Rearrange formulae

Objective. Change the subject when it appears once.

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Learn: the key idea

Rearranging a formula means changing which letter is the subject, using inverse operations to isolate it when it appears only once. The method mirrors solving an equation: undo operations in reverse order, working outward from the subject letter until the desired variable stands alone on one side. For example, to make x the subject of y = 3x + 2, first subtract 2 from both sides to get y − 2 = 3x, then divide by 3 to get x = (y − 2)/3. Square roots and squares are undone with their inverse, so making r the subject of A = πr² requires dividing by π then taking a square root.

Worked example

Rearrange the formula v = u + at to make t the subject.

1 $Subtract u from both sides: v - u = at.$
2 $The variable t is multiplied by a, so divide both sides by a.$
3 $t = (v - u)/a.$
4 $Check by substituting back into the original: u + a \times (v - u)/a = u + v - u = v, which matches.$

Answer: t = (v − u)/a

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Common mistake. Pupils often perform operations in the wrong order, trying to divide before subtracting when the formula has terms added after multiplication, which leaves the variable still tangled. Always undo addition or subtraction before undoing multiplication or division.

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