The percentage decrease formula
To measure a decrease, take the gap between the old and new values and divide it by the old value: (old − new) ÷ old × 100. A coat marked down from 80 to 60 fell by (80 − 60) ÷ 80 × 100 = 25%.
To apply a decrease, multiply by 1 minus the percentage as a decimal: new = old × (1 − percent ÷ 100). Taking 25% off 80 is 80 × 0.75 = 60.
Why a 50% fall then a 50% rise does not bring you back
Suppose 100 falls by 50% to 50. A 50% rise on 50 adds only 25, so you reach 75, not 100. The rise is a share of the smaller number, so it has to be bigger to cover the same distance. To get back from 50 to 100 you need a 100% rise.
The deeper the fall, the harder the climb back:
- A 10% fall needs an 11.11% rise.
- A 20% fall needs a 25% rise.
- A fall of one third (33.33%) needs a 50% rise.
- A 50% fall needs a 100% rise.
- A 75% fall needs a 300% rise.
- A 90% fall needs a 900% rise.
The formula is fall ÷ (100 − fall) × 100. The calculator above works it out for the numbers you enter and shows it under the answer.
Falls that follow each other
Two 10% falls in a row take 100 to 90 and then to 81, a 19% fall in total, not 20%. An investment that loses 30% and then gains 30% ends at 100 × 0.7 × 1.3 = 91, which is 9% below where it started.
For the opposite direction, see the percentage increase calculator. For a fall between two known values, the percentage change calculator does the sum for you.