Buoyancy
Find buoyant force and displaced mass for any submerged object using Archimedes' principle. Free physics buoyancy calculator with charts and breakdown tables.
About This Calculator
The Buoyancy Calculator computes the upward buoyant force on any object submerged in a fluid using Archimedes' principle. Enter the fluid density and the volume of displaced fluid to instantly calculate the buoyant force in newtons and the mass of the displaced fluid in kilograms. This tool is essential for physics students, engineers, scuba divers, marine architects, and anyone studying fluid mechanics.
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. Mathematically, B = ρ × V × g, where ρ is the fluid density (kg/m³), V is the volume of displaced fluid (m³), and g is the acceleration due to gravity (9.80665 m/s²). The mass of displaced fluid is simply ρ × V. This principle explains everything from why ships float to how hot air balloons rise.
How It Works
Enter the fluid density in kg/m³ (default 1000 kg/m³ for fresh water) and the volume of the object that is submerged in m³. The calculator applies Archimedes' formula to output the buoyant force and the mass of the displaced fluid. The breakdown table shows each component of the calculation, and the chart visualizes the relationship between density, volume, and buoyant force.
Common Fluid Densities
Fresh water at 4°C has a density of 1000 kg/m³, while seawater is approximately 1025 kg/m³. Other common fluid densities include gasoline at 720 kg/m³, ethanol at 789 kg/m³, crude oil at 870 kg/m³, and mercury at 13534 kg/m³. Air at sea level and 20°C has a density of about 1.225 kg/m³ — a hot air balloon rises because the heated air inside is less dense than the surrounding cooler air.
Practical Applications
Buoyancy calculations are used in ship and submarine design (to ensure vessels float or dive as intended), in life jacket certification (standards require at least 100 N for offshore use), in hot air ballooning (heating air reduces density to create lift), in scuba diving (weight belts counteract buoyant wetsuits), and in hydrometers and aerometers that measure fluid density from buoyancy. Understanding buoyancy is also critical in offshore engineering for calculating forces on subsea pipelines, risers, and floating platforms.
Frequently Asked Questions
What is the buoyant force?
The buoyant force is the upward force exerted by a fluid on an object immersed in it. It is caused by the increase in fluid pressure with depth, which creates a net upward pressure on the bottom of the object greater than the downward pressure on its top.
How do I calculate the buoyant force?
The buoyant force is calculated using Archimedes' principle: B = ρ × V × g, where ρ is the fluid density (kg/m³), V is the volume of displaced fluid (m³), and g is gravitational acceleration (9.80665 m/s²). Simply enter the fluid density and displaced volume to get instant results.
What is the SI unit of buoyant force?
The SI unit of buoyant force is the newton (N). One newton is the force required to accelerate a mass of one kilogram at one meter per second squared.
Why do objects float or sink?
An object floats if its average density is less than the fluid density. In that case, the buoyant force equals the object's weight before it is fully submerged. It sinks if its density is greater, because the maximum possible buoyant force is less than its weight.
What is the density of water for buoyancy calculations?
Fresh water at 4°C has a density of 1000 kg/m³. Seawater is approximately 1025 kg/m³. Other common fluid densities include gasoline at 720 kg/m³, ethanol at 789 kg/m³, and mercury at 13534 kg/m³.
How much buoyant force does a life jacket provide?
A standard life jacket provides at least 33 N (approximately 3.4 kg of buoyancy) for adults, with larger sizes providing up to 100 N or more. This is enough to keep a person's head above water even if unconscious.
Is this buoyancy calculator free to use?
Yes, this calculator is completely free to use with no registration required. You can also share your calculations via URL.