Why do objects float or sink?

An object floats when its average density is less than the fluid density (ρ_obj ρ_fluid. It achieves neutral buoyancy when ρ_obj = ρ_fluid. A steel ball sinks in water (ρ_steel ≈ 7850 kg/m³ > 1000) but a hollow steel ship floats because its average density including the air interior is less than water.

Why does an iceberg float with only about 10% above water?

Ice has a density of about 917 kg/m³ compared to seawater at 1025 kg/m³. The submerged fraction equals ρ_ice/ρ_seawater = 917/1025 ≈ 0.895 = 89.5%. So 89.5% is below the surface and only about 10.5% is visible above. This is the origin of the phrase 'tip of the iceberg'.

Does buoyancy work in air?

Yes. Air has density ≈ 1.225 kg/m³ at sea level, so objects experience a small buoyant force in air. A 1 m³ helium balloon (ρ_He ≈ 0.164 kg/m³) displaces air weighing 1.225 × 9.81 ≈ 12.02 N while the helium weighs only 0.164 × 9.81 ≈ 1.61 N, giving a net upward force of about 10.4 N.

What is apparent weight underwater?

Apparent weight is the weight an object seems to have when submerged in a fluid. It equals the true weight minus the buoyant force: W_apparent = mg − F_b = (ρ_obj − ρ_fluid) × V × g. A gold brick (ρ = 19300 kg/m³) in water appears to weigh about 94.8% of its true weight because water buoys it up slightly.

Does buoyancy depend on the shape of the object?

No. Buoyant force depends only on the volume of fluid displaced, not the shape of the object. A cubic metre of any material displaces the same volume of water and experiences the same buoyant force regardless of its shape — as long as the total displaced volume is the same.

Buoyancy Calculator – Archimedes' Principle & Buoyant Force

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Fluid Density ρ_f

Volume V

Gravity g

Buoyant Force F_b

Object Mass m (kg)

Object Volume V (m³)

Fluid Density ρ_f

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What Is Buoyancy?

Buoyancy is the upward force exerted by a fluid on any object submerged in it — whether partially or fully. It arises because fluid pressure increases with depth; the pressure on the bottom of a submerged object is greater than on the top, creating a net upward force.

F_b = ρVg

Buoyant force

ρ_obj < ρ_f → Floats

Float condition

f = ρ_obj / ρ_f

Submerged fraction

Archimedes' Principle Explained

Archimedes' Principle (c. 250 BC): "Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced."

F_b = ρ_fluid × V_displaced × g

where ρ_fluid = fluid density (kg/m³), V = displaced volume (m³), g = gravitational acceleration (m/s²)

Note: if the object is only partially submerged (floating), V_displaced is the volume of the submerged portion, not the total object volume.

Float vs Sink: The Density Rule

Whether an object floats depends entirely on the comparison of average densities:

Condition	Result	Example
ρ_obj < ρ_fluid	Floats	Wood in water
ρ_obj = ρ_fluid	Neutral	Submarine at depth
ρ_obj > ρ_fluid	Sinks	Steel in water

Submerged Volume Fraction

For a floating object, the fraction of its volume below the surface equals the ratio of densities:

f_submerged = ρ_object / ρ_fluid

Ice (917 kg/m³) in seawater (1025 kg/m³): f = 917/1025 = 89.5% submerged — the famous iceberg.

Buoyancy in Air (Balloons)

Air is a fluid too. A helium balloon floats because helium (ρ ≈ 0.164 kg/m³) is much less dense than air (ρ ≈ 1.225 kg/m³). The balloon displaces air heavier than itself, producing a net upward force.

F_b = 1.225 kg/m³ × 1 m³ × 9.81 = 12.02 N (air buoyancy)

W_He = 0.164 kg/m³ × 1 m³ × 9.81 = 1.61 N (helium weight)

Net lift = 12.02 − 1.61 = 10.41 N per m³

Engineering Applications (Ships, Submarines, Hot-Air Balloons)

Ships

A steel ship floats because its hollow hull displaces a large water volume. The ship's average density (steel + air) is less than water. Designers calculate displacement tonnage to ensure adequate buoyancy.

Submarines

Submarines control buoyancy using ballast tanks. Filling tanks with water increases average density (sinks); blowing water out with compressed air decreases density (rises). They achieve neutral buoyancy to hover at depth.

Hot-Air Balloons

Heating air inside the balloon reduces its density below ambient air. The buoyant force on the now-lighter-than-air balloon lifts it skyward. Altitude is controlled by adjusting burner temperature.

Worked Examples

Example 1 — Iceberg

ρ_ice = 917, ρ_sea = 1025

f = 917 / 1025 = 0.8946

89.5% submerged — FLOATS

Example 2 — Helium Balloon 1 m³

ρ_air=1.225, V=1, g=9.81

F_b = 1.225 × 1 × 9.81

F_b = 12.02 N upward

Example 3 — Steel Block in Water

m=7850 kg, V=1 m³, ρ_f=1000

ρ_obj = 7850 / 1 = 7850 kg/m³

7850 > 1000 — SINKS

Example 4 — Human in Pool

m=70 kg, V=0.068 m³

ρ_obj = 70/0.068 = 1029 kg/m³

~1029 vs 1000 — just sinks (nearly neutral)

Frequently Asked Questions

Buoyancy is the upward force exerted by a fluid on an object submerged in it. It arises because fluid pressure increases with depth, creating a net upward force on the submerged object. This force equals the weight of fluid displaced by the object.

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 it displaces: F_b = ρ_fluid × V_displaced × g. This principle was discovered by Archimedes of Syracuse around 250 BC.

An object floats when its average density is less than the fluid density (ρ_obj < ρ_fluid), meaning the buoyant force exceeds its weight. It sinks when ρ_obj > ρ_fluid. A steel ball sinks in water but a hollow steel ship floats because its average density including the air interior is less than water.

Ice has a density of about 917 kg/m³ compared to seawater at 1025 kg/m³. The submerged fraction equals ρ_ice/ρ_seawater = 917/1025 ≈ 89.5%. So 89.5% is below the surface and only about 10.5% is visible above — the origin of "tip of the iceberg."

Yes. Air has density ≈ 1.225 kg/m³ at sea level, so objects experience a small buoyant force in air. A 1 m³ helium balloon displaces air weighing ≈ 12.02 N while the helium weighs only ≈ 1.61 N, giving a net upward force of about 10.4 N.

Saltwater is denser than freshwater (1025 kg/m³ vs 1000 kg/m³), so it exerts a greater buoyant force. Objects that barely float in freshwater float more easily in saltwater. The Dead Sea (density ≈ 1240 kg/m³) is famous for allowing people to float effortlessly.

Apparent weight is the weight an object seems to have when submerged: W_apparent = mg − F_b = (ρ_obj − ρ_fluid) × V × g. A gold brick (ρ = 19300 kg/m³) in water appears to weigh about 94.8% of its true weight.

No. Buoyant force depends only on the volume of fluid displaced, not the shape. A cubic metre of steel and a sphere of steel with the same volume displace the same water and experience the same buoyant force.

Buoyancy Calculator (Archimedes' Principle)

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