Buoyancy Calculator

Frequently Asked Questions

What is Archimedes' principle?

The buoyant force on a submerged or floating object equals the weight of the fluid it displaces: F_b = ρ_fluid × V_displaced × g.

When does an object float?

When the buoyant force from the fluid it can displace equals its weight. Equivalently: when its average density is less than the fluid's density.

Why do steel ships float?

A solid block of steel sinks because steel is denser than water. A steel hull encloses a large air volume, lowering the ship's average density below water's.

How do submarines control depth?

They pump water in or out of ballast tanks to change average density. Heavier than water → sink; lighter → rise; equal → neutrally buoyant.

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How This Calculator Works

This calculator applies Archimedes' principle: the buoyant force on an object equals the weight of the fluid it displaces. Enter the submerged volume in cm³ and select a fluid such as fresh water (1,000 kg/m³), sea water (1,025 kg/m³), or mercury (13,534 kg/m³). If you also supply the object's density, the tool reports whether it floats and what fraction sits below the surface. Internally the cm³ input is divided by 1,000,000 to convert to m³ before applying the force formula.

Formula

The buoyant force is Fₛ = ρ × V × g, where ρ is fluid density in kg/m³, V is displaced volume in m³, and g = 9.81 m/s². An object floats when its density is less than the fluid density, and the submerged fraction equals object density ÷ fluid density. Equal densities give neutral buoyancy - the object neither rises nor sinks.

Worked Example

Submerge a 1,000 cm³ block in fresh water. Convert: 1,000 ÷ 1,000,000 = 0.001 m³. Buoyant force = 1,000 × 0.001 × 9.81 = 9.81 N, and the displaced mass is 1,000 × 0.001 = 1 kg (1,000 g). If the block is ice (917 kg/m³), it floats with 917 ÷ 1,000 = 91.7% submerged - matching why icebergs hide most of their bulk underwater.

Common Mistakes

Entering volume in m³ when the field expects cm³ - that overstates force a millionfold.

Using the object's total volume instead of the submerged volume for a partially floating object.

Forgetting that denser fluids (sea water, mercury) give more buoyant force for the same volume.

Assuming heavy materials always sink - lead (11,340 kg/m³) floats on mercury (13,534 kg/m³).

Tips & FAQ

Why do steel ships float? Steel is ≈ 7,850 kg/m³, but a hull full of air has a low average density, so it displaces enough water to stay up.

Why is floating easy in the Dead Sea? Its ≈ 1,240 kg/m³ density (about 34% salt) far exceeds the human body's, so people bob effortlessly.

How do balloons rise? Helium or heated air is less dense than the ≈ 1.225 kg/m³ surrounding air, so net buoyancy lifts them.

Buoyancy Calculator

Frequently Asked Questions

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