Rearranging a formula uses the same balance method as solving an equation, with letters where the numbers would be. When a fraction is involved, clear it first and the rest becomes familiar.
What is the order of steps?
Follow this order every time.
- Clear fractions by multiplying both sides by the denominator.
- Expand any brackets.
- Get every term containing the required letter on one side.
- Isolate the letter with the opposite operations.
Worked example
The formula for the distance covered at constant acceleration is s = (u + v)t ÷ 2. Make v the subject. This example is built for the page.
Multiply both sides by 2 to clear the fraction: 2s = (u + v)t. Divide both sides by t: 2s ÷ t = u + v. Subtract u from both sides: v = 2s ÷ t − u.
Check with numbers. Let u = 3, v = 7 and t = 4. Then s = (3 + 7) × 4 ÷ 2 = 20.
The new formula gives v = 2 × 20 ÷ 4 − 3 = 10 − 3 = 7. It matches the v we began with.
What does the common mistake look like?
A student writes v = 2s ÷ t + u. The sign of u did not change when it moved, which is the same slip as in equations. Test with u = 3, t = 4 and s = 20: the wrong formula gives v = 10 + 3 = 13, not 7.
A second slip is to divide only one term by t. From 2s = (u + v)t, dividing gives 2s ÷ t = u + v, where the whole bracket is divided. Writing 2s = u + v ÷ t divides only v, which changes the meaning.
Steps to follow
- Write the letter you need to isolate and circle it in the formula.
- Clear the fraction, then undo what is attached to the letter one operation at a time, working from the outermost.
- Substitute simple numbers to check.
Self-check
Make m the subject of E = ½mv².
Answer
Multiply both sides by 2: 2E = mv². Divide both sides by v²: m = 2E ÷ v².
Check with m = 3 and v = 4: E = ½ × 3 × 16 = 24. The new formula gives m = 2 × 24 ÷ 16 = 3, which matches. A typical slip is dividing by v instead of v².
Where to go next
Formula rearranging is used constantly in Physics, so practise with a formula from that subject. The algebra step repair trainer offers more rearranging drills. If the balance idea itself feels unsteady, go back to solving a linear equation step by step, or see the algebra readiness hub.