Recall and apply: density (kg/m³) = mass (kg) / volume (m³)

Density tells you how much mass is packed into each cubic metre of a material. That single idea links two quantities you already measure: mass, in kilograms, and volume, in cubic metres. In this lesson we use the density equation, rearrange it, and convert units before we calculate. The equation is density equals mass divided by volume. In symbols, rho equals m over V. Density is measured in kilograms per cubic metre, mass in kilograms, and volume in cubic metres. Keep those units matched, because the unit of the answer follows from them. To apply the equation, identify the mass and the volume from the question. Convert them to kilograms and cubic metres. Then divide the mass by the volume. Converting first keeps the answer in kilograms per cubic metre, which is the unit the question usually wants. Here is a block with a mass of two point four kilograms and a volume of zero point zero zero three cubic metres. Both are already in the right units. Pause here and try the division yourself before I show it. Dividing two point four by zero point zero zero three gives eight hundred. So the density is eight hundred kilograms per cubic metre. The same equation rearranges to find either quantity. To find mass, multiply: mass equals density times volume. To find volume, divide: volume equals mass divided by density. Write the rearranged equation first, then substitute the numbers with their units. Three mistakes are easy to make. Multiplying mass by volume instead of dividing gives the wrong answer. Using grams or cubic centimetres without converting leaves the wrong unit. And assuming a bigger sample must be denser is wrong: two samples of the same material have equal density, even when their volumes differ. Density is a property of the material, not the size of the sample. Density equals mass divided by volume, in kilograms per cubic metre. Convert mass and volume first, then divide. Rearrange to mass equals density times volume, or volume equals mass divided by density. And remember: a larger volume of the same material has more mass but the same density.