Decreasing a number by a percentage means multiplying by one minus that percentage as a decimal. Taking 20% off 50 is 50 × 0.8, which is 40. The multiplier 0.8 is also the retained share, so the same single number tells you both what you removed and what is left.
The asymmetry between cuts and rises catches people out constantly. A 20% fall needs a 25% rise to recover, because the rise is measured against the smaller number. The larger the fall, the worse the asymmetry: a 50% drop needs a 100% gain, and a 90% drop needs 900%.
The formula
V- The starting value
p- The percentage decrease
1 − p ÷ 100- The retained multiplier
How it works, step by step
- Enter the value you are starting from.
- Enter the percentage you want to remove.
- The gauge shows what is left after the cut.
- Read the recovery percentage below to see what rise would restore the original.
Worked examples
Taking 20% off 50
The retained multiplier is 0.8, so the result is 40 and the saving is 10. To get back to 50 from 40 you would need a rise of 25%, not 20%.
A 35% clearance discount on 89.99
89.99 × 0.65 = 58.49, a saving of 31.50. Applying a further 35% staff discount to that price gives 38.02, not 30% of the original.
How to read your score
Frequently asked questions
Why does a 20% fall need a 25% rise to recover?
Because the rise is measured against the reduced value. Going from 40 back to 50 is a gain of 10 on a base of 40, which is 25%. Percentage changes are not symmetric.
Can two discounts be added together?
No. 20% off then 10% off is 0.8 × 0.9 = 0.72, a total discount of 28% rather than 30%. Stacked discounts always come to less than their sum.
What does a 100% decrease mean?
It reduces the value to exactly zero, since the multiplier becomes 0. Decreases greater than 100% are not meaningful for a quantity, which is why this page caps the input there.
How do I find the original price from a sale price?
Divide the sale price by the retained multiplier. A price of 40 after 20% off means 40 ÷ 0.8 = 50.
Discounts and the recovery they require
| Decrease | Multiplier | 100 becomes | Rise needed to recover |
|---|---|---|---|
| 5 | 0.95 | 95.00 | 5.26% |
| 10 | 0.90 | 90.00 | 11.11% |
| 15 | 0.85 | 85.00 | 17.65% |
| 20 | 0.80 | 80.00 | 25.00% |
| 25 | 0.75 | 75.00 | 33.33% |
| 30 | 0.70 | 70.00 | 42.86% |
| 40 | 0.60 | 60.00 | 66.67% |
| 50 | 0.50 | 50.00 | 100.00% |
| 60 | 0.40 | 40.00 | 150.00% |
| 75 | 0.25 | 25.00 | 300.00% |
| 90 | 0.10 | 10.00 | 900.00% |
The recovery figure is 1 divided by the retained multiplier, minus one.