Density and Relative Density in Physics- Definitions and Formulas

What Is Density in Physics?

Density is how much mass is packed into a given volume. It's a fundamental property of matter that tells you how "heavy" a substance is relative to its size.

The formula is simple:

ρ = m / V

Where ρ is density, m is mass, and V is volume.

That's it. No complicated derivations. Mass divided by volume gives you density.

Units of Density

The standard unit is kg/m³ (kilograms per cubic meter). In everyday contexts, you might see g/cm³ (grams per cubic centimeter) or g/mL (grams per milliliter).

Quick conversion: 1 g/cm³ = 1000 kg/m³

Water has a density of approximately 1000 kg/m³ or 1 g/cm³ at 4°C. This is why water is often used as a reference point.

What Is Relative Density (Specific Gravity)?

Relative density compares a substance's density to the density of water. It's a dimensionless number — no units attached.

The formula:

Relative Density = Density of substance / Density of water

Since water's density is 1 g/cm³ at 4°C, the relative density of a substance is numerically equal to its density in g/cm³.

For example, if a liquid has a relative density of 0.8, it means that liquid weighs 0.8 times as much as an equal volume of water.

Density vs. Relative Density: Key Differences

Relative density tells you how many times heavier or lighter something is compared to water. Density tells you the actual mass contained in a specific volume.

Common Densities of Familiar Substances

Materials with relative density less than 1 float on water. Those above 1 sink. Simple as that.

How to Calculate Density: Worked Examples

Example 1: Finding Density

A block of metal has a mass of 500 grams and a volume of 65 cm³. Find its density.

Solution:

ρ = m / V
ρ = 500 g / 65 cm³
ρ = 7.69 g/cm³

Converting to kg/m³: 7.69 g/cm³ × 1000 = 7690 kg/m³

Example 2: Finding Relative Density

An unknown liquid has a density of 800 kg/m³. Find its relative density.

Solution:

Relative Density = 800 kg/m³ / 1000 kg/m³
Relative Density = 0.8

This liquid will float on water.

Example 3: Finding Mass from Density

Find the mass of 2 m³ of concrete (density = 2400 kg/m³).

Solution:

m = ρ × V
m = 2400 kg/m³ × 2 m³
m = 4800 kg

Example 4: Finding Volume from Density

A gold ring has a mass of 15 g and gold has a density of 19.32 g/cm³. Find the ring's volume.

Solution:

V = m / ρ
V = 15 g / 19.32 g/cm³
V = 0.78 cm³

How to Measure Density in Practice

• For regular solids: Measure mass with a scale. Calculate volume from dimensions (length × width × height). Divide mass by volume.
• For irregular solids: Use water displacement. Submerge the object in water and measure how much water is displaced. That's the volume.
• For liquids: Use a hydrometer. It floats at different depths depending on liquid density. The scale gives you relative density directly.
• For gases: More complex equipment needed — typically a gas density balance or calculated from pressure, temperature, and molecular weight.

Why Density Matters

Density explains why:

• Ice floats on water (ice is less dense)
• Oil spreads on water's surface (oil is less dense)
• Steel ships float (the overall density of the ship — including air inside — is less than water)
• Hot air rises (heated air expands, becoming less dense)

Engineers use density to select materials. Scientists use it to identify substances. It's one of the most practical properties in all of physics.

Common Mistakes to Avoid

• Confusing mass and density. A small piece of lead is dense but not heavy overall. A large wooden beam is low density but weighs plenty.
• Forgetting temperature effects. Density changes with temperature. Water is densest at 4°C, not at 0°C.
• Ignoring units. Always convert to consistent units before calculating. Mixing g/cm³ with kg/m³ gives wrong answers.
• Using weight instead of mass. Weight depends on gravity. Mass is intrinsic. Density uses mass.

Quick Reference Formulas

• Density: ρ = m / V
• Mass: m = ρ × V
• Volume: V = m / ρ
• Relative Density: RD = ρ_substance / ρ_water

Memorize these four. They cover most problems you'll encounter.