balloons). If the object floats, the calculator also reports what fraction of its volume sits below the surface.
The calculation assumes the object is solid with a uniform average density, the fluid is at rest, and standard gravity of 9.80665 m/s². For hollow objects like hulls, enter the total enclosed volume and total mass to get the right average density.
With the default inputs, the buoyant force (fully submerged) is 98.066 N. Change any value above to recalculate instantly.
How to use the buoyancy calculator
- 1Choose the fluid or enter a custom density.
- 2Enter the object’s volume in liters (1 m³ = 1,000 L).
- 3Enter the object’s mass in kilograms.
- 4Compare the buoyant force with the weight to see if it floats.
- 5If it floats, read the percentage submerged and the extra load it can carry.
Formula and method
Archimedes’ principle says the upward buoyant force equals the weight of fluid displaced: fluid density × displaced volume × gravity. When the object is fully submerged, the displaced volume is the object’s own volume. Comparing this with the object’s weight tells you whether it rises or sinks.
Equivalently, an object floats when its average density is less than the fluid’s. A floating object sinks only until it displaces its own weight, so the fraction submerged equals ρ_object ÷ ρ_fluid — the reason about 90% of an iceberg is hidden in seawater.
- F_b
- Buoyant force (N)
- ρ_fluid
- Fluid density (kg/m³)
- V
- Volume of fluid displaced (m³)
- g
- Gravitational acceleration (9.80665 m/s²)
- m
- Object mass (kg)
Worked examples
10 L block weighing 6 kg in fresh water
Fully submerged, the block displaces 0.01 m³ of water: 1000 × 0.01 × 9.80665 = 98.07 N up against 58.84 N of weight. Its density is 600 kg/m³, so it floats with 60% of its volume underwater.
1 L of steel (7.85 kg) in seawater
The steel displaces 1 L of seawater, giving 1025 × 0.001 × 9.80665 = 10.05 N of lift, far less than its 76.98 N weight. At 7,850 kg/m³ it sinks — steel ships float only because their hulls enclose lots of air.
1 m³ of ice in seawater
Ice at 917 kg/m³ in seawater at 1,025 kg/m³ floats with 917 ÷ 1025 = 89.5% of its volume below the waterline — the origin of “the tip of the iceberg”.
Frequently asked questions
What is the formula for buoyant force?+
Buoyant force F = ρ × V × g: fluid density times the volume of fluid displaced times gravitational acceleration. With ρ in kg/m³, V in m³ and g = 9.81 m/s² the answer is in newtons.
How do I know if something will float?+
Compare the object’s average density (mass ÷ volume) with the fluid’s density. If it is lower, the object floats; if higher, it sinks; if equal, it is neutrally buoyant and hovers.
Why is it easier to float in seawater?+
Salt makes seawater about 2.5% denser than fresh water (around 1,025 kg/m³), so the same volume displaced produces more upward force. Very salty water like the Dead Sea is denser still.
How do steel ships float?+
A ship’s hull encloses a large volume of air, so its average density — steel plus air plus cargo divided by total enclosed volume — is lower than water. It settles until it displaces its own weight of water.
Does depth change buoyant force?+
For an incompressible object in a uniform liquid, no — the force depends only on the volume displaced. Compressible things like wetsuits and lungs shrink with depth, which reduces their buoyancy.