How to Calculate Density (Mass, Volume, and Formula)

Density is one of the most fundamental properties of matter. It tells you how much mass is packed into a given volume, and it plays a central role in physics, chemistry, engineering, and everyday life. Whether you are trying to figure out if an object will float, identifying an unknown material, or converting between mass and volume, understanding density is essential.

In this guide, we cover the density formula, its standard units, how to measure density for regular and irregular objects, worked examples with full calculations, a reference table of common material densities, and practical applications including buoyancy and specific gravity.

What Is Density?

Density describes how tightly matter is packed together. A block of lead feels much heavier than a block of wood of the same size because lead has a much higher density. Formally, density is defined as mass per unit volume:

Where:

• (the Greek letter rho) is the density
• is the mass of the object
• is the volume of the object

This formula can be rearranged to solve for mass or volume:

Units of Density

The SI unit of density is kilograms per cubic metre (). However, in chemistry and everyday use, you will often encounter other units:

• g/cm³ (grams per cubic centimetre) is the most common in chemistry. Water has a density of approximately 1 g/cm³.
• g/mL (grams per millilitre) is numerically identical to g/cm³ because 1 cm³ = 1 mL.
• kg/m³ is used in physics and engineering. Water is approximately 1000 kg/m³.
• kg/L (kilograms per litre) is convenient for liquids. Water is approximately 1 kg/L.

To convert between g/cm³ and kg/m³, multiply by 1000. For example, iron at 7.87 g/cm³ is 7870 kg/m³.

Measuring Density

Regular Objects

For objects with simple geometric shapes (cubes, cylinders, spheres), you can measure the dimensions directly and calculate the volume using geometry formulas. Then weigh the object on a balance and apply .

For a rectangular block, the volume is length times width times height:

For a cylinder, the volume is:

Irregular Objects (Water Displacement)

For objects with complex shapes, such as a stone or a metal figurine, you cannot easily calculate the volume from dimensions. Instead, use the water displacement method, which dates back to Archimedes:

1. Fill a graduated cylinder or overflow can with water and record the initial volume.
2. Carefully lower the object into the water, making sure it is fully submerged.
3. Record the new water level (or collect the overflow water and measure its volume).
4. The volume of the object equals the difference: .
5. Weigh the object on a balance to find its mass.
6. Calculate density: .

Measuring the Density of Liquids

To find the density of a liquid, weigh an empty graduated cylinder, pour in a known volume of the liquid, and weigh again. The mass of the liquid is the difference in weights, and the volume is read from the cylinder markings.

Alternatively, a hydrometer can measure liquid density directly by floating in the liquid and reading the scale at the surface level.

Worked Example 1: Rectangular Block

Problem: A metal block has dimensions 5 cm × 3 cm × 2 cm and a mass of 237 g. Find its density and identify the material.

Step 1: Calculate the volume.

Step 2: Apply the density formula.

Result: The density is 7.9 g/cm³. Checking the reference table below, this closely matches iron (7.87 g/cm³), so the block is most likely made of iron or steel.

Worked Example 2: Irregular Object (Water Displacement)

Problem: A small rock has a mass of 52 g. When placed in a graduated cylinder containing 40 mL of water, the water level rises to 60 mL. What is the density of the rock?

Step 1: Find the volume by displacement.

Step 2: Calculate density.

Result: The density is 2.6 g/cm³, which is consistent with granite or similar common rocks.

Worked Example 3: Finding the Density of a Liquid

Problem: An empty graduated cylinder weighs 85 g. After pouring in 50 mL of olive oil, the total mass is 131 g. What is the density of the olive oil?

Step 1: Find the mass of the liquid.

Step 2: Calculate density.

Result: The density of this olive oil sample is 0.92 g/mL. Since this is less than 1 g/mL (the density of water), olive oil floats on water, which matches everyday observation.

Worked Example 4: Converting Units

Problem: Aluminium has a density of 2.70 g/cm³. Express this in kg/m³.

The conversion factor of 1000 arises because there are 1,000,000 cm³ in 1 m³ and 1000 g in 1 kg: .

Density of Common Materials

Applications of Density

Buoyancy and Floating

An object will float in a fluid if its density is less than the density of the fluid. This is why wood (density around 0.6 - 0.9 g/cm³) floats on water (1.0 g/cm³), while iron (7.87 g/cm³) sinks. Ships, despite being made of steel, float because the overall density of the ship (including all the air inside the hull) is less than the density of water.

Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces:

Material Identification

Density can help identify unknown materials. If you measure the density of a metallic sample and find it to be approximately 8.96 g/cm³, you can be fairly confident it is copper. This technique is used in geology, archaeology, and quality control in manufacturing.

Engineering and Design

Engineers must account for density when selecting materials. Aircraft are built from aluminium and composites (low density, high strength) rather than steel, because reducing weight improves fuel efficiency. In construction, the density of concrete and steel determines the load capacity of structures.

Specific Gravity

Specific gravity (also called relative density) is the ratio of a substance's density to the density of a reference substance, usually water at 4°C:

Since the density of water is 1.00 g/cm³, the specific gravity is numerically equal to the density in g/cm³. A substance with a specific gravity greater than 1 will sink in water; less than 1, and it will float.

Specific gravity is dimensionless (it has no units), which makes it useful for comparing substances regardless of the measurement system used. It is widely used in brewing, petroleum engineering, and gemology.

Temperature and Pressure Effects

Density is not constant for a given material. It changes with temperature and pressure. Most substances expand when heated, meaning their volume increases while mass stays the same, so density decreases. Water is unusual: it reaches maximum density at approximately 4°C, which is why ice floats.

Gases are highly compressible, so their density changes significantly with pressure. The ideal gas law relates density to temperature and pressure:

Where is pressure, is molar mass, is the universal gas constant, and is temperature in kelvin.

Frequently Asked Questions

What is the difference between density and weight?

Density is mass per unit volume (), while weight is the gravitational force on an object (). Density is an intrinsic property of a material that does not change with location, whereas weight depends on the strength of gravity. An object weighs less on the Moon than on Earth, but its density stays the same.

Why does ice float on water?

Ice has a density of about 0.917 g/cm³, which is lower than liquid water at 1.00 g/cm³. This is because water molecules in ice form a crystalline structure with open hexagonal spaces, making it less dense than liquid water. This unusual property is critical for aquatic ecosystems, as it insulates the water below and prevents lakes from freezing solid.

Can two objects with the same mass have different densities?

Absolutely. A 1 kg block of aluminium occupies about 370 cm³, while a 1 kg block of lead occupies only about 88 cm³. They have the same mass but different volumes, so their densities are different (2.70 g/cm³ for aluminium vs 11.34 g/cm³ for lead).

How do you find the density of an irregularly shaped object?

Use the water displacement method. Submerge the object in a graduated cylinder or overflow can, measure the volume of water displaced, weigh the object on a balance, and then divide mass by volume. This is the same principle Archimedes famously used to determine whether a crown was made of pure gold.

What is the densest substance on Earth?

Osmium is the densest naturally occurring element, with a density of 22.59 g/cm³. It is a hard, brittle, bluish-white transition metal in the platinum group. Iridium is a close second at 22.56 g/cm³.