What you can work out
- Decrease a number: subtract a percent from a value, such as a 30% drop in price.
- Find the % decrease: compare an old and a smaller new value, such as weight before and after a diet.
- Find the original: recover the starting value from the reduced value and the percent it fell by.
Formulas
New value = Old value × (1 − Percent ÷ 100)
Percent decrease = (Old value − New value) ÷ Old value × 100
Original value = Final value ÷ (1 − Percent ÷ 100)
Examples
| Situation | Calculation | Result |
|---|---|---|
| 200 reduced by 15% | 200 × 0.85 | 170 |
| A phone of 800 down by 30% | 800 × 0.70 | 560 |
| Weight of 90 kg reduced by 10% | 90 × 0.90 | 81 kg |
| A share falls from 50 to 40 | (50 − 40) ÷ 50 | 20% decrease |
Why recovering a loss takes a bigger percent
A decrease and the increase that undoes it are not the same percent, because they use different bases. If 100 falls by 50% it becomes 50, and to get back to 100 it must rise by 100%. A 20% drop needs a 25% rise to recover, and a 10% drop needs about 11.1%.
Limits
A decrease of 100% leaves zero. A decrease above 100% takes the value below zero, which is only meaningful for quantities that can be negative, such as a bank balance. In reverse mode, a 100% decrease cannot be undone, because the final value is always zero whatever the original was.
For growth, use the percentage increase calculator. If you only have a before and an after and do not mind the direction, the percentage change calculator handles both. Shop prices are easier in the percent off calculator, which also adds tax and a second discount.