Formula
Percentage decrease = ((Old − New) ÷ Old) × 100. The original value is always the denominator. A positive result means the value fell; a negative result means it actually rose.
How to use this percentage decrease calculator
Enter the original (old) value and the new value. The percentage decrease appears instantly, along with the absolute change and a three-step breakdown of the calculation. If the new value is larger than the original, the result will be negative - indicating the value increased rather than decreased.
Explained to a beginner
Picture a jacket on sale: it was $100 last week, now $75. The price dropped $25. To find the percentage decrease, ask what fraction of the original $100 the price fell - $25 out of $100 is 25%. The formula does exactly this: divide the drop by the original, then multiply by 100. The critical detail is always dividing by the original price, not the sale price.
Percentage decrease formula
The percentage decrease formula measures how much a value has fallen relative to its original level:
$$\% \text{ Decrease} = \frac{\text{Old} - \text{New}}{\text{Old}} \times 100$$
The original value is always the denominator. The numerator is (Old − New), so when the new value is smaller, the result is positive - confirming a real decrease. This is the mirror of the percentage increase formula, which uses (New − Old) in the numerator.
Worked examples for percentage decrease
Example 1: price reduction
A product price falls from 200 to 150. What is the percentage decrease?
$$\frac{200 - 150}{200} \times 100 = \frac{50}{200} \times 100 = 25\%$$
The price decreased by 25%.
Example 2: retail discount
A jacket is originally priced at 89.99 and is on sale for 62.99. What is the discount percentage?
$$\frac{89.99 - 62.99}{89.99} \times 100 = \frac{27.00}{89.99} \times 100 \approx 30.0\%$$
The discount is approximately 30%. Note that "30% off 89.99" gives 89.99 × 0.70 = 62.99, confirming the calculation.
Reverse: finding the new value after a known percentage decrease
If you know the original value and the percentage decrease and want to find the reduced value:
$$\text{New Value} = \text{Old} \times \left(1 - \frac{\%\text{ Decrease}}{100}\right)$$
Example: What is 200 after a 25% decrease?
$$\text{New} = 200 \times \left(1 - \frac{25}{100}\right) = 200 \times 0.75 = 150$$
The multiplier (1 − %/100) is the key: a 10% decrease multiplies by 0.90, a 25% decrease by 0.75, and a 50% decrease by 0.50 (halving the value).
Decrease and increase are not symmetrical
A common misconception is that a percentage decrease and a percentage increase of the same magnitude cancel each other out. They do not, because the base changes between operations.
Example: Start at 100. A 20% decrease gives 80. A 20% increase on 80 gives 96, not 100. To return to the original after a 20% decrease, you need a 25% increase - because 80 × 1.25 = 100.
In general, to reverse a P% decrease you need an increase of P ÷ (100 − P) × 100 percent. For a 20% decrease: 20 ÷ 80 × 100 = 25%.
When I review quarterly performance reports for investing, this asymmetry is the most consistent source of errors. A team will report that results "recovered" after matching last quarter's percentage drop with the same percentage gain - but the figures are still below the starting point.
Running the multiplier takes five seconds and immediately shows the gap: 0.80 × 1.20 = 0.96, not 1.00.
Percentage decrease reference table
The multiplier for each percentage decrease is the number you multiply the original value by to get the reduced value.
The table below shows different examples to better understand this.
| % Decrease | Multiplier | Starting at 100 | Starting at 1,000 | Reverse increase needed |
|---|---|---|---|---|
| 1% | × 0.99 | 99 | 990 | ~1.01% |
| 5% | × 0.95 | 95 | 950 | ~5.26% |
| 10% | × 0.90 | 90 | 900 | ~11.11% |
| 20% | × 0.80 | 80 | 800 | 25% |
| 25% | × 0.75 | 75 | 750 | ~33.33% |
| 50% | × 0.50 | 50 | 500 | 100% |
| 75% | × 0.25 | 25 | 250 | 300% |
| 90% | × 0.10 | 10 | 100 | 900% |
Common mistakes when calculating percentage decrease
Using the new value as the denominator
The formula divides by the original value. Using the new value produces a larger, incorrect result. In the price example: (50 ÷ 150) × 100 = 33.3%, which overstates the decrease. The correct answer is 25% (dividing by the original 200).
Assuming a percentage decrease can exceed 100%
A percentage decrease is bounded at 100% - that is when the new value reaches zero. Values that go negative represent a different type of change (sign reversal) and are outside the normal domain of percentage decrease.
Confusing the decrease percentage with the remaining percentage
A 30% decrease leaves 70% of the original value. These two numbers (30 and 70) are complements that sum to 100. Confusing the decrease percentage with the remaining fraction is a common error in discount calculations.
When I spot a percentage decrease that looks suspiciously large, the denominator is the first thing I check. Dividing by the new value instead of the original always inflates the result - in the 200-to-150 example, that mistake turns a 25% decrease into a 33% one.
Frequently asked questions about percentage decrease
What is the formula for percentage decrease?
Percentage decrease = ((Original − New) ÷ Original) × 100. The original value is always the denominator.
How do you find the new value after a percentage decrease?
Multiply the original value by (1 − percentage ÷ 100). A 25% decrease on 200 gives 200 × 0.75 = 150.
Can a percentage decrease exceed 100%?
No. A 100% decrease reduces the value to exactly zero. Percentage decreases are bounded between 0% and 100% for positive starting values.
Is a 50% decrease followed by a 50% increase the same as the start?
No. A 50% decrease on 100 gives 50. A 50% increase on 50 gives 75, not 100. To return to the original after a 50% decrease, you need a 100% increase.
What is the difference between percentage decrease and percentage change?
Percentage change covers both increases and decreases in one formula with a signed result. Percentage decrease uses (Old − New) in the numerator, making it positive when the value falls. They use the same underlying formula, framed differently.
How do you calculate a discount percentage?
Subtract the sale price from the original price, divide by the original price, and multiply by 100. A product marked down from 90 to 63 has a discount of (27 ÷ 90) × 100 = 30%.
Quiz: how well do you know percentage decrease?
1. In the percentage decrease formula, what value is always the denominator?
2. A jacket originally costs $89.99 and is on sale for $62.99. What is the discount percentage?
3. A value drops by 20% and then rises by 20%. Where does it end up relative to the original?
4. According to the reference table, what multiplier do you apply to find a value after a 25% decrease?
5. What is the maximum possible percentage decrease for a positive starting value?