How to calculate percentage change (increase and decrease)

The one formula behind price rises, pay raises, and sale prices — with worked examples and the mistakes that trip people up.

Percentage change tells you how much something grew or shrank compared with where it started. It is the number behind headlines like “prices rose 8%” and shop signs like “30% off”. There is only one formula to learn, and almost every mistake comes from dividing by the wrong number. The formula Percentage change = (new value − old value) ÷ old value × 100. A positive answer is an increase. A negative answer is a decrease. The old value always goes on the bottom, because the change is measured against where you started. Percentage increase, step by step Your rent goes from $1,200 to $1,320 a month. The difference is $120. Divide by the old rent: 120 ÷ 1,200 = 0.10. Multiply by 100 and you get a 10% increase. Percentage decrease, step by step A coat drops from $80 to $60. The difference is −$20. Divide by the old price: −20 ÷ 80 = −0.25. Multiply by 100 and you get −25%, so the price fell by 25%. Why a fall and a recovery are not the same percentage A share price falls 50%, from $100 to $50. To get back to $100 it has to rise by $50 — and $50 is 100% of $50, not 50%. Each percentage is measured against a different starting number, so a drop and the rise that undoes it never match. Per…