# Changing the subject

Rearranging a formula so a different letter stands on its own on one side.

Maths (school) · Part 03: Equations and formulae · Card 3 of 8 · Last updated 2026-10-19

## Analogy

Like turning a recipe round: instead of 'time gives distance', you want 'distance gives time'.

## Example

**v = u + at, make a the subject**

v - u = at
(v - u) / t = a
With v = 20, u = 5, t = 3:
a = 15 / 3 = 5

## In practice

Speed = distance / time can be rearranged to find how long a journey takes.

## Practice

### Flashcards

- **Make a the subject of v = u + at.** a = (v - u) / t.

## Questions people ask

### What does 'make x the subject' mean?

It means rearrange the formula so x is alone on one side, with everything else on the other. The formula v = u + at has v as the subject. After rearranging it to a = (v - u) / t, the subject is a.

### Do the rules for solving equations work on formulae?

Yes. You do the same thing to both sides, exactly as you would with numbers. The only difference is that the answer has letters in it. Keep undoing operations in reverse order until your chosen letter is alone. To make t the subject of d = st, divide by s: t = d / s.

## Related concepts

- [Solving linear equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-1)
- [Unknowns on both sides](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-2)
- [Inequalities](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-4)
- [Simultaneous equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-5)

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