Buoyancy & Archimedes' Principle Calculator

Archimedes' Principle & Buoyant Force

Archimedes' Principle:

F_buoyant = ρ_fluid × g × V_displaced
Where: F_b = buoyant force, ρ = fluid density, g = gravity, V = volume of displaced fluid
The buoyant force equals the weight of displaced fluid

Fluid Density (ρ) - kg/m³:

Displaced Volume (V) - m³:

Buoyant Force (F_b) - N:

Gravity (g) - m/s²:

Common Fluid Densities (kg/m³):
Water: 1000
Seawater: 1025
Oil: 850
Mercury: 13,600
Air: 1.225
Alcohol: 790

Key Insight:
Buoyant force depends only on displaced fluid volume, not object shape

Floating Objects & Equilibrium

Floating Equilibrium:

For floating: Weight = Buoyant Force
ρ_object × V_object × g = ρ_fluid × V_submerged × g
Fraction submerged = ρ_object / ρ_fluid
Fraction above water = 1 - (ρ_object / ρ_fluid)

Object Density (ρ_obj) - kg/m³:

Object Volume (V_obj) - m³:

Fluid Density (ρ_fluid) - kg/m³:

Submerged Volume (V_sub) - m³:

Object Densities (kg/m³):
Ice: 917
Wood (oak): 750
Wood (pine): 500
Plastic: 900-1400
Steel: 7850
Aluminum: 2700

Floating Rules:
ρ_obj < ρ_fluid: Floats
ρ_obj = ρ_fluid: Neutral buoyancy
ρ_obj > ρ_fluid: Sinks

Submerged Objects & Apparent Weight

Apparent Weight Formula:

W_apparent = W_actual - F_buoyant
W_apparent = mg - ρ_fluid × V_object × g
Where: W = weight, m = mass, V = object volume

Object Mass (m) - kg:

Object Volume (V) - m³:

Fluid Density (ρ) - kg/m³:

Actual Weight (W_actual) - N:

Apparent Weight (W_apparent) - N:

Applications:
• Underwater weighing
• Density measurement
• Submarine ballast
• Diving equipment

Note:
Apparent weight can be negative if buoyant force exceeds actual weight

Density Measurement Using Buoyancy

Density from Buoyancy:

ρ_object = (W_air / (W_air - W_fluid)) × ρ_fluid
Where: W_air = weight in air, W_fluid = weight in fluid
This method determines density by comparing weights

Weight in Air (W_air) - N:

Weight in Fluid (W_fluid) - N:

Fluid Density (ρ_fluid) - kg/m³:

Object Density (ρ_object) - kg/m³:

Density Measurement Method:
1. Weigh object in air
2. Weigh object in known fluid
3. Calculate density from weight difference

Accuracy Tips:
• Use precise scale
• Account for air density
• Ensure complete submersion
• Remove air bubbles

Submarine & Hot Air Balloon Buoyancy

Buoyancy Control:

Net Force = F_buoyant - Weight
For submarines: Control water in ballast tanks
For balloons: Control air temperature/density
Neutral buoyancy: F_buoyant = Weight

Vehicle Type:

Vehicle Volume (V) - m³:

Vehicle Mass (empty) - kg:

Fluid Density (ρ_fluid) - kg/m³:

Payload Mass - kg:

Typical Densities:
Water: 1000 kg/m³
Air (sea level): 1.225 kg/m³
Air (10,000 ft): 0.905 kg/m³
Hot air (100°C): 0.946 kg/m³
Helium: 0.179 kg/m³

Control Methods:
Submarine: Ballast tanks
Balloon: Heating/cooling air