Density Calculator — Step-by-Step Solutions

The Density Calculator helps you find density, mass, or volume using the fundamental relationship ρ = m/V. Choose a mode to calculate the unknown variable from the other two, or use the unit converter to switch between common density units.

Enter your values and get instant results with step-by-step working. The calculator supports kg/m³, g/cm³, lb/ft³, kg/L, and g/mL.

Mass (kg)

Volume (m³)

Your calculations will appear here

How to Use the Density Calculator

Select a calculation mode: Find Density, Find Mass, Find Volume, or Unit Converter.
For Find Density, enter the mass (in kg) and volume (in m cubed). The calculator applies the formula density = mass / volume.
For Find Mass, enter the density and volume. The calculator multiplies density by volume to find the mass.
For Find Volume, enter the mass and density. The calculator divides mass by density to find the volume.
For Unit Converter, enter a density value and select the source and target units to convert between kg/m cubed, g/cm cubed, lb/ft cubed, kg/L, and g/mL.

Formula and Theory

Density is a measure of how much mass is contained in a given volume. It is one of the most fundamental physical properties of matter. The SI unit of density is kilograms per cubic metre (kg/m cubed).

The density formula is straightforward: rho = m / V, where rho is density, m is mass, and V is volume. This relationship can be rearranged to solve for any of the three variables.

Different materials have characteristic densities. Water has a density of approximately 1,000 kg/m cubed (1 g/cm cubed) at 4 degrees Celsius. Objects with density less than water float, while denser objects sink. This principle underpins Archimedes' principle of buoyancy.

Density depends on temperature and pressure. Most substances expand when heated, causing their density to decrease. Gases are particularly sensitive to pressure changes according to the ideal gas law.

Worked Examples

Example 1: Finding the density of an object

Problem: A block has a mass of 500 kg and a volume of 0.25 m cubed. What is its density?

Solution: Apply the formula: rho = m / V = 500 / 0.25 = 2,000.

Answer: 2,000 kg/m cubed

Example 2: Finding mass from density and volume

Problem: A liquid has density 800 kg/m cubed and occupies 0.5 m cubed. What is its mass?

Solution: Rearrange: m = rho x V = 800 x 0.5 = 400.

Answer: 400 kg

Example 3: Finding volume from mass and density

Problem: A 1,000 kg steel beam has density 7,850 kg/m cubed. What is its volume?

Solution: Rearrange: V = m / rho = 1,000 / 7,850 = 0.1274.

Answer: 0.1274 m cubed

Example 4: Unit conversion

Problem: Convert 2,700 kg/m cubed to g/cm cubed.

Solution: 1 g/cm cubed = 1,000 kg/m cubed. So 2,700 / 1,000 = 2.7.

Answer: 2.7 g/cm cubed

Frequently Asked Questions

What is the density of water?

Pure water has a density of approximately 1,000 kg/m cubed (1 g/cm cubed) at 4 degrees Celsius, which is the temperature at which water reaches its maximum density.

How does temperature affect density?

Most substances become less dense as temperature increases because thermal expansion causes them to occupy a larger volume. Water is an exception between 0 and 4 degrees Celsius, where it actually becomes denser as it warms.

What is the difference between density and specific gravity?

Specific gravity is the ratio of a substance's density to the density of a reference substance (usually water at 4 degrees Celsius). It is dimensionless, whereas density has units.

Why do some objects float?

An object floats when its average density is less than the density of the fluid it is placed in. This is described by Archimedes' principle: the buoyant force equals the weight of displaced fluid.

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