How it works
Percentage change tells you how much a value grew or shrank compared with where it started. It is used for price rises, salary increases, sales growth, weight loss, exam scores and stock returns. The starting value is always the base.
percentage change = (new − old) ÷ |old| × 100 increase by p% = value × (1 + p ÷ 100) · decrease by p% = value × (1 − p ÷ 100)Worked examples. A price going from 80 to 100 is a +25% increase (20 ÷ 80). Going back from 100 to 80 is a −20% decrease (20 ÷ 100). A salary of 4,000 raised by 7.5% becomes 4,300.
Why up and down are not symmetric
Because the base changes, a 25% rise followed by a 20% fall brings you back to the start, while a 50% fall needs a 100% rise to recover. Two changes of +10% and −10% leave you 1% lower (1.1 × 0.9 = 0.99). Multiply the factors, never add the percentages.
| Fall | Rise needed to recover |
|---|---|
| −10% | +11.1% |
| −20% | +25% |
| −25% | +33.3% |
| −50% | +100% |
Percentage change vs percentage points
If an interest rate moves from 4% to 5%, it rose by 1 percentage point but by 25 percent. News reports often mix the two. The calculator gives the percent change; the plain difference is shown in the first row.
Percentage change vs difference
Use percentage change when there is a clear before and after. When two values are simply compared with no direction — two shops’ prices, two lab measurements — use the percentage difference calculator, which divides by the average.
For “what is X% of Y” questions, use the percentage calculator. For prices and profit, try the margin calculator.