Quick answer: Percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase and a negative result is a decrease. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase. From 100 to 80 is (80 − 100) ÷ 100 × 100 = 20% decrease. The two differ because each is measured against a different starting value.
The percentage change formula
% change = (new − old) ÷ old × 100Always divide by the starting (old) value.Calculate a percentage change
Percentage increase
25%
Percentage increase, step by step
A price rises from $45 to $54
- Find the change: 54 − 45 = 9.
- Divide by the old value: 9 ÷ 45 = 0.2.
- Multiply by 100: 0.2 × 100 = 20.
Result: 20% increase
Percentage decrease, step by step
Monthly visitors fall from 12,500 to 9,800
- Find the change: 9,800 − 12,500 = −2,700.
- Divide by the old value: −2,700 ÷ 12,500 = −0.216.
- Multiply by 100: −21.6.
Result: 21.6% decrease
Why up and down are not symmetric
A 50% loss needs a 100% gain to recover: $100 falls to $50, and getting back to $100 is +$50 on a base of $50. The same logic explains why a 10% rise followed by a 10% fall leaves you 1% lower: 100 × 1.10 × 0.90 = 99.
| Drop | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 25% | 33.3% |
| 33.3% | 50% |
| 50% | 100% |
| 75% | 300% |
Other percentage calculations people mix up
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 240 = 36 |
| X is what percent of Y? | X ÷ Y × 100 | 36 is 15% of 240 |
| Increase Y by X% | Y × (1 + X ÷ 100) | 240 + 15% = 276 |
| Decrease Y by X% | Y × (1 − X ÷ 100) | 240 − 15% = 204 |
| Original before an X% increase | new ÷ (1 + X ÷ 100) | 276 ÷ 1.15 = 240 |
| Percentage difference (no old or new) | |A − B| ÷ ((A + B) ÷ 2) × 100 | 10 and 12: 18.18% |
Percent versus percentage points
When a rate moves from 4% to 5%, it rose by 1 percentage point, but by 25 percent, because (5 − 4) ÷ 4 = 0.25. Use percentage points for changes in rates such as interest, tax or unemployment rates, and percent for the relative change.
Percentage change in Excel and Google Sheets
// Old value in A2, new value in B2
=(B2-A2)/A2
// Format the cell as Percentage
// Undo an increase: original before B2% was added to A2
=A2/(1+B2)Mistakes to avoid
- Dividing by the new value. Always divide by the starting value.
- Adding percentages across periods. +10% and +10% is +21%, not +20%.
- Reversing a discount by adding it back. A 20% discount is undone by +25%, not +20%.
- Calling a rate change percent when it is points.
- Percentage change from zero. It is undefined; report the absolute change instead.
Frequently asked questions
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 50 to 65 is 15 ÷ 50 × 100 = 30%.
How do I calculate percentage decrease?
Use the same formula. The result is negative: from 65 to 50 is −15 ÷ 65 × 100 = −23.08%, a 23.08% decrease.
Why is a 20% decrease not reversed by a 20% increase?
Because the base changes. 100 minus 20% is 80, and 80 plus 20% is 96. You need 25% to get back to 100.
What is the difference between percent and percentage points?
Percentage points are the arithmetic difference between two rates. Percent is the relative change. 4% to 5% is 1 point, or 25%.
How do I find the original number before a percentage increase?
Divide by 1 plus the percentage as a decimal. After a 15% increase to 276, the original was 276 ÷ 1.15 = 240.
What is the Excel formula for percentage change?
=(B2-A2)/A2, formatted as a percentage.
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