Login
Login Find a tutor

Density Calculator and Formula

The density formula is ρ = m/V: density = mass ÷ volume, with mass in kg, volume in m³ and density in kg/m³. Rearranged, mass = density × volume (m = ρV) and volume = mass ÷ density (V = m/ρ).

Density formula: ρ = m/V

ρ = mV
ρ = mVm = ρ·VV = mρ
ρ
density, kg/m³
m
mass, kg
V
volume, m³

Convert every value to SI units (m, s, kg, A, V, Ω) before substituting into the formula. The calculator does this for you and shows the conversion as a step.

2700 kg/m³
ρdensity
2700 kg/m³
density: 2700 kg/m³
The cube's density, 2700 kg/m³ (mass 0.54 kg, volume 2 · 10⁻⁴ m³), is greater than water's 1000 kg/m³, so it sinks to the bottom.

Step-by-step solution

  1. Formulaρ = mV
  2. In SI unitsm = 540 g = 0.54 kg
  3. V = 200 cm³ = 2 · 10⁻⁴ m³
  4. Substituteρ = 0.54 kg2 · 10⁻⁴ m³
  5. Answerρ ≈ 2700 kg/m³

Density examples

  1. Example 1

    A block of wood has a mass of 600 g and a volume of 750 cm³. Calculate the density of the wood.

    Given:m = 600 gV = 750 cm³
    1. Formulaρ = mV
    2. In SI unitsm = 600 g = 0.6 kg
    3. V = 750 cm³ = 7.5 · 10⁻⁴ m³
    4. Substituteρ = 0.6 kg7.5 · 10⁻⁴ m³
    5. Answerρ = 800 kg/m³

  2. Example 2

    A garden water butt holds 0.25 m³ of rainwater, and the density of water is 1000 kg/m³. Calculate the mass of the water in kilograms.

    Given:ρ = 1000 kg/m³V = 0.25 m³
    1. Formulam = ρ·V
    2. Substitutem = 1000 kg/m³ · 0.25 m³
    3. Answerm = 250 kg

  3. Example 3

    An aluminium block has a mass of 5.4 kg, and the density of aluminium is 2700 kg/m³. Calculate the volume of the block in m³.

    Given:m = 5.4 kgρ = 2700 kg/m³
    1. FormulaV = mρ
    2. SubstituteV = 5.4 kg2700 kg/m³
    3. AnswerV = 0.002 m³

Density and unit conversions confusing? Get help from a tutor

Mathema physics tutors work with you one to one online, from Year 10 to A-level, at your pace. Start with a trial lesson to find the gaps and plan how to close them.

Find a physics tutor Book a trial lesson

What does density mean?

Density tells you how much mass is packed into each unit of volume. At GCSE it is written density = mass ÷ volume, or ρ = m/V, where ρ (the Greek letter rho) is the density in kg/m³, m is the mass in kg and V is the volume in m³. Density belongs to the material, not the object: a steel paperclip and a steel girder have the same density.

Density links to the particle model. In a solid the particles are packed closely together, so solids are usually dense; in a gas they are far apart, so gases have very low densities. Water is an unusual case, because ice is less dense than liquid water, which is why ice floats.

A real-life picture: an object floats in water if its density is less than 1000 kg/m³ and sinks if it is greater. A pine log floats and an iron nail sinks, while a steel ship floats because its average density, including all the air inside the hull, is less than that of water. For a regular block, volume = length × width × height; for an irregular object you can find the volume by displacement in a eureka can, as in the GCSE required practical.

Common mistakes

  • Mixing g with m³ or kg with cm³. Since 1 g/cm³ = 1000 kg/m³, a mixed answer can be a thousand times out.
  • Converting cm³ to m³ by dividing by 100. One metre is 100 cm, so one cubic metre is 100 × 100 × 100 cm³: divide by a million.
  • Turning the formula upside down: volume ÷ mass is not density.
  • Forgetting that 1 litre = 1 dm³ = 1000 cm³ = 0.001 m³.

Related formulas

Kinetic energySpeed, distance and timeEfficiencyAll physics equations

Frequently asked questions

Density = mass ÷ volume, written ρ = m/V. With mass in kg and volume in m³, density comes out in kg/m³.

About 1000 kg/m³, which is the same as 1 g/cm³. Objects with a lower density float in water, and objects with a higher density sink.

Multiply by 1000. For example, aluminium has a density of 2.7 g/cm³, which is 2700 kg/m³.

Measure its mass on a balance, then find its volume by displacement: lower it into a eureka can or a measuring cylinder of water and measure the volume of water it displaces. Divide the mass by the volume.

ρ is the Greek letter rho, the usual symbol for density. At A-level it is also used for resistivity, so check the context.