How to Calculate Density of a Metal: Mass, Volume, and Worked Examples

Calculate a metal sample’s density by dividing its mass by its volume:

Density = mass ÷ volume, or ρ = m / V

Measure the mass with a balance. Find the volume from the sample’s dimensions or by water displacement, then divide. Keep units consistent: grams and cubic centimeters give density in g/cm³; kilograms and cubic meters give kg/m³. One milliliter equals one cubic centimeter, so you can use a volume measured in mL directly with mass in grams.

Measure the mass

Use a clean, dry sample and a balance. Zero the balance before weighing. Tare any container that holds the sample. Exclude wire, tape, or other hardware unless you include its volume too.

Record the reading to the precision the balance supports. A precise mass reading cannot compensate for an imprecise volume measurement.

Find the volume

Choose a method suited to the sample’s shape.

For a regular shape

Measure the dimensions with a ruler or calipers, then use the matching formula.

For a rectangular block:

V = length × width × height

For a cylinder:

V = π × (diameter ÷ 2)² × height

Use the same length unit for every dimension. For example, dimensions measured in centimeters give a volume in cubic centimeters.

For an irregular shape

Use water displacement if the sample can be safely submerged and does not absorb water.

1. Add enough water to a graduated cylinder to cover the sample, then record the initial volume.
2. Lower the sample gently into the water. Check for air bubbles attached to it.
3. Record the final volume.
4. Subtract the initial volume from the final volume.

Sample volume = final water volume − initial water volume

The result is in milliliters, which are equivalent to cubic centimeters. Read the cylinder at eye level and use the same point on the meniscus for both readings.

Water displacement measures the volume of water displaced by the sample. Bubbles clinging to the sample or water entering its pores can give a misleading result. For a hollow object, the result may describe the object’s overall average density, not the density of the metal alone.

Calculate the density

Divide the measured mass by the measured volume. Keep units consistent throughout the calculation.

For example, mass in grams divided by volume in cubic centimeters gives density in g/cm³. To convert a result in g/cm³ to kg/m³, multiply by 1,000.

Worked example

A rectangular metal bar has a mass of 243.6 g. Its measured dimensions are 5.00 cm long, 2.00 cm wide, and 1.80 cm high.

First, calculate its volume:

V = 5.00 × 2.00 × 1.80 = 18.0 cm³

Then divide the mass by the volume:

ρ = 243.6 g ÷ 18.0 cm³ = 13.5 g/cm³

In SI units, that is:

13.5 × 1,000 = 13,500 kg/m³

This calculation gives the density of the sample as measured. If the bar is hollow, coated, or made from an alloy, the result applies to the whole sample and may differ from a reference value for a pure metal.

Interpreting the result

Density can help compare a sample with reference values, but it cannot identify a metal on its own. Alloys, coatings, porosity, measurement error, and temperature can affect the result. Reference values are most useful when the sample’s composition and measurement conditions are known.

Density is an intensive property: for a uniform material, cutting a sample into smaller pieces does not change its density. Temperature can change a material’s volume, so reference values may specify a temperature. For general classroom measurements, recording the conditions is often enough. For precision work, follow the requirements of the task.

Key Takeaways

• Use ρ = m / V: divide the sample’s mass by its volume.
• Find volume from measured dimensions for regular shapes or by water displacement for suitable irregular shapes.
• Keep units consistent. 1 mL = 1 cm³, and 1 g/cm³ = 1,000 kg/m³.
• In the example, 243.6 g ÷ 18.0 cm³ = 13.5 g/cm³, or 13,500 kg/m³.
• Report whether the result describes a solid metal, an alloy, or the sample as a whole.