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    Density Calculator (ρ = m/V)

    GCSE PhysicsAQAEdexcelOCRFoundation & Higher

    Find density, mass or volume using ρ = m ÷ V. Enter grams, cm³, litres or g/cm³ and the solver converts to kg and m³ for you.

    Quick answer

    Density = mass ÷ volume. Use mass in kg and volume in m³ to get kg/m³. For example, 540 g (0.54 kg) in 200 cm³ (0.0002 m³) gives ρ = 0.54 ÷ 0.0002 = 2700 kg/m³. To convert g/cm³ to kg/m³, multiply by 1000.

    By Engr. Mehmood Kakar · Updated

    ρ = m ÷ V
    Find:

    1 cm³ is the same as 1 ml. There are 1,000,000 cm³ in 1 m³.

    Simulation

    Will it float?

    Set the mass and volume of a block. Its density decides whether it floats or sinks in water (1.0 g/cm³).

    270 g
    100 cm³

    An object floats in water if its density is less than 1.0 g/cm³ (1000 kg/m³). To convert g/cm³ to kg/m³, multiply by 1000.

    Put these numbers in the calculator above

    How to calculate density

    Density tells you how much mass is packed into each cubic metre of a material. The equation is:

    density = mass ÷ volume

    • ρ (the Greek letter rho) is density in kilograms per cubic metre (kg/m³)
    • m is mass in kilograms (kg)
    • V is volume in cubic metres (m³)

    A block with a mass of 540 g and a volume of 200 cm³ has a density of 0.54 ÷ 0.0002 = 2700 kg/m³. That is the density of aluminium.

    Volume conversions cause most lost marks. A cubic metre is 100 cm × 100 cm × 100 cm, so 1 m³ = 1,000,000 cm³. Divide cm³ by 1,000,000 to get m³, not by 100. You can also work in g/cm³ and convert at the end: multiply g/cm³ by 1000 to get kg/m³. Water is 1 g/cm³, or 1000 kg/m³.

    Density explains the particle model. Solids and liquids have closely packed particles, so they are much denser than gases, where the particles are far apart.

    Common mistakes that cost marks

    1. Dividing cm³ by 100 or 1000. 1 m³ = 1,000,000 cm³, so 200 cm³ = 0.0002 m³.
    2. Mixing units. Grams with m³, or kilograms with cm³, gives an answer 1000 times out. Use kg with m³, or g with cm³.
    3. Dividing the wrong way. Density is mass ÷ volume. A metal block with a density of 0.00037 kg/m³ means you divided volume by mass.
    4. Forgetting the unit. Write kg/m³ or g/cm³. Both are correct; a missing unit loses the mark.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A metal block has a mass of 540 g and a volume of 200 cm³. Calculate its density in kg/m³.[3 marks]
    1. ρ = m ÷ V
    2. Convert: m = 0.54 kg; V = 200 ÷ 1,000,000 = 0.0002 m³
    3. ρ = 0.54 ÷ 0.0002
    4. ρ = 2700 kg/m³
    Q2Water has a density of 1000 kg/m³. Calculate the mass of 0.25 m³ of water.[2 marks]
    1. Rearrange: m = ρ × V
    2. m = 1000 × 0.25
    3. m = 250 kg
    Q3A steel bar has a mass of 3.9 kg. The density of steel is 7800 kg/m³. Calculate the volume of the bar.[3 marks]
    1. Rearrange: V = m ÷ ρ
    2. V = 3.9 ÷ 7800
    3. V = 0.00050 m³ (5.0 × 10⁻⁴ m³, or 500 cm³)

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation for density?

    Density = mass ÷ volume (ρ = m/V). Density is in kg/m³, mass in kg and volume in m³.

    How do I convert g/cm³ to kg/m³?

    Multiply by 1000. For example, 2.7 g/cm³ = 2700 kg/m³, and water at 1 g/cm³ is 1000 kg/m³.

    How many cm³ are in 1 m³?

    1,000,000. A cubic metre is 100 cm long, 100 cm wide and 100 cm high, and 100 × 100 × 100 = 1,000,000.

    How do I find the volume of an irregular object?

    Lower it into a eureka can or a measuring cylinder of water and measure the volume of water it displaces. 1 ml of water displaced is 1 cm³ of volume.