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Density calculator

GCSEA-level Forces

Density is the mass of a substance in each unit of volume.

ρ = m / V

This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

ρDensity to find 7800 kg/m³

mMass

VVolume

Significant figures

Working

Write the equation
ρ = m / V
Substitute the values
ρ = 7.8 ÷ 0.001
Calculate
ρ = 7800 kg/m³
Give the answer to 3 significant figures
ρ = 7800 kg/m³

Worked example

Find ρ, the density. Given: mass m = 7.80 kg; volume V = 0.00100 m³.

Write the equation
ρ = m / V
Substitute the values
ρ = 7.8 ÷ 0.001
Calculate
ρ = 7800 kg/m³
Give the answer to 3 significant figures
ρ = 7800 kg/m³

Symbols and units

Symbol	Quantity	SI unit
ρ	Density	kg/m³
m	Mass	kg
V	Volume	m³

Density: rearranged

To find density: ρ = m / V
To find mass: m = ρ V
To find volume: V = m / ρ

Exam tip

Watch the units: 1 g/cm³ is 1000 kg/m³. 1 cm³ is 0.000001 m³.

Common questions

What is the formula for density?

The equation is ρ = m / V, where ρ is the density (kg/m³); m is the mass (kg); V is the volume (m³).

What units should I use for density?

In SI units: density in kg/m³, mass in kg, volume in m³. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange ρ = m / V?

Rearranging gives these forms: to find density: ρ = m / V. to find mass: m = ρ V. to find volume: V = m / ρ.

Practise density questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Read the full explanation on the Density formula page. More forces equations: Newton’s second law, Weight, Moment of a force, Hooke’s law, Pressure, Pressure in a liquid, Horizontal component of a force, Vertical component of a force. See the full list on the physics equation calculator page.