Buoyancy Calculator
Calculate the buoyant force on any object using Archimedes' principle.
Enter object volume, fluid density, and object density to determine float or sink.
How Buoyancy Is Calculated
Buoyancy is the upward force a fluid exerts on a submerged or floating object. It equals the weight of the fluid that the object displaces. This principle was discovered by Archimedes in ancient Greece.
Archimedes’ Principle formula:
Buoyant Force (F_b) = Fluid Density × g × Displaced Volume
Where:
- ρ_fluid = density of the fluid (kg/m³)
- g = gravitational acceleration = 9.81 m/s²
- V = volume of fluid displaced by the object (m³)
Common fluid densities:
- Fresh water: 1,000 kg/m³
- Seawater: 1,025 kg/m³
- Air (at sea level): 1.225 kg/m³
- Mercury: 13,534 kg/m³
Worked example — wooden block:
A wooden block (density 600 kg/m³) measures 0.2 m × 0.3 m × 0.1 m = 0.006 m³.
Block weight: 600 × 9.81 × 0.006 = 35.3 N
If fully submerged in fresh water:
F_b = 1,000 × 9.81 × 0.006 = 58.9 N
Since buoyant force (58.9 N) > weight (35.3 N), the block floats.
Floating depth calculation:
When an object floats, buoyant force equals weight:
ρ_fluid × V_submerged = ρ_object × V_total Fraction submerged = ρ_object ÷ ρ_fluid = 600 ÷ 1,000 = 0.6 (60% below waterline)
Practical applications:
- Ship design: A steel ship floats because its hull is hollow — total density including air is less than water
- Hot air balloons: Heated air is less dense than surrounding air, generating positive buoyancy
- Submarines: Control depth by adjusting ballast tank water volume to match desired buoyancy exactly
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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