Percentage Change: Increase and Decrease
How to calculate percentage increase and decrease with the percentage change formula, worked examples and the mistake to avoid.
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Frequently asked questions
What is the percentage change formula?
Percentage change = (new value − old value) ÷ old value × 100. A positive answer is an increase; a negative answer is a decrease.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30%.
How do I add a percentage to a number?
Multiply by 1 plus the percentage as a decimal. To add 15%, multiply by 1.15; to subtract 15%, multiply by 0.85.
Why is a 30% rise not cancelled by a 30% fall?
Because the base changes. A 30% rise from 50 gives 65, but a 30% fall from 65 gives 45.5 — not back to 50. Each percentage uses its own starting value.
Percentage Change: Increase and Decrease
Percentage change tells you how much a value has gone up or down, relative to where it started. It is the language of price rises, pay raises, discounts and growth rates.
The percentage change formula
Percentage change = (New value − Old value) ÷ Old value × 100. A positive result is an increase; a negative result is a decrease.
| From → To | Calculation | Change |
|---|---|---|
| 50 → 65 | (65 − 50) ÷ 50 × 100 | +30% (increase) |
| 80 → 60 | (60 − 80) ÷ 80 × 100 | −25% (decrease) |
| 200 → 250 | (250 − 200) ÷ 200 × 100 | +25% (increase) |
Applying an increase or decrease
To add 15% to a price, multiply by 1.15. To take 15% off, multiply by 0.85. The multiplier is 1 plus or minus the percentage written as a decimal.
The mistake to avoid
Always divide by the old (starting) value, not the new one. Going from 50 to 65 is a 30% increase, but going back from 65 to 50 is a 23% decrease — the percentages differ because the starting points differ.
Results are estimates for general guidance in Brazil and may not reflect the latest local rates, fees or rules. Check official sources before making decisions.