Enter an original value and a new value to calculate the percentage change.
Percentage Change Formula & Examples
Percentage increase is (new − old) ÷ old × 100, so a rise from $50,000 to $55,000 is a 10% increase. To increase a number by a percent, multiply it by 1 plus the percent as a decimal: 20% more than 85 is 85 × 1.20 = 102. The calculator above also shows the multiplier and the decrease that would undo the change.
The percentage increase formula measures how much a value has grown relative to its original amount. It is used everywhere: salary raises, price changes, population growth, stock returns, and test score improvements.
Formula: Percentage Change = ((New Value − Old Value) / |Old Value|) × 100. A positive result is a percentage increase; a negative result is a percentage decrease.
Percentage Increase Formula
Percentage Decrease Formula
Multiplier Method
Compound Percentage Changes
Percentage Increase Multiplier Table
Multiply by the multiplier to apply the increase. The last column is the decrease that takes the new value back to where it started.
| Increase | Multiplier | $100 becomes | $2,500 becomes | Decrease to undo |
|---|---|---|---|---|
| 1% | 1.01 | $101 | $2,525 | 0.99% |
| 2% | 1.02 | $102 | $2,550 | 1.96% |
| 3% | 1.03 | $103 | $2,575 | 2.91% |
| 5% | 1.05 | $105 | $2,625 | 4.76% |
| 7.5% | 1.075 | $107.50 | $2,687.50 | 6.98% |
| 10% | 1.10 | $110 | $2,750 | 9.09% |
| 15% | 1.15 | $115 | $2,875 | 13.04% |
| 20% | 1.20 | $120 | $3,000 | 16.67% |
| 25% | 1.25 | $125 | $3,125 | 20% |
| 50% | 1.50 | $150 | $3,750 | 33.33% |
| 75% | 1.75 | $175 | $4,375 | 42.86% |
| 100% | 2.00 | $200 | $5,000 | 50% |
| 200% | 3.00 | $300 | $7,500 | 66.67% |
| 300% | 4.00 | $400 | $10,000 | 75% |
Worked Examples
A pay raise
Your salary rises from $62,400 to $65,520. The increase is $3,120, and 3,120 ÷ 62,400 × 100 = 5%.
A rent increase
Rent goes from $1,450 to $1,595 a month. That is $145 more, and 145 ÷ 1,450 × 100 = 10%. Over a year you pay $1,740 more.
An increase above 100%
A share price climbs from $5 to $50. The gain is $45, and 45 ÷ 5 × 100 = 900%. The price is 10 times higher, which is a 900% increase, not 1,000%.
Adding a percent to a number
To add 8.25% to $240, multiply by 1.0825: $240 × 1.0825 = $259.80. The same method adds sales tax, a markup or a cost of living adjustment in one step.
Repeated Increases Compound
When a value rises by the same percent every year, each rise applies to a larger base, so the total grows faster than the yearly rate times the number of years.
| Yearly increase | After 1 year | 2 years | 3 years | 5 years | 10 years |
|---|---|---|---|---|---|
| 3% | 3% | 6.09% | 9.27% | 15.93% | 34.39% |
| 5% | 5% | 10.25% | 15.76% | 27.63% | 62.89% |
| 7% | 7% | 14.49% | 22.50% | 40.26% | 96.72% |
Ten years of 5% increases add up to 62.89%, not 50%. A handy check is the rule of 72: divide 72 by the yearly percent to estimate how many years it takes to double. At 6% that gives 12 years; the exact figure is 11.9. To go the other way and find the average yearly rate from a total change, use the CAGR formula in the FAQ below, or the percentage change calculator for single steps.
A start value of 0 has no percentage increase, because the formula divides by zero. The calculator tells you so and shows the absolute change instead.