Buoyancy Calculator — Archimedes' Principle
Calculate buoyant force using Archimedes' principle F = ρVg. Find whether objects sink or float, apparent weight underwater, and displaced fluid volume.
Archimedes reportedly leaped from his bath shouting "Eureka!" when he realized that a submerged object displaces fluid equal to its own volume. That simple insight connects volume, density, and the upward force of fluid in a way that explains why massive steel ships float while small rocks sink.
The CalcHub buoyancy calculator computes buoyant force, apparent weight, and float/sink status from object and fluid properties.
Archimedes' Principle
F_b = ρ_fluid × V_submerged × g- F_b = buoyant force (Newtons, N)
- ρ_fluid = density of the fluid (kg/m³)
- V_submerged = volume of fluid displaced (m³)
- g = gravitational acceleration (9.81 m/s²)
Will It Float?
Compare average densities:
- ρ_object < ρ_fluid → floats
- ρ_object > ρ_fluid → sinks
- ρ_object = ρ_fluid → neutral buoyancy
An object floating at the surface has ρ_object/ρ_fluid fraction of its volume submerged. Ice (917 kg/m³) in seawater (1025 kg/m³): fraction submerged = 917/1025 = 0.895, so 89.5% is underwater.
Apparent Weight
When an object is submerged, it feels lighter by the buoyant force:
W_apparent = W_actual − F_bA 5 kg steel bolt (ρ = 7800 kg/m³):
- Volume = 5/7800 = 0.000641 m³
- F_b = 1000 × 0.000641 × 9.81 = 6.29 N
- W_actual = 5 × 9.81 = 49.05 N
- W_apparent = 49.05 − 6.29 = 42.76 N
How do ships float if they're made of steel?
A steel ship is hollow — its effective density includes all the air inside. The average density of the whole ship (steel hull + interior air + everything inside) must be less than water. Aircraft carriers displace over 100,000 tonnes of water, but their average density is less than 1.
How does a submarine control depth?
By filling or emptying ballast tanks. Fill them with water → average density increases → submarine sinks. Blow water out with compressed air → average density decreases → submarine rises. It's buoyancy control, not thrust.
Can I use this for gases?
Yes — balloons and blimps work the same way. A hot air balloon floats because heated air (low density, ~0.9 kg/m³) fills the envelope, making the total average density less than surrounding cool air (~1.22 kg/m³). Helium balloons work the same principle but with cold gas.