A percentage decrease compares a new number with an old one, as a share of the old one. It’s the way price changes, pay rises, population growth and exam improvements are usually reported.
You can go either way: find the drop between two numbers, or take a percentage off one.
How to use the Percentage Decrease Calculator#
- Choose a mode. Find a percentage between two numbers, or apply a percentage to one.
- Enter your numbers. Type the original value and either the new value or the percentage.
- Read the result. The result also shows the amount of the change.
The formula#
A change from 100 to 80 is 20 percent. Divide the change by the original value and multiply by 100. To apply a percentage, multiply the original by 1 - the percentage as a decimal.
Why the starting value matters#
A percentage always depends on what it’s measured against. A fall of 20 percent followed by a rise of 20 percent doesn’t get you back to where you started: 100 falls to 80, then rises to 96. To undo a 20 percent fall you need a 25 percent rise. This catches out a lot of people when they read headlines about gains and losses.
Related calculators#
For a plain percentage of a number, use the percentage calculator. For the opposite change, try the percentage increase calculator.
Recovering from a fall#
A fall needs a bigger rise to undo it, because the rise is measured from a smaller number.
| Fall | Rise needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 30% | 42.9% |
| 50% | 100% |
The same idea applies to prices, savings and share values. The formula is 1 ÷ (1 − fall) − 1, with the fall written as a decimal.
Why a loss needs a bigger gain to recover#
A fall of 50 percent needs a rise of 100 percent to get back to where you started. That is because the gain is measured against the smaller, reduced figure. If a share falls from 200 to 100, you must double it to return to 200. The table below shows the gain needed to undo each fall.
| Fall | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25.0% |
| 25% | 33.3% |
| 33.3% | 49.9% |
| 50% | 100.0% |
| 75% | 300.0% |
| 90% | 900.0% |
The formula for the recovery is 1 ÷ (1 − fall) − 1. A fall of 20 percent needs 1 ÷ 0.8 − 1 = 25 percent. This is why investors and business owners worry more about large drops than the percentage might suggest.
Repeated decreases#
Percentage decreases compound. If a price drops 10 percent a year for three years, the result is not 30 percent lower. It is 1 − 0.9³ = 27.1 percent lower. A car that loses 15 percent of its value each year has 0.85⁵ = 44.4 percent of its original value after five years, a fall of 55.6 percent. If a population shrinks by 2 percent a year, it takes about 35 years to fall by half, and the number you get by repeated multiplication is always more accurate than adding the percentages.
Everyday uses#
- Discounts and sale prices: use the percent off calculator for stacked offers.
- Falling sales, costs or website traffic, month on month.
- Weight loss, where a drop from 90 kg to 81 kg is 10 percent.
- Depreciation of equipment and vehicles.
If the new value is higher than the original, the calculator reports an increase instead. For growth in the other direction, see the percentage increase calculator.
Frequently asked questions#
Subtract the old value from the new value, divide by the old value and multiply by 100.
A decrease can’t go beyond 100 percent, because that would take the value below zero.
The percentage change is undefined.
Multiply the original by 1 plus or minus the percentage as a decimal.
No. A 50 percent increase takes 100 to 150, but a 50 percent decrease takes 150 back to 75, not 100. To undo a 50 percent increase you need a fall of one third, and to undo a 50 percent decrease you need a rise of 100 percent. Percent changes are always relative to the current value.