How to Calculate Percentage Increase and Decrease
Percentage change = (new value − old value) ÷ old value × 100. If the result is positive it is an increase, if negative a decrease. For example, a price rising from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase, and falling from 100 to 80 is (80 − 100) ÷ 100 × 100 = 20% decrease.
The formula
Percentage change = (new − old) ÷ old × 100
- Subtract the old value from the new value to get the change.
- Divide the change by the old value.
- Multiply by 100. Positive means an increase; negative means a decrease.
Worked examples
| Situation | Calculation | Result |
|---|---|---|
| Rent rises from 1,200 to 1,290 | (1,290 − 1,200) ÷ 1,200 × 100 | 7.5% increase |
| Salary rises from 42,000 to 45,000 | (45,000 − 42,000) ÷ 42,000 × 100 | ≈ 7.14% increase |
| Phone price falls from 799 to 649 | (649 − 799) ÷ 799 × 100 | ≈ 18.8% decrease |
| Test score goes from 60 to 75 | (75 − 60) ÷ 60 × 100 | 25% increase |
Applying a percentage change
- Increase by P%: multiply by (1 + P ÷ 100). 250 + 8% = 250 × 1.08 = 270.
- Decrease by P%: multiply by (1 − P ÷ 100). 250 − 8% = 250 × 0.92 = 230.
Reverse percentages: finding the original value
If you know the value after a change, divide by the same multiplier instead of subtracting the percentage:
- A price of 120 that includes 20% tax: 120 ÷ 1.20 = 100 before tax (not 120 − 20% = 96).
- A sale price of 68 after 15% off: 68 ÷ 0.85 = 80 originally.
Mistakes to avoid
- Dividing by the new value. Always divide by the starting (old) value.
- Assuming increases and decreases cancel out. +50% then −50% turns 100 into 150 and then 75, not back to 100.
- Adding successive changes. Two 10% rises make 21% in total (1.10 × 1.10 = 1.21), not 20%.
- Confusing percent with percentage points. A rate moving from 4% to 5% is a 1 percentage point rise, which is a 25% increase in the rate.
Percentage difference vs percentage change
Percentage change compares a new value with an old one, so direction matters. Percentage difference compares two values with no "before" or "after", such as two shops' prices, and divides the gap by their average: |A − B| ÷ ((A + B) ÷ 2) × 100. For 40 and 50 that is 10 ÷ 45 × 100 ≈ 22.2%.
To skip the arithmetic, the percentage calculator works out each of these and shows the steps.
Frequently asked questions
What is the formula for percentage increase?
(New value − old value) ÷ old value × 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30% increase.
What is the formula for percentage decrease?
The same formula; the result is negative. From 65 to 50: (50 − 65) ÷ 65 × 100 ≈ −23.1%, a 23.1% decrease.
Why is going from 80 to 100 a 25% increase but 100 to 80 only a 20% decrease?
Because the change of 20 is divided by a different starting value each time: 20 ÷ 80 = 25%, but 20 ÷ 100 = 20%.
How do I increase a number by a percentage?
Multiply by (1 + percentage ÷ 100). 250 increased by 8% = 250 × 1.08 = 270.
How do I find the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). A price of 68 after a 15% discount was 68 ÷ 0.85 = 80.