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

980.70 N
Buoyant Force
100.000 kg
Displaced Fluid Mass
0.100000
Displaced Volume
10.2 kg/m³
Object Density
FLOAT
1.0% submerged

Archimedes' Principle: B = ρ_fluid × V_displaced × g

Calculation: 1000 × 0.100000 × 9.807 = 980.70 N

Pressure at depth: 4552 Pa

Buoyancy Analysis

✅ Object will float - density (10.2 kg/m³) < fluid density (1000 kg/m³)
⚠️ Large buoyant force (981 N) - significant upward thrust

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)

Water1000
Seawater1025
Fresh Water998
Ice917
Oil850
Gasoline680
Mercury13534
Ethanol789
Ethylene Glycol1113
Honey1420
Milk1030
Blood1060
Air1.225
Helium0.1786
Hydrogen0.08988
Note: Densities may vary with temperature and pressure

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