Three questions this calculator answers
- Increase a number: you know the number and the percent to add, for example a price that rises by 15%.
- Find the % increase: you know the old and the new value and want to know how much it grew.
- Find the original: you know the value after the increase and the percent it rose by, and want the starting value.
Formulas
New value = Old value × (1 + Percent ÷ 100)
Percent increase = (New value − Old value) ÷ Old value × 100
Original value = Final value ÷ (1 + Percent ÷ 100)
The number (1 + Percent ÷ 100) is the multiplier. A 15% increase has a multiplier of 1.15, and multiplying by it is the same as adding 15% in one step.
Examples
| Situation | Calculation | Result |
|---|---|---|
| 200 increased by 15% | 200 × 1.15 | 230 |
| Salary of 3,500 with an 8% raise | 3,500 × 1.08 | 3,780 |
| Rent of 1,800 up by 5% | 1,800 × 1.05 | 1,890 |
| Followers grow from 12,000 to 15,000 | (15,000 − 12,000) ÷ 12,000 | 25% increase |
Increases do not simply add up
Two increases of 10% in a row make 21%, not 20%. The second 10% is taken from the already larger number: 100 becomes 110, and 110 becomes 121. To apply several increases, multiply the multipliers, or run the calculator once for each step.
Working backwards
If a price is 230 after a 15% rise, the original was 230 ÷ 1.15 = 200. It is not 230 minus 15%, which would give 195.5. The percent was taken from the original, so you have to divide, not subtract.
If the value went down instead, use the percentage decrease calculator. For a neutral comparison in either direction, there is the percentage change calculator, and the guide explains the maths in detail.