GCSE · Physics · Edexcel · Spec 1PH0

Density equation

Drag a block bigger and bigger and watch one number refuse to budge. That stubborn number is density.

Physics · Density

Same material, bigger lump
0 cm³10 cm³20 cm³30 cm³40 cm³50 cm³60 cm³drag the block bigger or smaller →

Size of the Material X block: 2/6. Volume 20 cm³. Mass 50 g. Mass in every 1 cm³ (the density) 2.5 g/cm³

Volume20 cm³Mass50 gMass in every 1 cm³ (the density)2.5 g/cm³

Drag the block to change its volume. Watch the mass, and watch the mass in every 1 cm³.

Exam line: Density is the mass in each unit of volume. Make the lump bigger and the mass grows with it, so the mass per unit volume stays put.
Watch out: Material X is made up for practice, so its numbers are illustrative.

The density triangle

Cover the quantity you want. What is left tells you what to do.

Tap the quantity you want to find. The triangle shows you the formula.

÷

Cover mass, density or volume to reveal its rearranged formula, then plug in numbers to solve.

Physics · Density

Your turn to fill the gaps

A solid block has a mass of 3000 g and a volume of 1500 cm³. Find its density in kg/m³.

  1. We know m = 3000 g and V = 1500 cm³, and we want ρ in kg/m³. The units do not match what we want, so we convert first.
  2. missing step
Which line is step 2?

Physics · Density

How big is the conversion?

A density of 1 g/cm³ is the same as how many kg/m³? Slide to your best estimate, then reveal.

Your estimate

1000 kg/m³

0 kg/m³2000 kg/m³

Physics · Density

Find where the working goes wrong

A student finds the density of a stone with a mass of 2.4 kg and a volume of 800 cm³, giving the answer in kg/m³. One line of the working is wrong. Which one?

A student's working — which line goes wrong?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

  • Density is the mass of a substance per unit volume: how much mass fits in each unit of volume.
  • Take more of the same material and mass and volume grow together, so the mass per unit volume stays the same.
  • Have a goA 20 cm³ piece of some material has a mass of 60 g. Predict the mass of a 40 cm³ piece of the same material before you look.

    120 g

    Same material means the same mass in every cm³, so twice the volume means twice the mass.

  • The equation is density = mass ÷ volume, written ρ = m ÷ V.
  • In standard units, mass is in kg, volume is in m³ and density comes out in kg/m³.
  • Rearranged, it gives mass = density × volume and volume = mass ÷ density.
  • Have a goYour mate Sam is sure: "The lump has a density of 5 kg/m³ and a volume of 2 m³, so its mass is 5 ÷ 2 = 2.5 kg." Sam sounds confident. What did Sam get wrong?

    Sam divided. Mass = density × volume = 5 × 2 = 10 kg.

    Mass is density times volume. The divide belongs to finding density or finding volume, not mass.

  • Density can also be given in g/cm³ when mass is in grams and volume is in cm³, and 1 g/cm³ = 1000 kg/m³.
  • Before you substitute, mass and volume must be in consistent units.
  • Two conversions to know: 1 kg = 1000 g, and 1 m³ = 1 000 000 cm³.
  • Have a goA tank has a mass of 4500 g and a volume of 3 m³. Before you divide to find the density, which number has to change, and into what?

    The mass: 4500 g becomes 4.5 kg.

    The volume is in m³, so the mass needs to be in kg. 1 kg = 1000 g, so you divide 4500 by 1000.

The big picture

Density is the mass of a substance per unit volume, found with density = mass ÷ volume. Rearrange it to find mass or volume, and always put mass and volume in matching units before you substitute.

Key points

1Density is mass per unit volume, and it is a fixed number for a material however big the lump.
2Density = mass ÷ volume. Rearrange to mass = density × volume and volume = mass ÷ density.
3Standard units are kg, m³ and kg/m³. For g and cm³ the density is in g/cm³.
41 g/cm³ = 1000 kg/m³. Convert so the units match before you substitute.

Worked example

Problem

A solid has a density of 8 g/cm³ and a volume of 25 cm³. Find its mass in kg.

⚠ Watch out

Substituting a mass in grams with a volume in m³ (or a mass in kg with a volume in cm³) without converting first. The units have to match before you divide or multiply.

🧠

Memory hook

Match, then divide. Check that the units match first, and only then put mass over volume.

✓

Check yourself

A 2 m³ tank of liquid has a mass of 1600 kg. Find the density. What would 5 m³ of the same liquid weigh in kg?

Flashcards

(10)
What is density?
The mass of a substance per unit volume.
Write the density equation in words and symbols.
density = mass ÷ volume, so ρ = m ÷ V.
What are the standard units for mass, volume and density?
Mass in kg, volume in m³, density in kg/m³.
Rearrange the density equation to find mass, and to find volume.
mass = density × volume (m = ρ × V); volume = mass ÷ density (V = m ÷ ρ).
When can you give density in g/cm³?
When mass is in grams and volume is in cm³.
1 g/cm³ equals how many kg/m³?
1000 kg/m³.
How many grams in 1 kg, and how many cm³ in 1 m³?
1 kg = 1000 g and 1 m³ = 1 000 000 cm³.
You cut a lump of a material into a bigger and a smaller piece. How do their densities compare?
They are the same, because mass and volume grow together.
What must you check before substituting into the density equation?
That mass and volume are in consistent units.
How do you convert a volume from cm³ to m³?
Divide by 1 000 000.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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How this lesson was checked. This Edexcel GCSE Physics (specification 1PH0)lesson was published through Lightbulb Learning's human-designed editorial process — the educational standards, accuracy rules and publication checks it must pass were authored and approved by Philip Halpin. It passed subject-specific assessment, automated educational checks and technical publication verification before going live (publication checks completed 9 October 2026). Published pages are monitored, human spot-checking is ongoing across the lesson library, and anything found wrong is corrected or withdrawn. How our lessons are made and checked. Spotted a mistake? Email hello@lightbulblearning.co and we'll review it.