Archimedes' Principle Calculator
Calculate buoyant force, object density, and floating behavior using Archimedes' principle
Archimedes' Principle Calculator
True mass of the object in air
Volume of the immersed object
Select the fluid the object is immersed in
Density of the fluid at standard conditions
Standard gravity: 9.807 m/s² (Earth surface)
Calculation Results
Buoyant Force
Object Density
Floating Behavior
Archimedes' Principle: F_B = V × ρ_fluid × g
Where: F_B = Buoyant force, V = Volume displaced, ρ = Fluid density, g = Gravity
Mass displaced: 0.000 kg
Physics Analysis
Example Calculation - Aluminum Block in Water
Given Parameters
Object: Aluminum block
Mass: 1,000,000 kg (1000 metric tons)
Aluminum density: 2,700 kg/m³
Fluid: Water (density = 1,000 kg/m³)
Calculation Steps
Step 1: Calculate volume of aluminum block
V = mass / density = 1,000,000 kg ÷ 2,700 kg/m³ = 370.4 m³
Step 2: Calculate buoyant force
F_B = V × ρ_water × g = 370.4 m³ × 1,000 kg/m³ × 9.807 m/s²
Result: F_B = 3.63 × 10⁶ N (3.63 MN)
Conclusion: Block will sink (density ratio: 2.7)
Common Fluid Densities
Applications
Ship Design: Determining displacement and stability
Hot Air Balloons: Calculating lift force
Hydrometers: Measuring fluid density
Geology: Determining mineral density
Swimming: Understanding buoyancy in humans
Understanding Archimedes' Principle
What is Archimedes' Principle?
Archimedes' principle states that when an object is partially or wholly immersed in a fluid, the buoyant force acting on it is equal to the weight of the fluid displaced by the object. This principle explains why some objects float while others sink.
The Physics Behind Buoyancy
- •Pressure increases with depth in fluids
- •Higher pressure at bottom creates net upward force
- •Buoyant force depends on fluid density, not object density
- •Volume of displaced fluid equals immersed volume
Archimedes' Principle Formula
F_B = V × ρ_fluid × g
- F_B: Buoyant force (N)
- V: Volume of displaced fluid (m³)
- ρ_fluid: Density of fluid (kg/m³)
- g: Acceleration due to gravity (m/s²)
Floating vs Sinking
Object floats if: ρ_object < ρ_fluid
- Float: Buoyant force ≥ Object weight
- Sink: Buoyant force < Object weight
- Neutral: Buoyant force = Object weight
Historical Note: Discovered by Archimedes of Syracuse (c. 287-212 BCE)
Practical Applications and Examples
Ship Design
Displacement Principle
Ships are designed so the weight of water they displace equals their total weight, allowing massive steel vessels to float.
Density Measurement
Hydrostatic Weighing
By measuring an object's weight in air and in water, its density can be calculated using Archimedes' principle.