Relative density

Densities come with clunky units — g/cm³, kg/m³ — that make it hard to instantly feel how "heavy" one substance is compared to another. Relative density solves this by comparing a substance's density to the density of water and leaving the units out entirely. It is one of the simplest ideas in the CBSE Class 8 chapter "The Amazing World of Solutes, Solvents, and Solutions," yet it quietly does a lot of work: it tells you at a glance whether something will float or sink in water, and it lets you compare metals, liquids and gases on one common, unitless scale. This article builds the idea from density itself, works through the chapter's own numbers step by step, and flags the traps students fall into when relative density questions appear in exams.

The core insight

Relative density is the density of a substance divided by the density of water at the same temperature, so it has no units and directly signals whether the substance floats (less than 1) or sinks (greater than 1) in water.

The core idea

Density measures how tightly packed the matter in a substance is — mass squeezed into a given volume. Relative density asks a different, comparative question: how many times denser is this substance than water?

Relative density=Density of the substanceDensity of water at that temperature\text{Relative density} = \frac{\text{Density of the substance}}{\text{Density of water at that temperature}}

where: the density of the substance and the density of water must both be expressed in the same units (for example, both in g/cm³) before dividing, and the comparison is made at the same temperature because water's own density shifts slightly as it warms or cools. Because the numerator and denominator carry identical units, those units cancel completely in the division. Relative density is a pure number, with no units at all. This single fact is the most commonly examined property of relative density, and it is the first thing to write down whenever a question asks you to define it. The value of that pure number tells a simple story. A relative density greater than 1 means the substance packs more mass into the same volume than water does — it is denser than water. A relative density less than 1 means the opposite — the substance is less dense than water and, all else being equal, tends to float on it. A relative density of exactly 1 means the substance matches water's density exactly. The chapter's anchor example makes this concrete: a piece of aluminium with mass 27 g and volume 10 cm³ has a density of 27 g÷10 cm3=2.7 g/cm327\ \text{g} \div 10\ \text{cm}^3 = 2.7\ \text{g/cm}^3. Dividing by water's density of 1 g/cm31\ \text{g/cm}^3 gives a relative density of 2.72.7 — aluminium is 2.7 times as dense as water, with no unit attached to that number.

Figure
A bar chart comparing the relative density of aluminium at 2.7, water at 1 as the reference line, and a light liquid at 0.8, showing which values sit above or below the water line
Relative density — a unitless comparison to water relative density water = 1 0.8 light liquid 1.0 water 2.7 aluminium

Relative density is useful precisely because it strips away the unit confusion: whether a density was originally quoted in kg/m³, g/cm³ or g/mL, converting both substance and water to the same unit before dividing always gives the same relative density. Saying "aluminium has a relative density of 2.7" is often more memorable to a student than quoting "2700 kg/m³," even though both describe the same physical fact — and because water is such a familiar reference, a relative density of 9 for a metal instantly tells you it would feel about nine times as heavy as an equal volume of water.

Derivation AFinding relative density from mass and volume

The goal is to show, in a fully general way that covers every relative-density question you will meet in this chapter, how to go from raw measurements of mass and volume all the way to a final unitless relative density, by first finding density and then dividing by water's density — the exact two-stage process the syllabus expects, written out so the units are tracked and shown to cancel at the very last step.

Step 1. Find the density of the substance from its measured mass and volume, using Density=MassVolume\text{Density} = \dfrac{\text{Mass}}{\text{Volume}}. This is an ordinary density calculation and gives an answer in units such as g/cm³ — nothing about relative density has entered yet.

Step 2. Write down the density of water at the same temperature, almost always taken as 1 g/cm31\ \text{g/cm}^3 in this chapter's problems, in the same units used for the substance in Step 1.

Step 3. Divide the substance's density by water's density: Relative density=Density of the substanceDensity of water\text{Relative density} = \dfrac{\text{Density of the substance}}{\text{Density of water}}. Because both quantities carry the same unit (g/cm³ over g/cm³), that unit cancels exactly, leaving a bare number.

Step 4. Read the result. If the number is above 1, the substance is denser than water; if it is below 1, the substance is less dense than water and tends to float; if it equals 1, the two match exactly. This final unitless number is the relative density, and it never needs a unit written next to it.

Worked example

Question: A sample of a metal has a mass of 45 g and a volume of 5 cm³. Taking the density of water as 1 g/cm31\ \text{g/cm}^3, find the relative density of the metal, and then use that result to find the density of a second liquid whose relative density is 0.80.8, stating whether it floats or sinks.

Step 1. Find the metal's density: Density=MassVolume=45 g5 cm3=9 g/cm3\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} = \dfrac{45\ \text{g}}{5\ \text{cm}^3} = 9\ \text{g/cm}^3.

Step 2. Apply the relative density formula: Relative density=9 g/cm31 g/cm3=9\text{Relative density} = \dfrac{9\ \text{g/cm}^3}{1\ \text{g/cm}^3} = 9. The metal is 9 times as dense as water, a value close to that of copper — this part of the answer is 9, with no units.

Step 3. Now reverse the formula for the liquid: Density of the substance=Relative density×Density of water=0.8×1 g/cm3=0.8 g/cm3\text{Density of the substance} = \text{Relative density} \times \text{Density of water} = 0.8 \times 1\ \text{g/cm}^3 = 0.8\ \text{g/cm}^3.

Step 4. Since 0.8 g/cm30.8\ \text{g/cm}^3 is less than water's 1 g/cm31\ \text{g/cm}^3, the liquid is less dense than water and would float on it, the same way oil floats on water. Final answers: the metal has relative density 9 (denser, would sink); the liquid has density 0.8 g/cm30.8\ \text{g/cm}^3 and floats.

Common traps

  • Writing units (like g/cm³) next to a relative density value — relative density is a pure ratio and must be written without units.
  • Confusing relative density with density itself — density needs units and a fixed volume, while relative density is always a comparison to water and is unitless.
  • Forgetting that relative density compares against water's density at the same temperature, since water's density itself changes slightly with temperature.
  • Assuming a relative density above 1 always means an object sinks in every situation — shape also affects floating and sinking, so density is a strong indicator, not the whole story.

Ask the tutor: Want to try a few more mass-and-volume relative density problems, or see how this idea connects to floating and sinking?

Why do we bother with relative density when we already have density?

Density already tells you everything physically, but its units vary — kg/m³, g/cm³, g/mL — which makes quick comparisons awkward. Relative density strips those units away by comparing to one fixed, familiar reference: water. Saying "9 times as dense as water" is often easier to picture and remember than "9000 kg/m³," even though the two statements describe exactly the same substance.

Does relative density ever have units if I use a different reference than water?

In this chapter, relative density is always defined against water, so it is always unitless as long as you convert both densities to the same unit before dividing. If a different reference liquid were ever used instead of water, the same cancellation would still happen, because relative density is always a ratio of two quantities measured in identical units — the units always cancel, regardless of what the reference substance is.

If relative density is greater than 1, does the substance always sink?

Usually yes for a solid lump of that material dropped into water, but "always" is too strong. A relative density above 1 means the material itself is denser than water, but whether an actual object sinks can also depend on its shape — a steel bowl floats even though steel's relative density is about 7.8, because its shape displaces enough water to support its weight. Relative density describes the material, not every possible shape made from it.

Before this

Where this leads