Formula
Percentage increase = ((New − Old) ÷ Old) × 100. The original value is always the denominator. A result above zero is an increase; below zero is a decrease.
How to use this calculator
Enter the original (old) value and the new value. The percentage increase appears instantly, along with the absolute change and a three-step breakdown of the calculation. If the new value is smaller than the original, the result will be negative — indicating a decrease.
Percentage increase formula
The percentage increase formula measures how much a value has grown relative to its starting point:
$$\% \text{ Increase} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100$$
The original value is always the denominator. Dividing by the new value is the single most common error in percentage increase calculations.
The formula produces a signed result: positive means an increase, negative means a decrease. The word "increase" describes a direction — if the result is negative, the quantity has decreased rather than increased.
Worked examples
Example 1: salary increase
A salary rises from 50,000 to 58,000. What is the percentage increase?
$$\frac{58{,}000 - 50{,}000}{50{,}000} \times 100 = \frac{8{,}000}{50{,}000} \times 100 = 16\%$$
The salary increased by 16%.
Example 2: product price change
A product was priced at 11.99 and is now 13.99. By how much has it increased?
$$\frac{13.99 - 11.99}{11.99} \times 100 = \frac{2.00}{11.99} \times 100 \approx 16.68\%$$
The price increased by approximately 16.68%. Note that despite the same absolute change (2.00), the percentage is different because the base (original price) is different.
Reverse: finding the new value after a known percentage increase
If you know the original value and the percentage increase and want to find the new value, rearrange the formula:
$$\text{New Value} = \text{Old} \times \left(1 + \frac{\%\text{ Increase}}{100}\right)$$
Example: What is 50,000 after a 16% increase?
$$\text{New} = 50{,}000 \times \left(1 + \frac{16}{100}\right) = 50{,}000 \times 1.16 = 58{,}000$$
The multiplier (1 + %/100) is the key: a 10% increase multiplies by 1.10, a 25% increase by 1.25, and a 100% increase by 2.00 (doubling the value).
Percentage increase vs. percentage change
Percentage change is the general term; percentage increase is a specific case where the result is positive. The formula is identical for both:
- Positive result → percentage increase (the value grew)
- Negative result → percentage decrease (the value fell)
- Zero result → no change
Percentage change should not be confused with percentage points. If an approval rating rises from 40% to 50%, it has risen 10 percentage points but increased by 25% relative to the original rating (10 ÷ 40 × 100 = 25%).
Percentage increase reference table
The multiplier for each percentage increase is the number you multiply the original value by to get the new value. This is useful for mental estimates.
| % Increase | Multiplier | Starting at 100 | Starting at 1,000 |
|---|---|---|---|
| 1% | × 1.01 | 101 | 1,010 |
| 5% | × 1.05 | 105 | 1,050 |
| 10% | × 1.10 | 110 | 1,100 |
| 20% | × 1.20 | 120 | 1,200 |
| 25% | × 1.25 | 125 | 1,250 |
| 50% | × 1.50 | 150 | 1,500 |
| 75% | × 1.75 | 175 | 1,750 |
| 100% | × 2.00 | 200 | 2,000 |
| 200% | × 3.00 | 300 | 3,000 |
| 1000% | × 11.00 | 1,100 | 11,000 |
Common mistakes
Using the new value as the denominator
The formula divides by the original value, not the new one. Dividing by the new value gives a smaller, incorrect result. In the salary example: (8,000 ÷ 58,000) × 100 = 13.8%, which understates the increase. The correct answer using the original value as the base is 16%.
Confusing percentage increase with percentage points
If a tax rate rises from 20% to 25%, it has increased by 5 percentage points. But the percentage increase in the tax rate itself is (5 ÷ 20) × 100 = 25%. These are different quantities. Percentage points measure an absolute gap between two percentages; percentage increase measures relative growth.
Treating sequential increases as additive
A 10% increase followed by another 10% increase is not a 20% increase overall. After the first 10%, the base is higher, so the second 10% acts on a larger number. Starting at 100: 100 × 1.10 = 110, then 110 × 1.10 = 121. The total increase is 21%, not 20%.
Frequently asked questions
What is the formula for percentage increase?
Percentage increase = ((New Value − Original Value) ÷ Original Value) × 100. The original (old) value is always the denominator.
How do you find the new value after a percentage increase?
Multiply the original value by (1 + percentage ÷ 100). A 16% increase on 50,000 gives 50,000 × 1.16 = 58,000.
Can percentage increase be more than 100%?
Yes. A 100% increase doubles the original value. A 200% increase triples it. There is no mathematical upper limit on percentage increase.
What is the difference between percentage increase and percentage points?
A percentage increase is relative — it measures growth relative to the original value. A percentage point is an absolute difference between two percentages. If an interest rate rises from 2% to 3%, that is a 1 percentage point rise but a 50% increase relative to the original rate.
Is percentage increase the same as percentage change?
Percentage change is the broader term that covers both increases (positive) and decreases (negative). The formula is identical. "Percentage increase" refers specifically to cases where the new value exceeds the original.
Does a 50% increase followed by a 50% decrease return to the original?
No. A 50% increase on 100 gives 150. A 50% decrease on 150 gives 75, not 100. Because the base changes between operations, increases and decreases of the same percentage are not symmetrical.