A formula links several letters together, like C = 2\pi r for the circumference of a circle. The letter on its own — here C — is called the subject of the formula.

Sometimes you already know the circumference and want the radius instead. Then you need to change the subject: rewrite the formula so a different letter stands alone. The good news is you already know how — it is exactly the inverse-operation moves you use when solving two-step equations. You just do the same to both sides until the letter you want is by itself.

Treat every other letter as if it were an ordinary number and undo what is done to your target letter, one inverse at a time. To make r the subject of C = 2\pi r, the r is multiplied by 2\pi — so divide both sides by 2\pi:

It is the same idea as substitution in reverse: instead of putting numbers in, you keep the letters and isolate the one you want.

See it rearranged

Watch v = u + at become a = \dfrac{v - u}{t}, one inverse move per step: first undo the +\,u, then undo the \times\,t. Step through it.

See it explained

Sal Khan solves a formula for one of its letters by doing the same to both sides.