GCSE Maths Rearranging Formulae Notes
Rearranging a formula means making a different letter the subject. Use inverse operations in reverse order, just like solving an equation.
Key concepts
- Subject of a formula
- The letter on its own, usually before the equals sign, e.g. y is the subject of y = 3x + 2.
- Inverse operations
- Undo operations in reverse order: undo + and − first, then × and ÷, then powers and roots.
- Subject on both sides
- Collect the required letter on one side, factorise it out, then divide.
Key formulas
Undo a square
if x² = k then x = ±√k
Undo a square root
if √x = k then x = k²
Worked example
Make r the subject of A = πr².
- 1Divide both sides by π: A/π = r².
- 2Square root both sides: √(A/π) = r.
- 3Write r as the subject: r = √(A/π).
Answer: r = √(A/π)
Common mistakes
✗ Square rooting only one term, e.g. √(a² + b²) = a + b.
✓ You cannot split a root over addition — a² + b² must be combined first.
✗ Forgetting to apply the operation to every term.
✓ Whatever you do, do it to the whole of both sides.
✗ Not factorising when the subject appears twice.
✓ Collect the terms containing the letter, factorise it out, then divide.
Quick check
Try these, then reveal the answers.
Make x the subject of y = 2x + 5.Reveal answer
x = (y − 5)/2
Make t the subject of v = u + at.Reveal answer
t = (v − u)/a
Make x the subject of y = x².Reveal answer
x = ±√y
Exam tips
- Think of it as solving for a letter — the same inverse operations apply.
- When the new subject appears twice, factorising is the key step examiners reward.
- Leave answers as neat fractions or surds rather than rounding.
Related practice
Practise this topic
Exam-style questions with instant Gradion feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Gradion
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Frequently asked questions
How is rearranging a formula different from solving an equation?+
The method is identical — inverse operations — but the answer is a formula in the other letters, not a single number.
What do I do when the subject is inside a square root?+
Square both sides to remove the root, then continue rearranging as normal.
Create a free account to practise rearranging formulae with Gradion feedback
Try 5 questions now, get instant examiner-grade marking and ask the Gradion to explain anything. Free during our early launch period — no credit card required.