Percent Change Calculator
Enter an old and a new value to see the percent increase or decrease and the change in plain numbers. It also adds or takes off a percent and finds the percent difference.
Percent change from one number to another
From 80 to 100
25% increase
100 is 20 more than 80.
| Change: 100 − 80 | +20 |
|---|---|
| ÷ starting value (80) | +0.25 |
| × 100 = percent change | +25% |
Increase or decrease a number by a percent
80 increased by 25% is
100
| 25% of 80 | 20 |
|---|---|
| 80 + 20 | 100 |
| Same as 80 × 1.25 | 100 |
Percent difference between two numbers
Between 80 and 100
22.22%
The same in either order. It has no direction: it does not say which number is bigger.
| Difference: |80 − 100| | 20 |
|---|---|
| Average size: (80 + 100) ÷ 2 | 90 |
| 20 ÷ 90 × 100 | 22.22% |
How this is calculated
Percent change compares a new value with the starting value: (new − old) ÷ old × 100. From 80 to 100 that is (100 − 80) ÷ 80 × 100 = +25%. A positive result is an increase, a negative one a decrease.
The starting value matters. Going back from 100 to 80 is (80 − 100) ÷ 100 × 100 = −20%, not −25%. That is why a 25% raise followed by a 20% cut lands exactly where you started.
If the starting value is negative, the calculator divides by its size (the absolute value), so a rise still shows as an increase: from −50 to −25 is +50%. If the starting value is 0, there is no percent change, because that would mean dividing by zero. The calculator then shows the change in plain numbers.
Adding or taking off a percent
To increase 80 by 25%, multiply by 1 + 25 ÷ 100 = 1.25: the result is 100. To decrease 100 by 20%, multiply by 1 − 20 ÷ 100 = 0.8: the result is 80. A decrease of more than 100% gives a negative number.
Percent change or percent difference?
Use percent change when one value comes first: a price last year and this year, a weight before and after. Use percent difference when neither value is the starting point, such as the prices at two stores or two measurements of the same thing. It divides by the average of the two, so the order does not matter.
| Measure | Formula | Result |
|---|---|---|
| Percent change from 80 to 100 | (100 − 80) ÷ 80 × 100 | +25% |
| Percent change from 100 to 80 | (80 − 100) ÷ 100 × 100 | −20% |
| Percent difference of 80 and 100 | |80 − 100| ÷ 90 × 100 | 22.22% |
Percentage points are something else again. A rate that goes from 4% to 5% is up 1 percentage point, but up 25% as a percent change.
Questions people ask
How do you calculate percent change?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 50 to 65: 15 ÷ 50 × 100 = a 30% increase.
How do I calculate a percent decrease?
Use the same formula; the result comes out negative. From 120 to 90: (90 − 120) ÷ 120 × 100 = −25%, a 25% decrease.
What is the difference between percent change and percent difference?
Percent change divides by the starting value and has a direction. Percent difference divides by the average of the two values and has none. For 80 and 100 the change is +25% (or −20% the other way), the difference is 22.22%.
How do I add 20 percent to a number?
Multiply it by 1.2. For example, 45 plus 20% is 45 × 1.2 = 54. To take 20% off, multiply by 0.8.
Why does a 50% gain not undo a 50% drop?
The second percent is taken of a smaller number. 100 minus 50% is 50, and 50 plus 50% is 75. Getting back to 100 takes a 100% gain.
What is the percent change from 0?
It is not defined, because it would mean dividing by zero. Give the change in plain numbers instead, for example “up from 0 to 12”.