📈 g/cm3 to kg/m3
Multiply by 1000.
The brick: 1.9 g/cm3 = 1.9 × 1000 = 1900 kg/m3.
Density and Pressure » Density
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 5.1, 5.3
- What density means and the equation that links density, mass and volume
- The units kg/m3 and g/cm3 and how to change between them
- How to find the volume of a cuboid and rearrange the density equation
- How density decides whether an object floats or sinks in water
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Unlock This CourseWhat is density?
Pick up a house brick in one hand and a block of sponge of the same size in the other. They take up the same amount of space, but the brick is far heavier. The brick has more mass packed into the same volume. We say the brick is more dense.
Density does not depend on the size of the object. A gold ring and a gold bar have very different masses, but the same density, because they are made of the same material. Density is a property of the material, so it can help you to identify what something is made of.
Key terms:
- Volume: the amount of space an object takes up, measured in metres cubed (m3).
- Density: the mass of each unit of volume of a material. In kg/m3, it is the mass in kilograms of one metre cubed.
- Cuboid: a box shape with six rectangular faces, such as a brick.
The density equation
density = mass ÷ volume
ρ = m ÷ V
The symbol ρ is the Greek letter rho. It looks like a p, so write it with care. This equation is not given in the exam. You must learn it.
🧱 Mass, m
Measured in kilograms (kg). Smaller masses are often given in grams (g).
📦 Volume, V
Measured in metres cubed (m3). Smaller volumes are often given in centimetres cubed (cm3).
💧 Density, ρ
Measured in kilograms per metre cubed (kg/m3), or in grams per centimetre cubed (g/cm3).
The units must match. Use kg with m3 to get kg/m3, or g with cm3 to get g/cm3. Never mix the two sets.
| Material | Density in kg/m3 | Density in g/cm3 |
|---|---|---|
| Air | about 1.2 | about 0.0012 |
| Ice | 920 | 0.92 |
| Water | 1000 | 1.0 |
| Aluminium | 2700 | 2.7 |
| Iron | 7900 | 7.9 |
| Gold | 19 300 | 19.3 |
Worked example 1: finding the density
A stone statue has a mass of 540 kg and a volume of 0.20 m3. Calculate the density of the stone.
ρ = m ÷ V
ρ = 540 ÷ 0.20
ρ = 2700 kg/m3
Length, area and volume
Three of the units for this topic come from the metre (m), the unit of length. Area is measured in metres squared (m2), because you multiply two lengths. Volume is measured in metres cubed (m3), because you multiply three lengths.
volume of a cuboid = length × width × height
All three lengths must be in the same unit. Lengths in metres give a volume in m3. Lengths in centimetres give a volume in cm3.
Worked example 2: a cuboid
A brick is 20 cm long, 10 cm wide and 5.0 cm high. Its mass is 1900 g. Calculate the density of the brick in g/cm3.
volume = length × width × height
volume = 20 × 10 × 5.0 = 1000 cm3
ρ = m ÷ V
ρ = 1900 ÷ 1000
ρ = 1.9 g/cm3
Changing between g/cm3 and kg/m3
One metre cubed is a cube 100 cm long, 100 cm wide and 100 cm high. So 1 m3 = 100 × 100 × 100 = 1 000 000 cm3. That is far bigger than most people expect.
Think about water. One centimetre cubed of water has a mass of 1 g. So one metre cubed of water has a mass of 1 000 000 g, which is 1000 kg. This gives the rule:
1 g/cm3 = 1000 kg/m3
📉 kg/m3 to g/cm3
Divide by 1000.
Iron: 7900 kg/m3 = 7900 ÷ 1000 = 7.9 g/cm3.
To change a volume from cm3 to m3, divide by 1 000 000. For example, 250 cm3 = 250 ÷ 1 000 000 = 0.00025 m3.
Rearranging the equation
The equation can be rearranged to find the mass or the volume:
m = ρ × V and V = m ÷ ρ
Worked example 3: finding the mass
A fish tank holds 0.15 m3 of water. The density of water is 1000 kg/m3. Calculate the mass of the water.
m = ρ × V
m = 1000 × 0.15
m = 150 kg
That is about the mass of two adults, so a full fish tank needs a strong stand.
Worked example 4: finding the volume
A small gold bar has a mass of 386 g. The density of gold is 19.3 g/cm3. Calculate the volume of the bar.
V = m ÷ ρ
V = 386 ÷ 19.3
V = 20 cm3
The mass is in grams and the density is in g/cm3, so the volume comes out in cm3.
Floating and sinking
A solid object floats in water if its density is less than the density of water, 1000 kg/m3. It sinks if its density is greater. Ice (920 kg/m3) floats. A solid piece of iron (7900 kg/m3) sinks.
Units for this topic
You have now met the kilogram, the metre, the metre squared, the metre cubed and the kilogram per metre cubed. The other units for this topic are used in later lessons.
| Unit | Measures | Used in the lesson |
|---|---|---|
| newton (N) | force | Pressure |
| pascal (Pa) | pressure | Pressure |
| metre/second2 (m/s2) | acceleration | Pressure in Liquids and Gases |
| degree Celsius (°C) | temperature | Heating and Changes of State |
| joule (J) | energy | Specific Heat Capacity |
| metre/second (m/s) | speed | Gas Molecules and Pressure |
| kelvin (K) | temperature | Absolute Zero and the Kelvin Scale |
Common mistakes
- Turning the equation upside down. Density is mass ÷ volume, never volume ÷ mass.
- Mixing units, such as a mass in grams with a volume in m3. Convert first, then calculate.
- Dividing by 100 to change cm3 to m3. There are 1 000 000 cm3 in 1 m3.
- Saying a big object must be denser than a small one. Density depends on the material, not the size.
- Writing "heavier" when you mean "denser". A large block of ice can be heavier than an iron nail, yet the ice floats and the nail sinks.
- Leaving out the unit, or writing kg/m2 in place of kg/m3.
Exam-style question
A student has a solid block of plastic in the shape of a cuboid. The block is 5.0 cm long, 4.0 cm wide and 3.0 cm high. Its mass is 57 g.
(a) State the equation linking density, mass and volume. [1 mark]
(b) Calculate the volume of the block. [2 marks]
(c) Calculate the density of the plastic. Give the unit. [3 marks]
(d) The density of water is 1.0 g/cm3. State whether the block floats or sinks in water. Give a reason for your answer. [1 mark]
(e) A large tank is made from the same plastic. The volume of plastic in the tank is 0.020 m3. Calculate the mass of the tank in kg. [3 marks]
Model answer
(a) density = mass ÷ volume, or ρ = m ÷ V (1)
(b) volume = 5.0 × 4.0 × 3.0 (1) = 60 cm3 (1)
(c) ρ = 57 ÷ 60 (1) = 0.95 (1) g/cm3 (1)
(d) It floats, because its density is less than the density of water. (1)
(e) density = 0.95 × 1000 = 950 kg/m3 (1) m = ρ × V = 950 × 0.020 (1) = 19 kg (1)
Exam tip
In part (e) the volume is in m3 but your density from part (c) is in g/cm3. Change the density to kg/m3 before you multiply. Whenever a density question has several parts, check the units of every number before you put it into the equation.