Buoyancy Calculator

Archimedes' Principle

Archimedes discovered that a body submerged in fluid experiences an upward buoyant force equal to the weight of fluid it displaces. This principle governs ship design, submarine depth control, hot air balloon lift, and the floating of icebergs.

The Buoyant Force Formula

F_b = ρ_fluid × V_submerged × g

Where:

• F_b = buoyant force (N)
• ρ_fluid = density of the fluid (kg/m³) — fresh water: 1,000; sea water: ~1,025
• V_submerged = volume of fluid displaced (m³)
• g = 9.81 m/s²

The object floats if F_b ≥ Weight of object (mg). Net upward force = F_b − mg

Effective Weight (Apparent Weight)

W_apparent = mg − F_b = V × (ρ_object − ρ_fluid) × g

If ρ_object < ρ_fluid → object floats. If ρ_object > ρ_fluid → object sinks (but weighs less than in air).

Practical Examples

Example 1: Steel ball, radius 5cm (V = 5.24×10⁻⁴ m³), density 7,800 kg/m³, in water. Weight = 7800 × 5.24×10⁻⁴ × 9.81 = 40.0N. F_b = 1000 × 5.24×10⁻⁴ × 9.81 = 5.14N. Apparent weight = 40.0 − 5.14 = 34.9N (sinks, but feels lighter).

Example 2: 1,000kg submarine, volume 1.5m³ of hull vs 1m³ water displaced. F_b = 1000 × 1 × 9.81 = 9,810N. Weight = 1000 × 9.81 = 9,810N. Neutral buoyancy — adjusts ballast tanks to dive or surface.