Hong Life CalculatorsUnderstanding the buoyancy calculator — concept and principle
Buoyancy is the upward force a fluid exerts on anything immersed in it. It decides whether a boat floats, how much a diver must weigh down, how a hot-air balloon lifts and how far a floating object sinks. This calculator uses Archimedes' principle to find the buoyant force on a given volume, the net force once the object's weight is included, whether it floats, and what fraction would be under the surface if it does.
How it is calculated
- Buoyant force: F_b = ρ_fluid × V × g, with ρ in kg/m³, V converted from litres to m³ (÷ 1,000) and g = 9.80665 m/s². Result in newtons (N).
- Net force: F_b − m g, where m is the object's mass in kg. Positive means the fluid pushes it up more than gravity pulls it down.
- Floats? yes if ρ_fluid × V ≥ m, that is, if the fluid mass the object can displace is at least its own mass.
- Fraction submerged: m ÷ (ρ_fluid × V) × 100%, capped at 100%.
For the float check and fraction, V is treated as the object's whole volume when fully submerged.
The principle
Pressure in a fluid increases with depth, so the bottom of an object is pushed up harder than its top is pushed down. The difference is exactly the weight of the fluid that the object displaces, which is Archimedes' principle. A floating object sinks until the displaced fluid weighs as much as the object itself; this is why the fraction submerged equals the object's average density divided by the fluid density.
Worked example
- Inputs: V = 50 L, ρ = 1,000 kg/m³ (fresh water), m = 40 kg.
- Displaced fluid mass = 1,000 × 50 ÷ 1,000 = 50 kg, so F_b = 50 × 9.80665 = 490.3325 N.
- Weight = 40 × 9.80665 = 392.266 N, so net force = 490.3325 − 392.266 = 98.0665 N upward.
- 50 kg ≥ 40 kg, so it floats.
- Fraction submerged = 40 ÷ 50 = 80%.
| Object volume (L) | Buoyant force, fully submerged (N) |
|---|---|
| 12.5 | 122.583125 |
| 25 | 245.16625 |
| 37.5 | 367.749375 |
| 50 | 490.3325 |
| 62.5 | 612.915625 |
| 75 | 735.49875 |
| 100 | 980.665 |
How to read the result
The object's average density is 40 ÷ 0.05 = 800 kg/m³, so it floats with 80% under water, much like some woods. If fully pushed under, it needs about 98 N (roughly 10 kgf) to hold it down. In seawater at 1,025 kg/m³ the same object would float a little higher, with about 78% submerged. Ice at about 917 kg/m³ floats with roughly 90% submerged in fresh water.
Common mistakes
- Entering the object's material density instead of the fluid density.
- Entering only the part already under water as V when checking if a whole object floats.
- Forgetting that hollow objects (boats, bottles) float because their average density, including air inside, is low.
Frequently asked questions
Why does a steel ship float?
Its hull encloses a large volume of air, so the whole ship's average density is less than water and it displaces its own weight before the deck reaches the waterline.
Does buoyancy depend on depth?
Not for an incompressible object in uniform fluid. A compressible object, like a diver's suit or lungs, shrinks with depth and loses buoyancy.
Sources: Archimedes, On Floating Bodies, Book I · Halliday, Resnick and Walker, Fundamentals of Physics, chapter on fluids