Algebra · Lesson 14 of 16

Using and Rearranging Simple Formulas

A formula links quantities with letters. Substitute to find a value, or rearrange with inverse operations to make another letter the subject.

Secondary
Updated 14 November 2026

What you will learn

Use a formula by substituting.
Make a letter the subject.
Choose the inverse operation at each step.

Before you start: you should know substitution and how to solve equations. See Substitution into Expressions.

The idea

A formula is a rule that links quantities using letters. In $A = lw$ the letter $A$ is the subject, because it stands alone on one side.

Four common formulas. In each one the subject is the letter on its own.

Using a formula

Substitute the known values and calculate. If $s = 60$ and $t = 2.5$ then $d = 60 \times 2.5 = 150$ .

Rearranging

Treat the formula like an equation. Do the same thing to both sides until the letter you want is alone.

Rearranging keeps the formula true. d = st and s = d/t say the same thing in different forms.

Worked examples

Example 1: Using

Use $d = st$ with $s = 60$ and $t = 2.5$ .

Substitute: $d = 60 \times 2.5$ .
$d = 150$ .

Answer: $150$

Example 2: Rearranging

Make $x$ the subject of $y = 3x + 1$ .

Subtract $1$ : $y - 1 = 3x$ .
Divide by $3$ : $x = \dfrac{y - 1}{3}$ .

Answer: $x = \dfrac{y - 1}{3}$

Example 3: Rearrange then use

Find $x$ when $y = 13$ .

$x = (13 - 1) \div 3$ .
$x = 4$ .

Answer: $4$

Tip: undo operations in reverse order, just as when solving an equation.

Why it matters

Formulas are the working tools of science, building and finance. Being able to rearrange them lets you find whichever quantity you need.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.