How to calculate density with the correct units

Use density = mass ÷ volume, often written ρ = m/V. Mass might be measured in grams or kilograms. Volume might be measured in cubic centimetres or cubic metres. The units of density follow directly from the division: g/cm³ or kg/m³, for example.

A solid has a mass of 156 g and a volume of 20 cm³. Its density is 156 ÷ 20 = 7.8 g/cm³. That means each cubic centimetre has a mass of 7.8 g if the material is uniform. Write the unit beside the answer rather than leaving a bare number.

For a rectangular block, volume = length × width × height. If its dimensions are 5 cm, 2 cm and 3 cm, the volume is 30 cm³. With a mass of 81 g, its density is 81 ÷ 30 = 2.7 g/cm³.

All three dimensions must use the same length unit before you multiply. A block measuring 50 mm by 2 cm by 3 cm has the same dimensions as the example: convert 50 mm to 5 cm first. Multiplying the unconverted numbers and labelling the result cm³ would overstate the volume tenfold.

For a suitable solid that sinks and does not dissolve or react with the liquid, displacement can provide its volume. Suppose the water reading is 40 mL before immersion and 55 mL with the solid fully submerged. The displaced volume is 55 − 40 = 15 mL, equal to 15 cm³.

If the mass is 120 g, density = 120 ÷ 15 = 8 g/cm³. Do not divide by 55 mL: that reading includes the water already in the cylinder.

Read the cylinder at eye level and use the appropriate meniscus reading for the liquid, ordinarily the bottom for water in a glass cylinder. Trapped air bubbles, incomplete submersion or liquid splashed out can change the measured displacement. A floating or absorbent object needs a method that accounts for those complications.

Because 1 m = 100 cm, a cube measuring 1 m on each side contains 100 × 100 × 100 = 1,000,000 cm³. Therefore 1 cm³ = 0.000001 m³. A volume conversion cannot use the length factor of 100 alone.

To convert 2.7 g/cm³ to kg/m³, convert both parts: 2.7 g = 0.0027 kg and 1 cm³ = 0.000001 m³. The quotient is 0.0027 ÷ 0.000001 = 2700 kg/m³. In general, multiply a value in g/cm³ by 1000 to express it in kg/m³.

For a separate example, a mass of 0.54 kg occupies 200 cm³. Convert the mass to 540 g, giving density = 540 ÷ 200 = 2.7 g/cm³. Alternatively, convert the volume to 0.0002 m³ and calculate 0.54 ÷ 0.0002 = 2700 kg/m³. Both describe the same density.

Rearrange the relationship as mass = density × volume. For the first example, 7.8 g/cm³ × 20 cm³ = 156 g, matching the supplied mass. The volume units cancel, leaving grams.

At a fixed mass, a larger volume means a lower density. At a fixed volume, a larger mass means a higher density. These comparisons can catch an inverted fraction: volume divided by mass has units cm³/g and is not density.

Keep intermediate values unrounded and apply the precision requested in the question to the final answer. For a hollow object, clarify whether the stated volume includes the empty interior. Mass divided by the whole external volume gives its average density, not necessarily the density of the wall material.

Copy this record: mass and unit; volume measurement or calculation; conversions; density = mass ÷ volume; result and unit; mass recovered by multiplying back. For displacement, record both cylinder readings and their difference.

Try a solid with mass 96 g that raises water from 28 mL to 40 mL. Its volume is 12 cm³ and its density is 96 ÷ 12 = 8 g/cm³. The check is 8 × 12 = 96 g. The key step is using the increase in water level as the volume.