Buoyancy Calculator
Calculate the buoyant force on an object submerged in a fluid using Archimedes' principle: Fb = ρ×V×g. Enter the fluid density, submerged volume, and gravitational acceleration to determine the upward buoyant force. See also our Force Calculator and Specific Volume Calculator.
How to Calculate Buoyant Force
Buoyancy is the upward force exerted by a fluid on any object immersed in it. This fundamental principle was discovered by Archimedes of Syracuse around 250 BC, reportedly while taking a bath. The story goes that he noticed the water level rise as he entered the tub, leading to his famous exclamation "Eureka!" (I have found it!). Archimedes' principle states that the buoyant force on an object equals the weight of the fluid displaced by that object.
To calculate the buoyant force, multiply the fluid density (ρ) by the volume of fluid displaced (V) by the gravitational acceleration (g): Fb = ρ×V×g. The displaced volume equals the volume of the object that is submerged in the fluid. For a fully submerged object, this is the entire volume of the object. For a floating object, only the submerged portion counts.
An object floats when the buoyant force equals its weight. This occurs when the object's average density is less than the fluid's density. A steel ship floats because its overall density (including the air-filled interior) is less than water. The fraction submerged equals the ratio of object density to fluid density: fraction submerged = ρ_object / ρ_fluid. Ice (density 917 kg/m³) in water (1000 kg/m³) floats with about 91.7% submerged — hence the expression "tip of the iceberg."
Buoyancy applies to all fluids, including gases. Hot air balloons float because heated air is less dense than the surrounding cooler air. Helium balloons rise because helium (density 0.164 kg/m³) is much lighter than air (1.225 kg/m³). Even in everyday life, buoyancy affects everything from cooking (why pasta floats when done) to geology (why continents float on the mantle).
Buoyancy Formula
Archimedes' Principle:
Fb = ρ_fluid × V_displaced × g
Floating condition:
Fb = W_object (buoyant force = weight)
ρ_fluid × V_submerged × g = ρ_object × V_object × g
Fraction submerged (floating):
V_submerged / V_object = ρ_object / ρ_fluid
Net force on submerged object:
F_net = Fb - W = (ρ_fluid - ρ_object) × V × g
Apparent weight in fluid:
W_apparent = W - Fb = ρ_object×V×g - ρ_fluid×V×g
W_apparent = (ρ_object - ρ_fluid) × V × g
Example Calculation
A 0.01 m³ object is fully submerged in fresh water (ρ = 1000 kg/m³). Calculate the buoyant force:
Given: ρ = 1000 kg/m³, V = 0.01 m³, g = 9.81 m/s²
Fb = ρ×V×g = 1000 × 0.01 × 9.81 = 98.1 N
Mass of displaced water: 1000 × 0.01 = 10 kg
If the object has mass 8 kg (density 800 kg/m³):
Weight = 8 × 9.81 = 78.48 N
Net upward force = 98.1 - 78.48 = 19.62 N (object floats!)
Fraction submerged = 800/1000 = 0.8 (80% underwater)
If the object has mass 12 kg (density 1200 kg/m³):
Weight = 12 × 9.81 = 117.72 N
Net downward force = 117.72 - 98.1 = 19.62 N (object sinks)
Buoyancy Reference Table
| Fluid | Density (kg/m³) | Volume (m³) | Buoyant Force (N) |
|---|---|---|---|
| Fresh Water | 1000 | 0.001 | 9.81 N |
| Fresh Water | 1000 | 0.01 | 98.1 N |
| Fresh Water | 1000 | 0.1 | 981 N |
| Fresh Water | 1000 | 1.0 | 9810 N |
| Sea Water | 1025 | 0.01 | 100.55 N |
| Sea Water | 1025 | 1.0 | 10055 N |
| Mercury | 13600 | 0.001 | 133.42 N |
| Oil | 900 | 0.01 | 88.29 N |
| Glycerin | 1260 | 0.01 | 123.61 N |
| Air (sea level) | 1.225 | 1.0 | 12.02 N |
Frequently Asked Questions
What is Archimedes' principle?
Archimedes' principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This applies to all fluids — liquids and gases alike. The principle explains why ships float, why hot air balloons rise, and why objects feel lighter when submerged in water. It is one of the oldest and most fundamental principles in fluid mechanics, discovered over 2,200 years ago.
Why do objects float or sink?
An object floats when its average density is less than the fluid's density, meaning the buoyant force exceeds its weight. It sinks when its average density exceeds the fluid's density. A solid steel ball sinks in water (steel density ~7800 kg/m³ vs water 1000 kg/m³), but a steel ship floats because the ship's overall density (steel hull + air inside) is less than water. Submarines control their buoyancy by filling or emptying ballast tanks with water.
How does salt water affect buoyancy?
Salt water is denser than fresh water (about 1025 kg/m³ vs 1000 kg/m³ for seawater), so it provides greater buoyant force. Objects float higher in salt water — a ship's waterline is lower in fresh water than in the ocean. The Dead Sea (density ~1240 kg/m³) is so salty that humans float effortlessly on its surface. This density difference is why ships have Plimsoll lines marking safe loading depths for different water types.
What is neutral buoyancy?
Neutral buoyancy occurs when an object's weight exactly equals the buoyant force, so it neither floats nor sinks but remains suspended at whatever depth it's placed. This happens when the object's average density equals the fluid's density. Scuba divers achieve neutral buoyancy by adjusting their buoyancy compensator (BC) vest. Fish use swim bladders to control their buoyancy. NASA trains astronauts in neutrally buoyant pools to simulate weightlessness.
Does buoyancy work in gases?
Yes, Archimedes' principle applies to all fluids, including gases. Any object in air experiences a buoyant force equal to the weight of air it displaces. For most solid objects, this force is negligible (air density is only 1.225 kg/m³). But for large, lightweight objects like helium balloons or hot air balloons, the buoyant force exceeds their weight, causing them to rise. A typical party balloon displaces about 0.014 m³ of air, giving a buoyant force of about 0.17 N.
How is buoyancy used in engineering?
Buoyancy is fundamental to naval architecture (ship design), submarine engineering, offshore platform design, and hydrometer instruments. Ships are designed with specific hull shapes to maximize cargo while maintaining stability. Offshore oil platforms use buoyancy to support massive structures. Hydrometers measure fluid density by how deeply a calibrated float sinks. Even in civil engineering, buoyancy must be considered — underground tanks and basements can float upward if groundwater levels rise and the structure is lighter than the displaced water.
Buoyancy in Nature and Technology
Nature has evolved countless buoyancy solutions. Fish use swim bladders — gas-filled organs that adjust volume to control depth. Nautilus shells have gas-filled chambers for buoyancy control. Kelp uses gas-filled bladders to keep fronds near the sunlit surface. Ducks and other waterbirds trap air in their feathers for buoyancy. Even the Earth's crust "floats" on the denser mantle through isostasy — mountains have deep roots, like icebergs have submerged portions.
In technology, buoyancy enables everything from cargo ships carrying millions of tons to delicate density measurements in laboratories. Cartesian divers demonstrate pressure-buoyancy relationships. Lava lamps work through temperature-dependent buoyancy changes. Density gradient columns separate materials by their specific gravity. Understanding buoyancy is essential for designing anything that operates in or on fluids, from submarines to weather balloons to wastewater treatment systems.