Almost every calculation question in GCSE Physics asks you to use an equation, and many of them need you to rearrange it first. If rearranging makes you nervous, you’re not alone, but it’s a skill you can master with one simple rule.
The golden rule
Whatever you do to one side of the equation, you must do to the other. To move something across, do the opposite operation: if it’s multiplied, divide both sides by it; if it’s divided, multiply both sides by it.
Example: density
The density equation is ρ = m ÷ V (density = mass ÷ volume).
- To find mass: V is dividing m, so multiply both sides by V. This gives m = ρ × V.
- To find volume: start from m = ρ × V. ρ is multiplying V, so divide both sides by ρ. This gives V = m ÷ ρ.
Worked example
A block of aluminium has a density of 2700 kg/m³ and a volume of 0.002 m³. Calculate its mass.
- Write the equation: ρ = m ÷ V
- Rearrange: m = ρ × V
- Substitute: m = 2700 × 0.002
- Answer with units: m = 5.4 kg
Why not just use a formula triangle?
Triangles work for simple three-part equations, but they fall apart with equations like E = ½mv² or ΔE = mcΔθ. Learning to rearrange properly means you’ll be able to handle every equation, including the harder ones that appear at the end of the paper.
Top tips
- Always write the equation down first. You can pick up a mark just for that.
- Rearrange before you put the numbers in. It’s much easier to spot mistakes.
- Check your answer makes sense. A pencil with a mass of 500 kg means something has gone wrong.
- Always include units in your final answer.
Practise rearranging a few equations every day and it will soon become automatic. Try the questions in our question bank to put it into practice!
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