Density from measurements

Density is mass per unit volume. It tells us how much mass occupies a given amount of space.

Compare two samples that each occupy 10 cm³. If one has a mass of 27 g and the other 80 g, the second is denser: it has more mass in the same volume. A larger total mass alone does not show greater density when the volumes are different.

Mass is measured in g or kg; volume is measured in cubic units such as cm³ or m³. Review prefixes and volume conversions if needed. Density uses mass, not the weight in newtons.

Density is a scalar quantity: it has no spatial direction. For a uniform material under the same conditions, doubling the volume doubles the mass, leaving the ratio m / V unchanged.

An irregular solid: measure the displaced volume

Use a balance to find the solid's mass. To find the volume of a suitable irregular solid, record the water volume in a measuring cylinder before and after fully submerging the solid. The increase is the solid's volume.

The solid must be fully submerged, insoluble and non-absorbing, with no water lost. Remove trapped air bubbles: they displace extra water, making the calculated volume too large and the calculated density too small. A floating object's submerged portion is not automatically its whole volume, so this simple method is unsuitable unless the whole solid can be measured correctly.

Choose a cylinder that fits the object and final level while still having useful divisions. Keep it upright and read the bottom of the water meniscus at eye level. The measurement methods page explains the reading technique.

Convert both parts of a density unit

Changing g/cm³ to kg/m³ changes both the mass unit and the volume unit.

Therefore 2.7 g/cm³ = 2700 kg/m³. Dividing 2.7 by 1000 would convert the grams but leave the cubic centimetres unchanged. That would give kg/cm³, not kg/m³.

A regular solid: calculate volume from its shape

For a cuboid, measure its mass and its three perpendicular dimensions. Its volume is length x width x height. Use an instrument with a suitable range and resolution for each dimension.

V = 4.0 x 3.0 x 2.0 = 24 cm³, so ρ = 64.8 / 24 = 2.7 g/cm³. Here geometry provides the volume that displacement provided for the irregular sample.

Measure the actual solid, not a surrounding container or gaps around it. Repeat dimension readings at different positions to judge small variations. If the shape is substantially irregular, assuming a cuboid can give a misleading volume; choose a suitable displacement method instead.

A liquid: subtract the container's mass

1. Weigh a clean, dry, empty measuring cylinder, or zero the balance with the empty cylinder on it.
2. Add the liquid and record its volume at eye level using the appropriate meniscus reading. Keep the outside of the cylinder dry.
3. Weigh the cylinder and liquid. Subtract the empty cylinder's mass, unless it was correctly tared.
4. Divide the liquid's mass by the volume of that same liquid.

For example, an empty cylinder has a mass of 42.6 g. With 50 cm³ of liquid inside, its mass is 82.6 g. The liquid's mass is 82.6 - 42.6 = 40.0 g, giving a density of 40.0 / 50 = 0.80 g/cm³.

Keep the mass and volume measurements matched. If liquid spills after the volume is recorded but before weighing, the smaller measured mass divided by the old volume gives too small a density. Liquid on the outside adds mass without adding to the measured inside volume, so it can make the density too large.

Keep observations separate from calculations. Record the balance and cylinder readings with their units, then show the calculated liquid or solid volume and density. This makes a mistaken subtraction or unit conversion easier to find.