Archimedes' Principle Calculator
Find the buoyant force on a submerged object.
Archimedes' principle: the upward buoyant force equals the weight of displaced fluid.
How the Math Works
The formula F = ρ·g·V calculates the buoyant force exerted on a submerged object by a fluid. Here, ρ (rho) represents the fluid's density in kg/m³, g is gravitational acceleration (9.81 m/s² on Earth), and V is the volume of displaced fluid in m³. This equation derives from Archimedes' Principle, which states that the upward buoyant force equals the weight of the fluid displaced by the object. For example, displacing 1 m³ of water (ρ = 1000 kg/m³) generates a buoyant force of 9810 N (1000 × 9.81 × 1).
Practical Applications
Engineers use this principle to design ships, submarines, and underwater structures by calculating buoyant forces to ensure flotation and stability. Fluid mechanics in HVAC systems, dams, and hydraulic equipment rely on these calculations to manage pressure and flow. Scuba divers and marine biologists apply it to understand how objects behave in water, while manufacturers test product buoyancy for safety certifications. The formula also helps in determining whether an object will sink, float, or achieve neutral buoyancy in different fluids.
Day-to-Day Use
Understanding buoyant force helps explain why icebergs float (ice is less dense than seawater) or why a ship made of steel doesn't sink (its hollow structure displaces enough water). It applies to everyday situations like packing a suitcase—denser items sink in water while lighter ones float—and using floatation devices like life rings during swimming. Even cooking involves buoyancy when ingredients like pasta or eggs behave differently in boiling water, making this principle relevant beyond technical fields.
Worked example
0.01 m³ in water → about 98.1 N of buoyancy.
FAQ
Why do steel ships float?
Their shape displaces enough water to match their weight.