How to Calculate Percentage Decrease (Formula + Examples)
The formula: Percentage Decrease = ((Old − New) ÷ Old) × 100. Always divide by the original (old) value.
The standard formula
Three steps:
- Subtract: Old − New gives you the size of the drop.
- Divide: Divide the drop by the original (old) value.
- Multiply by 100: Convert the decimal to a percentage.
Worked example: a price drop
A jacket that was $120 is now on sale for $90. What's the percentage decrease?
- $120 − $90 = $30 (the size of the discount)
- $30 ÷ $120 = 0.25
- 0.25 × 100 = 25% off
The jacket is 25% off its original price.
Five more real-world percentage-decrease scenarios
Weight loss
Started at 200 lbs, now at 180 lbs:
(200 − 180) ÷ 200 × 100 = 20 ÷ 200 × 100 = 10% body weight lost
Stock price drop
A stock went from $80 to $60:
(80 − 60) ÷ 80 × 100 = 20 ÷ 80 × 100 = 25% drop
Quarterly revenue decline
Q3 revenue: $1.2 million. Q4 revenue: $900,000.
(1,200,000 − 900,000) ÷ 1,200,000 × 100 = 300,000 ÷ 1,200,000 × 100 = 25% revenue decline
Energy cost reduction
Monthly electric bill dropped from $150 to $105 after installing LED bulbs:
(150 − 105) ÷ 150 × 100 = 45 ÷ 150 × 100 = 30% lower bill
Population decline
A small town's population fell from 5,000 to 4,250 over a decade:
(5,000 − 4,250) ÷ 5,000 × 100 = 750 ÷ 5,000 × 100 = 15% population decline
The trap: percentage decrease is NOT symmetrical with percentage increase
If something drops 50%, then rises 50%, you'd think it's back to where it started. It isn't.
Example: a $100 stock drops 50% to $50. Then it rises 50% — but 50% of $50 is $25, so the stock is now $75, not $100. To recover from a 50% drop, you actually need a 100% gain.
This asymmetry hurts investors who panic-sell during downturns. The percentage gain needed to recover from any drop is always larger than the drop itself:
| Drop | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 33% | 50% |
| 50% | 100% |
| 75% | 300% |
| 90% | 900% |
Finding the new value if you only know the percentage
If you know the percentage decrease and the old value, you can find the new value directly:
Examples:
- $200 with 30% off: 200 × (1 − 0.30) = 200 × 0.70 = $140
- $500 with 15% drop: 500 × 0.85 = $425
- $80 with 25% off: 80 × 0.75 = $60
Negative numbers and the "decrease of a decrease"
What if a value drops below zero? The formula still works, but interpretation gets tricky. A drop from $100 to −$50 (debt) is technically a 150% decrease. In business reporting, you'd usually phrase this differently: "swung from a $100 profit to a $50 loss" is clearer than "150% decline."
Frequently asked questions
What's the difference between "20% off" and "20% lower"?
Both mean the same thing — a 20% percentage decrease from the original. "20% off" is retail language; "20% lower" or "20% decrease" is the analytical equivalent.
Can a percentage decrease be greater than 100%?
Only if the new value goes negative (the original was a positive amount and we now have a debt or deficit). For non-negative values like prices, weight, or temperature-in-Kelvin, the maximum decrease is 100% — that means the value is now zero.
How do I calculate the percentage decrease for multiple sequential drops?
Don't add the percentages. Multiply (1 − drop) for each one. Two consecutive 20% drops: 1 × 0.8 × 0.8 = 0.64, so the total is 36% lower, not 40%. This is the same multiplicative math as stacked discounts.
Why do news headlines often misreport percentage changes?
Two common errors: confusing percentage points with percentages (a tax rate going from 20% to 22% is a "2 percentage point" increase but a "10% relative" increase), and dividing by the new value instead of the old. Both distort the magnitude of the change.
Skip the math
The percentage calculator handles percentage change in either direction — just enter the old and new values. For retail-specific scenarios, the discount calculator shows the final price and savings side by side. For investment scenarios, the compound interest calculator reveals how compounding decreases (negative returns) eat into your principal.