This percentage increase and decrease calculator handles four related questions: the percent change from one value to another, how to increase or decrease a number by a percentage, the percent difference between two values, and how to find the original value before a percentage change. Each result shows the working, so you can check it or do it by hand.
1. Percent change from one value to another
2. Increase or decrease a number by a percentage
3. Percent difference between two values
4. Original value before a percentage change
Percentage Increase Formula
Percent increase = (New value − Original value) ÷ Original value × 100
Example: rent goes up from $1,200 to $1,350 a month. (1,350 − 1,200) ÷ 1,200 × 100 = 12.5% increase.
Percentage Decrease Formula
Percent decrease = (Original value − New value) ÷ Original value × 100
Example: a stock falls from $120 to $90. (120 − 90) ÷ 120 × 100 = 25% decrease.
Both are the same formula. If the result is positive it is an increase, and if it is negative it is a decrease.
Increasing or Decreasing a Number by a Percentage
Multiply by 1 plus the percentage (as a decimal) for an increase, or 1 minus it for a decrease:
- Increase 80 by 15%: 80 × 1.15 = 92
- Decrease 200 by 35%: 200 × 0.65 = 130
Finding the Original Value
To reverse a percentage change, divide by the same factor. Do not subtract the percentage from the new value.
- A price is $120 after a 20% increase. The original was 120 ÷ 1.20 = $100, not $96.
- A jacket costs $60 after 25% off. The original price was 60 ÷ 0.75 = $80.
Percent Change vs Percent Difference
Percent change compares a new value with an original value, so the direction matters. Going from 40 to 60 is a 50% increase, but going from 60 to 40 is a 33.3% decrease.
Percent difference compares two values when neither is the “original”, such as two prices from different stores. It divides the difference by the average of the two values: |40 − 60| ÷ 50 × 100 = 40%, whichever order you enter them in.
Percentage points vs percent: if an interest rate rises from 4% to 5%, it has increased by 1 percentage point, which is a 25% increase in the rate itself.
Why a 50% Drop Needs a 100% Gain to Recover
Percent changes are measured from different starting values, so they are not symmetric. If an investment falls 50% from $1,000 to $500, it then needs to rise 100% to get back to $1,000. A 10% rise followed by a 10% fall leaves you with 99% of where you started: 100 × 1.10 × 0.90 = 99.
Frequently Asked Questions
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original value, and multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100 = 30%.
How do I calculate percentage decrease?
Subtract the new value from the original, divide by the original, and multiply by 100. From 120 to 90 is a 25% decrease.
How do I add a percentage to a number?
Multiply the number by 1 plus the percentage as a decimal. Adding 15% to 80 is 80 × 1.15 = 92.
How do I find the original price before a percentage increase?
Divide the new price by 1 plus the percentage as a decimal. $120 after a 20% increase was originally 120 ÷ 1.2 = $100.