Why does a steel ship float?

A ship floats because its hull encloses a large volume of air, making the average density of the entire ship less than water. The hull displaces enough water to create a buoyant force equal to the ship's total weight.

What is neutral buoyancy?

Neutral buoyancy occurs when an object's weight exactly equals the buoyant force, so it neither rises nor sinks. Scuba divers adjust air in their buoyancy compensator to achieve this state.

Does buoyancy work in air?

Yes. Hot air balloons and helium balloons float because they displace air that weighs more than they do. However, since air is about 800 times less dense than water, the volumes involved are much larger.

How does salt water affect buoyancy?

Salt water is denser than fresh water (1025 vs 1000 kg/m^3), so objects experience about 2.5% more buoyant force in the ocean. This is why you float more easily in the Dead Sea, where salinity makes the water about 1240 kg/m^3.

Buoyancy Calculator

Calculate buoyant force (Archimedes' principle)

Buoyancy

Fb = rho x V x g

Fluid Density (kg/m³)

Displaced Volume (m³)

Formula

Fb = rho x V x g

What Is Buoyancy?

Buoyancy is the upward force exerted by a fluid on an object submerged in it. This force opposes gravity and is responsible for objects floating or sinking. Archimedes' Principle states that the buoyant force equals the weight of the fluid displaced by the object.

Buoyancy is fundamental to naval architecture, submarine design, scuba diving, and balloon aeronautics. Engineers calculate buoyant force to design ships, predict how loads affect vessel draft, ensure structural components don't float away during underwater construction, and size life vests.

How to Use the Buoyancy Calculator

Enter the volume of the submerged object in cubic meters (m³).
Enter the density of the fluid (e.g., 1000 kg/m³ for fresh water, 1025 for seawater).
Click Calculate to get the buoyant force in Newtons.
Compare with the object's weight to determine if it floats or sinks.

Formula & Explanation

F_b = ρ_f × V × g

F_b  = buoyant force (N)
ρ_f  = fluid density (kg/m³)
V    = submerged volume (m³)
g    = gravitational acceleration (9.81 m/s²)

An object floats when F_b ≥ its weight (mg). It sinks when weight > F_b. Neutral buoyancy occurs when F_b = mg exactly.

Worked Examples

Steel Ball in Water

A solid steel ball with volume 0.001 m³ is submerged in fresh water (ρ = 1000 kg/m³). F_b = 1000 × 0.001 × 9.81 = 9.81 N. Steel weighs ~78 N for this volume, so it sinks since weight (78 N) > F_b (9.81 N).

Wooden Block Floating

A wooden block (ρ_wood = 600 kg/m³, volume = 0.01 m³) floats in water. Its weight = 600 × 0.01 × 9.81 = 58.86 N. It displaces just enough water to equal this: V_submerged = 58.86 / (1000 × 9.81) = 0.006 m³, so 60% is submerged.

Submarine Ballast

A submarine with volume 500 m³ needs neutral buoyancy in seawater (ρ = 1025 kg/m³). Required F_b = 1025 × 500 × 9.81 = 5,028,375 N ≈ 512.6 tonnes of buoyant force. Ballast tanks are flooded to match this to the sub's weight.

Frequently Asked Questions

What is Archimedes' Principle?▾

Archimedes' Principle states that the buoyant force on an object equals the weight of the fluid it displaces. Legend has it Archimedes discovered this while observing water overflow when he stepped into a bath, leading to his famous 'Eureka!' moment.

Why does a ship made of steel float?▾

A steel ship floats because its hull encloses a large air volume. The average density of the ship (steel + air) is less than water. The ship displaces enough water weight to equal its total weight before becoming fully submerged.

What is specific gravity?▾

Specific gravity is the ratio of a substance's density to a reference substance (usually water at 4°C = 1000 kg/m³). Objects with specific gravity < 1 float in water; those > 1 sink. Ice has SG ≈ 0.917 — it floats with 91.7% submerged.

How do submarines control depth?▾

Submarines use ballast tanks that can be flooded with seawater or blown empty with compressed air. Flooding increases weight until it exceeds buoyancy (dive); blowing expels water to reduce weight until buoyancy lifts the sub (surface).

Does buoyancy change with depth?▾

For incompressible objects, buoyant force stays constant with depth — it depends only on displaced volume, not depth. However, compressible objects (like gas-filled chambers) decrease in volume under pressure, reducing F_b and causing them to sink further.