Buoyancy Calculator

The Buoyancy Calculator works out the buoyant force on an object and tells you at a glance whether it will float, sink, or hover in a fluid — all based on Archimedes' principle. Enter the fluid, the object's volume and mass, and the tool returns the buoyant force, the object's density, the exact submerged fraction, the apparent (underwater) weight, and how much extra load a floating object could still carry, drawn on an animated float/sink tank diagram.

What is Buoyancy?

Buoyancy is the upward force a fluid exerts on any object placed in it. That upward push comes from pressure increasing with depth: the bottom of a submerged object sits in higher-pressure fluid than its top, and the difference is a net upward force. Whether an object rises or sinks is a tug-of-war between this buoyant force and the object's weight.

Archimedes' Principle

Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces. In symbols:

where \( \rho_{fluid} \) is the fluid density (kg/m³), \( V_{displaced} \) is the volume of fluid pushed aside (m³), and \( g \) is gravitational acceleration (9.81 m/s² on Earth). When an object is fully submerged, the displaced volume is simply the object's own volume.

Will it Float or Sink?

The verdict comes down to a single density comparison, because volume and gravity appear on both sides of the force balance and cancel out:

• Floats — object density is less than the fluid density (\( \rho_{obj} < \rho_{fluid} \)).
• Sinks — object density is greater than the fluid density (\( \rho_{obj} > \rho_{fluid} \)).
• Neutral buoyancy — the densities are equal, so the object hovers at any depth.

This is why about 90% of an iceberg hides below the surface: ice (≈917 kg/m³) is roughly 92% as dense as seawater (≈1025 kg/m³).

Apparent Weight Underwater

A submerged object feels lighter because the buoyant force supports part of its weight. What a scale reads underwater is the apparent weight:

This is the very effect Archimedes reportedly used to test whether a king's crown was pure gold: a gold crown and an equal-mass silver-adulterated crown displace different volumes of water and therefore lose different amounts of apparent weight.

Typical Densities

What Affects Buoyancy?

How to Use This Calculator

1. Choose the fluid: Pick a preset such as fresh water, seawater or oil, or type a custom fluid density in kg/m³.
2. Enter the object: Type the object's volume and mass and choose the units for each (cm³, litres, kg, lb, and more).
3. Set gravity (optional): Keep Earth's 9.81 m/s² or switch to the Moon, Mars, Jupiter or Venus.
4. Click Calculate: Read the float or sink verdict, the buoyant force, the submerged fraction, the reserve buoyancy, and follow the step-by-step working on the animated tank diagram.

Frequently Asked Questions

What is buoyant force?

Buoyant force is the upward push a fluid exerts on any object placed in it. By Archimedes' principle it equals the weight of the fluid the object displaces, calculated as buoyant force = fluid density × displaced volume × gravitational acceleration.

How do I know if an object will float or sink?

Compare densities. If the object is less dense than the fluid it floats, if it is denser it sinks, and if the densities are equal it has neutral buoyancy and hovers at any depth. The volume and gravity cancel out, so only density decides the verdict.

How is the buoyant force calculated?

Buoyant force F_b = ρ × V × g, where ρ is the fluid density in kg/m³, V is the submerged volume in m³, and g is gravity in m/s². When an object is fully submerged, V is its whole volume; when it floats, it displaces only enough fluid to equal its own weight.

What fraction of a floating object is underwater?

The submerged fraction equals the object's density divided by the fluid's density. Ice has a density of about 917 kg/m³ and water about 1000 kg/m³, so roughly 92 percent of an iceberg sits below the surface and only 8 percent shows above.

What is apparent weight underwater?

Apparent weight is what a scale reads when the object is submerged. It equals the object's true weight minus the buoyant force. This is why heavy objects feel lighter underwater, and it is the effect Archimedes used to test the king's gold crown.

Does gravity change whether something floats?

No. Both weight and buoyant force scale with gravity, so the float or sink verdict is identical on the Moon, Mars or Earth. Only the size of the forces changes, which is why this calculator lets you switch gravity to see the forces on other worlds.

Additional Resources

• Buoyancy - Wikipedia
• Archimedes' Principle - Wikipedia