Archimedes' Principle
Calculate buoyant force, object volume, and density using Archimedes' Principle F_b = ρgV. Enter true mass, apparent mass in fluid, and fluid density for instant physics results.
About This Calculator
The Archimedes' Principle Calculator helps you compute the buoyant force, volume, and density of an object submerged in a fluid. Simply enter the object's true mass (measured in air), its apparent mass when fully submerged in the fluid, and the fluid density to get instant results with detailed breakdowns and charts.
Archimedes' Principle states that the upward buoyant force exerted on a body immersed in a fluid equals the weight of the fluid that the body displaces. Mathematically, Fb = ρ × V × g, where ρ is the fluid density, V is the volume of displaced fluid, and g is the acceleration due to gravity (9.80665 m/s²). The apparent mass loss (true mass − apparent mass) directly gives the mass of displaced fluid.
This calculator also determines whether the object will float or sink by comparing its average density to the fluid density — objects with lower density than the fluid float, while denser objects sink. This is the fundamental principle behind ships (steel ships float because their average density including air is less than water), submarines (adjustable ballast tanks), hydrometers, and hot air balloons.
How It Works
Volume of displaced fluid = (true mass − apparent mass) / fluid density. Object density = true mass / object volume. Buoyant force = (true mass − apparent mass) × g. The float status is determined by comparing the calculated object density with the fluid density.
Regional Notes
India: Uses SI units (kg, kg/m³, N). Standard reference values apply universally since this is a physics principle.
United States: This calculator uses SI metric units (kg, kg/m³). Convert from imperial units if needed: 1 lb = 0.4536 kg, 1 ft³ = 0.02832 m³.
United Kingdom: Uses SI units. Reference values match international physics standards.
Common Fluid Densities
Water: 1000 kg/m³, Seawater: 1025 kg/m³, Gasoline: 720 kg/m³, Ethanol: 789 kg/m³, Mercury: 13534 kg/m³, Air: 1.225 kg/m³.
Frequently Asked Questions
What is Archimedes' Principle?
Archimedes' Principle states that the upward buoyant force on an object immersed in a fluid equals the weight of the fluid displaced by the object. This principle explains why objects float or sink and is fundamental to fluid mechanics.
How do I calculate buoyant force using Archimedes' Principle?
Buoyant force is calculated as F_b = ρ × V × g, where ρ is fluid density, V is the volume of fluid displaced (equal to the object volume when fully submerged), and g is gravitational acceleration (9.81 m/s²). Enter the true mass, apparent mass in fluid, and fluid density to get instant results.
How do I find the density of an object using Archimedes' Principle?
To find object density, measure its mass in air (true mass) and its apparent mass when fully submerged in water. The volume equals (true mass - apparent mass) / fluid density. Object density = true mass / volume. For example, a 540 g rock with 340 g apparent mass in water has density 2.70 g/cm³.
Why does an object float or sink according to Archimedes' Principle?
An object floats if its average density is less than the fluid density, because the buoyant force (weight of displaced fluid) equals the object's weight before it is fully submerged. It sinks if its density is greater, as the buoyant force is insufficient to support its weight.
Is this Archimedes' Principle calculator free?
Yes, this calculator is completely free to use with no registration required. You can also share your calculations via URL.
What are real-world applications of Archimedes' Principle?
Archimedes' Principle is used in designing ships and submarines, hydrometers for measuring fluid density, hot air balloons, and in geology to determine the purity of precious metals and gemstones by measuring their density.
Can I use this calculator for any fluid?
Yes, you can use any fluid by entering its density. Common fluid densities include water (1000 kg/m³), seawater (1025 kg/m³), gasoline (720 kg/m³), ethanol (789 kg/m³), and mercury (13534 kg/m³). Simply change the fluid density value to match your fluid.