Percentage decrease (often written percent decrease in the US) is (starting value − final value) ÷ starting value × 100. A price that falls from £750 to £590 has dropped by £160, and £160 is 21.33% of £750, so the decrease is 21.33%.
The starting value is always the number you divide by. Most wrong answers come from dividing by the other one.
What is the formula for percentage decrease?
percentage decrease = (starting value − final value) ÷ starting value × 100- Starting value is the number before the fall: the original price, last year’s figure, the weight you began at.
- Final value is the number after the fall.
- Both must be in the same unit. £750 and 590 euros cannot be compared until one is converted.
Statisticians use the same sum. Ireland’s Central Statistics Office divides the change in its consumer price index by the earlier figure, so (119.0 − 111.6) ÷ 111.6 × 100 = 6.6% is its inflation rate between May 2022 and May 2023. A fall works identically and simply comes out negative.
A worked example: £750 down to £590
- Find the fall. £750 − £590 = £160.
- Divide by the starting value. £160 ÷ £750 = 0.2133.
- Multiply by 100. 0.2133 × 100 = 21.33% (to two decimal places).
There is a shortcut that gives the same answer. Divide the final value by the starting value (590 ÷ 750 = 0.7867) and take the result away from 1. That works because the decrease and the share left always add up to 100%: 21.33% fell away, so 78.67% remains.
Try it with your own numbers
The calculator below opens with the same 750 and 590, so you will see 21.33%, a difference of −160 and 78.67% of the original left. Change either value and the figures update as you type.
What do other percentage decreases look like?
The same fall means different things from different starting points. A £50 drop is a 5% decrease from £1,000 but a 50% decrease from £100.
| Change | Difference | Decrease |
|---|---|---|
| 1,000 → 950 | −50 | 5% |
| 140 → 112 | −28 | 20% |
| 750 → 590 | −160 | 21.33% |
| 5,000 → 1,000 | −4,000 | 80% |
| 200 → 0 | −200 | 100% |
A value that falls to zero has always decreased by exactly 100%.
How do you take a percentage off a price?
When you know the percentage and want the new figure, multiply the starting value by 1 minus the percentage as a decimal. That decimal is the multiplier.
final value = starting value × (1 − percentage ÷ 100)- 25% off £80: the multiplier is 0.75, and £80 × 0.75 = £60.
- 20% off £750: the multiplier is 0.8, and £750 × 0.8 = £600.
The percentage calculator does this sum with its “A decreased by B%” option. For stacked offers such as “20% off, then a further 10% off” and for sales tax, use the discount calculator.
How do you find the original price after a percentage decrease?
Divide the reduced price by the share that is left. You cannot take the percentage off the sale price, because the sale price is already the result of the decrease.
starting value = final value ÷ (1 − percentage ÷ 100)A coat costs £60 after 25% off. That leaves 75% of the original, so the original was £60 ÷ 0.75 = £80.
Why does a 25% rise not undo a 25% fall?
Because the rise is measured from a smaller number. £80 falls 25% to £60. A 25% rise on £60 adds £15 and gets you to £75. To return to £80 you need to add £20, which is 33.33% of £60.
The rise needed to recover is the fall divided by what is left, times 100, and it grows quickly as the fall gets bigger:
| Fall | Rise needed to recover |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 50% | 100% |
| 80% | 400% |
A price that halves has to double to get back. You can confirm any row in the percentage increase calculator: from 50 to 100 is a 100% increase.
Do two percentage decreases add up?
No, for the same reason. Take 20% off 100 and you have 80. Take another 20% off that and you have 64, not 60, because the second 20% is of 80.
Overall that is a 36% decrease, not 40%. The quick way is to multiply the multipliers: 0.8 × 0.8 = 0.64, and 1 − 0.64 = 0.36.
What mistakes should you avoid?
- Dividing by the wrong number. £160 ÷ £590 gives 27.12%, which is the increase from £590 back up to £750. The decrease from £750 is 21.33%.
- Mixing up percentages and percentage points. A rate that falls from 5% to 4% has dropped 1 percentage point, and that is also a 20% decrease. Both are correct; they answer different questions.
- Starting from zero. Dividing by zero is undefined, so no percentage decrease can be measured from a starting value of zero.
- Expecting more than 100%. An ordinary fall stops at 100%. Only a value that passes below zero can go beyond it: from 200 to −50 is a 125% decrease.
What is the difference between percentage decrease and percentage change?
Percentage change is the same sum with the sign kept. Per the mathcentre guide, a negative answer is a decrease: you drop the minus sign and call it a percentage decrease, and a positive answer is an increase.
If you know the value fell, use the percentage decrease calculator. If you are not sure which way it moved, the percentage change calculator works it out and says so.
What to do next
Enter your own starting and final values in the percentage decrease calculator to see the decrease, the amount lost and the share left. To price a sale, try the discount calculator, and to see what it takes to win the loss back, use the percentage increase calculator.
Frequently asked questions
How do you calculate percentage decrease?
How do you find the original price before a percentage decrease?
What is the difference between a percentage decrease and a percentage point decrease?
Do two percentage decreases add together?
Can a percentage decrease be more than 100%?
Sources: Central Statistics Office (Ireland): How to calculate a percentage change, mathcentre: What is the change in percentage?.