Density: divide mass by volume and keep the units
Two original worked examples explain density, equal-volume comparisons and unit conversion.
Density is mass divided by volume; equal masses can occupy different volumes when their densities differ.
The relationship and its units
OpenStax defines density as mass per unit volume. Write density = mass / volume, then attach the units used in the question. Kilograms per cubic metre and grams per cubic centimetre are both density units, but their numerical values are not interchangeable.
A statement that one sample has greater mass does not establish that it has greater density. Its volume must also be known.
Original worked example: compare two samples
Sample A has a mass of 180 g and volume of 60 cubic centimetres. Its density is 180 / 60 = 3 g per cubic centimetre. Sample B has a mass of 240 g and volume of 120 cubic centimetres, giving 2 g per cubic centimetre.
B has greater mass but lower density. These invented samples show why comparing mass alone answers the wrong question. No substance identification is claimed from these teaching numbers.
Original worked example: change units
One gram is 0.001 kg, while one cubic centimetre is 0.000001 cubic metres. Therefore 1 g per cubic centimetre equals 1,000 kg per cubic metre. A sample at 3 g per cubic centimetre is consequently at 3,000 kg per cubic metre.
The cubic conversion is important: converting a centimetre to a metre and forgetting to cube the length factor creates a large error. Write the volume conversion separately before dividing.
Reverse the calculation as a check
If a uniform sample has a density of 2 g per cubic centimetre and a volume of 15 cubic centimetres, its mass is 2 × 15 = 30 g. Substituting back gives 30 / 15 = 2, confirming the calculation.
In a short answer, give the formula, substitution, result and unit. If the unit ends in volume per mass, the ratio has been inverted. The examples here explain average mass density and do not require assumptions about a sample’s chemical identity.
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Frequently asked questions
Does a larger mass always mean a greater density?
No. Density depends on both mass and volume.
What is 1 g per cubic centimetre in SI density units?
1,000 kg per cubic metre.