Buoyant Force Calculator
Calculate buoyant force using Archimedes' principle with comprehensive fluid mechanics analysis
Buoyancy Calculator
Choose your preferred calculation method
Fluid density: 1000.000 kg/m³
Volume in m³: 0.100000
Advanced Settings▼
Standard Earth gravity: 9.807 m/s²
Buoyancy Results
Archimedes' Principle: B = ρ_fluid × V_displaced × g
Calculation: 1000 × 0.100000 × 9.807 = 980.70 N
Pressure at depth: 4552 Pa
Buoyancy Analysis
Example: Steel Ball in Water
Problem Setup
Object: Steel ball with volume 0.001 m³ (1 liter)
Fluid: Water (ρ = 1000 kg/m³)
Gravity: 9.807 m/s²
Steel density: 7850 kg/m³
Solution
1. Buoyant force: B = ρ_water × V × g
2. B = 1000 × 0.001 × 9.807 = 9.807 N
3. Object weight: W = ρ_steel × V × g = 7850 × 0.001 × 9.807 = 77.0 N
4. Net force downward: 77.0 - 9.807 = 67.2 N
Result: Steel ball sinks because its density > water density
Fluid Densities (kg/m³)
Buoyancy Principles
Archimedes' Principle
Buoyant force equals weight of displaced fluid
Floating Condition
Object density < fluid density
Sinking Condition
Object density > fluid density
Neutral Buoyancy
Object density = fluid density
Real-World Applications
Ship Design
Hull design for optimal displacement and stability
Swimming & Diving
Body buoyancy affects swimming technique
Balloons & Airships
Hot air and helium provide lift in atmosphere
Density Measurement
Determining material properties through buoyancy
Understanding Buoyant Force
What is Buoyant Force?
Buoyant force is the upward force exerted by a fluid on an object immersed in it. This force arises due to the pressure difference between the top and bottom of the object caused by the fluid's weight and gravity.
Archimedes' Principle
- •Any object immersed in a fluid experiences an upward buoyant force
- •The magnitude equals the weight of displaced fluid
- •This principle applies to all fluids: liquids and gases
- •The buoyant force acts at the center of buoyancy
Mathematical Foundation
B = ρ_fluid × V_displaced × g
B = W_displaced_fluid
- B: Buoyant force (N)
- ρ_fluid: Density of the fluid (kg/m³)
- V_displaced: Volume of displaced fluid (m³)
- g: Gravitational acceleration (m/s²)
Float or Sink Conditions
Float: ρ_object < ρ_fluid
Sink: ρ_object > ρ_fluid
Neutral: ρ_object = ρ_fluid
Practical Applications
Naval Architecture
Ships are designed with large hulls to displace enough water to create sufficient buoyant force to support their weight
Submarine Operation
Ballast tanks control buoyancy by taking in or expelling water to achieve neutral buoyancy for diving
Material Science
Density determination through buoyancy measurements helps identify and characterize materials
💡 Interesting Facts
- • A human body has approximately the same density as water, allowing for easy floating
- • Icebergs float with about 90% of their volume underwater due to ice density (917 kg/m³)
- • Hot air balloons work because heated air is less dense than cold air
- • Dead Sea's high salt content (density ~1240 kg/m³) makes swimming nearly impossible to sink