Buoyancy Calculator
Archimedes' Principle states that the buoyant force on a submerged object equals the weight of the fluid it displaces. This calculator computes buoyant force, net force, and whether the object sinks or floats.
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Formula
F_b = ρ_fluid × V × g
Buoyant force F_b equals the fluid density (ρ) times the submerged volume (V) times gravitational acceleration (g = 9.81 m/s²). This equals the weight of displaced fluid. If buoyant force > object weight, the object floats; if less, it sinks. Net force = Weight − Buoyancy.
How to use the Buoyancy Calculator
- 1
Enter your fluid density
Value should be in kg/m³.
- 2
Enter your volume of object
Value should be in m³.
- 3
Enter your mass of object
Value should be in kg.
- 4
Read your results instantly
Results update in real time as you type.
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Archimedes' Principle
Legend has it that Archimedes discovered his principle when stepping into a bath and noticing the water level rise. He ran through the streets shouting 'Eureka!' ('I have found it!') — he had just solved how to determine if King Hiero's crown was pure gold without melting it.
The principle: any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. This force acts upward through the centroid of the displaced volume. Whether an object sinks or floats depends on whether its average density exceeds or is less than the fluid's density.
Ships, submarines, and hot air balloons
Ships exploit buoyancy by being hollow — their average density (hull + enclosed air) is less than water. A 100,000-tonne aircraft carrier displaces 100,000 tonnes of water, producing exactly enough buoyant force to float.
Submarines control buoyancy with ballast tanks. Filling tanks with water increases average density, causing descent. Blowing water out with compressed air decreases density, causing ascent. Hot air balloons work identically in air: heating the air inside decreases its density below that of surrounding cooler air, generating lift. Blimps use lighter-than-air helium (density 0.164 kg/m³ vs. air at 1.225 kg/m³).
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Buoyancy in everyday life
Buoyancy affects swimming, scuba diving, fishing (bobbers and sinkers), hydrometers, and even the sensation of weightlessness in water. In the Dead Sea (salinity ~33%, density ~1,240 kg/m³), the buoyant force on a human is dramatically higher — people effortlessly float on their backs.
For fish, swim bladders are internal gas-filled organs that adjust buoyancy precisely. By secreting or absorbing gas, fish can hover at any depth without expending energy on swimming. This elegant solution inspired the design of submarines.
Tips & Insights
Water density = 1,000 kg/m³
Fresh water: 1,000 kg/m³. Seawater: ~1,025 kg/m³. The Dead Sea: ~1,240 kg/m³. Objects float more easily in denser fluids.
Convert liters to m³
1 liter = 0.001 m³. A 10-liter submerged object displaces 0.01 m³ of water. Buoyant force = 1,000 × 0.01 × 9.81 = 98.1 N.
Partially submerged objects
For a floating object, only the submerged volume counts. At equilibrium, the buoyant force from the submerged portion equals total weight.
Worked Examples
Block of wood
Buoyancy = 98.1 N. Weight = 58.86 N. Net = −39.2 N (floats — buoyancy exceeds weight).
Steel block
Buoyancy = 98.1 N. Weight = 769.8 N. Net = +671.7 N (sinks rapidly).
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Frequently Asked Questions
What is Archimedes' Principle?
The buoyant force on a submerged object equals the weight of fluid displaced: F_b = ρ_fluid × V × g.
Why does a ship float?
A ship's hollow hull makes its average density less than water. It displaces water equal to its total weight, generating enough buoyancy to float.
What is neutral buoyancy?
When buoyant force exactly equals weight, the object neither sinks nor rises — it hovers. Scuba divers achieve this by adjusting their BCD (buoyancy compensator device).
Does buoyancy depend on depth?
No — buoyant force depends only on volume displaced and fluid density, not depth. (For compressible objects like foam, depth can compress volume, changing buoyancy.)
How is buoyancy used in hot air balloons?
Heated air is less dense than cool air. The balloon displaces cool air, generating buoyancy. When buoyancy > total weight (balloon + basket + passengers), it rises.
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