Grow or Shrink? Mastering Percentage Change

A pair of trainers cost £80 last month. This month they cost £100. Something has changed — but by how much, really? You might say '£20 more', and you'd be right. But £20 means something very different if the original price was £80 versus if it was £800. That's why we use percentage change: it tells us how big a change is relative to where we started. Before we dive in, try this quick retrieval check.

Percentage change tells you how much something has grown or shrunk compared to its original value, expressed as a percentage. The formula is: Percentage change (%) = (Change ÷ Original value) × 100 Step 1 — Find the change. Subtract the original value from the new value. Change = New value − Original value Step 2 — Divide the change by the original value. Step 3 — Multiply by 100 to convert the decimal to a percentage. If your answer is positive, it is a percentage increase (the value went up). If your answer is negative, it is a percentage decrease (the value went down). One important rule: you always divide by the ORIGINAL value — the number you started with — not the new value. Getting this wrong is the most common mistake. Worked Example: Last year a tree was 50 cm tall. This year it is 65 cm tall. What is the percentage increase in height? Step 1: Change = 65 − 50 = 15 cm Step 2: 15 ÷ 50 = 0.3 Step 3: 0.3 × 100 = 30% The tree grew by 30%. Because the answer is positive, it is a percentage increase. Now try a decrease: A shop had 200 items in stock. After a sale it has 150. What is the percentage decrease? Step 1: Change = 150 − 200 = −50 Step 2: −50 ÷ 200 = −0.25 Step 3: −0.25 × 100 = −25% The stock decreased by 25%. We state this as a 25% decrease.