Buoyancy Calculator
This buoyancy calculator uses the volume and the density of the fluid: a body of 1,000 litres displaces 998 kg of fresh water and feels 9,789 N of buoyancy. It also tells you whether the body floats and handles balloons.
Example: What do you want to calculate: Body in liquid or air · Mass of the body 800 kg · Volume of the body 1,000 litres · Liquid or gas: Fresh water (998.2 kg/m³) → Buoyancy: Buoyant force 9,789 N, the body floats. Source: Wikipedia – Archimedisches Prinzip. Updated: .
How it is calculated
According to Archimedes, buoyancy equals the weight of the displaced fluid: F = ρ · V · g with the fluid density ρ, the submerged volume V and g = 9.80665 m/s². It depends neither on the shape nor on the material of the body.
Float, hover or sink
Whether a body floats depends on its average density: if it is lower than the fluid density, the body floats and sinks in only until buoyancy carries its weight (share = body density divided by fluid density). If both are equal it hovers, if it is higher the body sinks. The payload shows how many kilograms a boat can still take before it is fully submerged.
Balloons
A balloon rises because its filling gas is lighter than the surrounding air. The lift is the volume times the density difference: about 1.04 kg per m³ for helium and 1.12 kg per m³ for hydrogen. Hot air gets thinner with temperature: at 100 °C it is only 0.946 kg/m³ and gives about 0.26 kg of lift per m³.
- Volume in litres: 1,000 litres equal 1 m³.
- Sea water carries more than fresh water because it is denser.
- The own mass of envelope, basket and burner is subtracted from the lift.
Frequently asked questions
How do you calculate buoyancy?
F = ρ · V · g: fluid density times displaced volume times 9.81 m/s². For 1 litre of water that is about 9.79 N, roughly the weight of 1 kg.
When does a body float?
When its average density is lower than that of the liquid. Wood at 800 kg/m³ floats in water with about 80 % submerged.
How much can a hot-air balloon carry?
With 100 °C inside and 20 °C outside air, 2,800 m³ give about 720 kg of lift. After envelope, basket and burner, the rest is payload.
Sources and legal basis
- Wikipedia – Archimedisches Prinzip
- Wikipedia – Buoyancy
- Wikipedia – Dichte (density: tables for liquids and gases)
- Wikipedia – Heißluftballon (hot-air balloon: lift from the density difference)
As of: · Editorial policy
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