Percentage Change Calculator: Increase and Decrease
By Hesaplayıcı
The percentage change calculator finds by what percentage a value rose or fell from an old value to a new one. Enter the old and the new value. You get the percentage change, the difference and the ratio of the new value to the old one. A positive result is an increase, a negative one a decrease.
Worked example: A price went from 250 to 300: what is the percentage increase?
Percentage change
20.00%
- Difference (new − old)
- 50
- Ratio new / old
- 1.2
Step by step
Difference (new − old)
difference = new − old
difference = 300 − 250 = 50
Percentage change
percentage change = difference / |old| × 100
percentage change = 50 / 250 × 100 = 20.00%
Ratio new / old
ratio = new / old
ratio = 300 / 250 = 1.2
How to use
- Enter the Old value, the starting value. It cannot be zero.
- Enter the New value.
- Press Calculate. You get the percentage change, the difference and the ratio.
Formula
percentage change = (new − old) / |old| × 100difference = new − oldratio = new / old
Old is the starting value and new is the final value. |old| is the absolute value of the old value: it keeps an increase positive when the old value is negative. A ratio above 1 means the value went up, below 1 that it went down.
Worked example
The worked example on this page finds the percentage change of a price that went from 250 to 300. The steps give the difference, the percentage change and the ratio in turn.
Limits
When the old value is zero, the percentage change is undefined and the calculator returns an error. A change between two percentages is given in percent, not in percentage points. The calculator does not compute the symmetric percent difference, which divides by the mean of the two values, or a percentage of a number. The result is not rounded; the page shows the percentage with two decimals.
Frequently Asked Questions
How do you calculate a percentage change?
Subtract the old value from the new value, divide by the old value and multiply by 100. For example, going from 200 to 240 is (240 − 200) / 200 × 100 = a 20% increase.
Are a percentage increase and a percentage decrease symmetric?
No, because you always divide by the old value. Going from 200 to 240 is a 20% increase, but going from 240 back to 200 is a decrease of about 16.67%.
What is the difference between percent change and percentage points?
A percentage point is the difference between two percentages. A rise from 10% to 12% is 2 percentage points, and as a percentage change it is a 20% increase.
What if the old value is zero?
Division by zero is undefined, so there is no percentage change and the calculator returns an error. You can still compare the difference.
Calculation rules
- Percentage change = (new − old) / |old| × 100. A positive result is an increase, a negative one a decrease.
- When the old value is negative, its absolute value is the divisor, so an increase is still positive. When the old value is zero, the percentage change is undefined and the calculator returns an error.
- A change between two percentages is given in percent, not in percentage points: going from 10% to 12% is a 20% increase, or 2 percentage points.
- The result is not rounded; the page shows the percentage with two decimals.