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How can weighing an object in air and water help determine its density?

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Portrait of Archimedes by Giuseppe Nogari shows an elderly man with white hair and beard, holding a compass, gazing downward, set against a dark background. — Archimedes Archimedes, oil on canvas by Giuseppe Nogari, 18th century; in the Pushkin Fine Arts Museum, Moscow. Archimedes was an ancient Greek mathematician and inventor.

Weighing an object in air and water is a practical application of Archimedes’ principle, which states that a submerged object experiences an upward buoyant force equal to the weight of the fluid it displaces.1

To determine the specific gravity of an object denser than water, you can follow these steps:

Weigh the object in air: This provides the object's actual weight.1
Weigh the object submerged in water: When submerged, the object will weigh less due to the upward buoyant force.1
Calculate the weight loss: Subtract the submerged weight from the weight in air. This difference represents the weight of the displaced water.1
Determine specific gravity: Divide the object's weight in air by the weight lost when submerged.1

Because density is defined as mass per unit volume, this method effectively uses the displaced water to calculate the object's volume, allowing for the determination of its density relative to water.12