Percentage Decrease
$$\text{Percentage Decrease} = \frac{\text{Old} - \text{New}}{\text{Old}} \times 100$$
What is Percentage Decrease?
A percentage decrease is a special case of percentage change where the new value is strictly less than the original. It expresses how much a quantity has fallen relative to its starting point: $$\text{Percentage Decrease} = \frac{\text{Old} - \text{New}}{\text{Old}} \times 100$$ The result is always a positive number representing the magnitude of the decline.
The original value always anchors the denominator. This means the largest possible percentage decrease is 100% — when a value falls to zero. A value cannot decrease by more than 100% of itself, because there is nothing left to remove. Statements like "profits fell 150%" are mathematically incoherent unless the starting value was already negative.
Because the base shifts after each change, percentage decreases do not undo percentage increases of the same magnitude. A 33.3% decrease exactly reverses a 50% increase, not a 33.3% increase. Reversing a percentage increase always requires a smaller percentage decrease.
When to use Percentage Decrease
Use percentage decrease when quantifying losses, declines, or reductions where the original (higher) value is the reference point. Pairing the percentage decrease with the absolute change prevents misreading — a 50% decrease on a small number is not the same impact as a 10% decrease on a large number.
Worked examples
| Original value | New value | Absolute decrease | Percentage decrease |
|---|---|---|---|
| $1,000 | $750 | $250 | 25.00% |
| 80,000 units | 60,000 units | 20,000 units | 25.00% |
| 5.0% rate | 3.5% rate | 1.5 pp | 30.00% |
| 200 calories | 150 calories | 50 calories | 25.00% |
| €4,800 | €0 | €4,800 | 100.00% |
Common pitfalls
A 100% decrease means the value has reached exactly zero — not below zero. If a quantity turns negative (a profit becomes a loss), the percentage decrease calculation breaks down conceptually. In such cases, report the absolute change and note the sign reversal explicitly.
Frequently asked questions
How do I find the original value after a percentage decrease?
If you know the new value and the percentage decrease, the original is: Original = New / (1 − Decrease% / 100). For example, if a price is $80 after a 20% decrease, the original was $80 / (1 − 0.20) = $80 / 0.80 = $100.
What percentage decrease reverses a 25% increase?
Use the reversal formula: Decrease% = P / (100 + P) × 100 = 25 / 125 × 100 = 20%. After a 25% increase from $100 to $125, a 20% decrease on $125 returns to $100. The reversal percentage is always smaller than the original increase.
Can you have a percentage decrease greater than 100%?
No, not when the original value is positive. A 100% decrease reduces the value to zero. Decreases beyond 100% imply a negative result, which requires a different framing — for example, a value crossing from positive to negative territory.