How to Calculate Density

Worked Example Problem

Density column showing colored liquids with different densities.
Density column showing colored liquids with different densities. Anne Helmenstine

Density is the measurement of the amount of mass per unit of volume. In order to calculate density, you need to know the mass and volume of the item. The mass is usually the easy part while volume can be tricky. Simple shaped objects are usually given in homework problems such as as a cube, brick or sphere. The formula for density is:

density = mass/volume

This example problem shows the steps needed to calculate the density of an object and a liquid when given the mass and volume.

Question 1: What is the density of a cube of sugar weighing 11.2 grams measuring 2 cm on a side?

Step 1: Find the mass and volume of the sugar cube.

Mass = 11.2 grams
Volume = cube with 2 cm sides.

Volume of a cube = (length of side)3
Volume = (2 cm)3
Volume = 8 cm3

Step 2: Plug your variables into the density formula.

density = mass/volume
density = 11.2 grams/8 cm3
density = 1.4 grams/cm3

Answer 1: The sugar cube has a density of 1.4 grams/cm3.

Question 2: A solution of water and salt contains 25 grams of salt in 250 mL of water. What is the density of the salt water? (Use density of water = 1 g/mL)

Step 1: Find the mass and volume of the salt water.

This time, there are two masses. The mass of the salt and the mass of the water are both needed to find the mass of the salt water. The mass of the salt is given, but the only the volume of water is given. We've also been given the density of water, so we can calculate the mass of the water.

densitywater = masswater/volumewater

solve for masswater,

masswater = densitywater·volumewater
masswater = 1 g/mL · 250 mL
masswater = 250 grams

Now we have enough to find the mass of the salt water.

masstotal = masssalt + masswater
masstotal = 25 g + 250 g
masstotal = 275 g

Volume of the salt water is 250 mL.

Step 2: Plug your values into the density formula.

density = mass/volume
density = 275 g/250 mL
density = 1.1 g/mL

Answer 2: The salt water has a density of 1.1 grams/mL.

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