How to use the percent change calculator
- Choose percent increase or decrease (old to new) or percent difference (two values with no direction).
- Enter the two values.
- Read the percent, the direction and the absolute change.
Formula
Percent change = (new - old) / |old| x 100
Percent difference = |a - b| / ((a + b) / 2) x 100
Percent change uses the old value as the base. Percent difference uses the average of the two values, so it is the same whichever number you list first.
Worked examples
Increase: 80 to 100. (100 - 80) / 80 = 0.25, which is a 25% increase.
Decrease: 100 to 80. (80 - 100) / 100 = -0.20, which is a 20% decrease. Going up 25% and then down 20% returns to the start, and that asymmetry is why percent changes are not reversible by the same number.
Difference: 80 and 100 have an average of 90, and the gap is 20, so the percent difference is 20 / 90 = 22.22%.
Change or difference?
Use percent change when one value comes before the other, such as last year and this year. Use percent difference when neither value is the reference, such as comparing two products or two measurements.
When the old value is negative or zero
A starting value of zero has no percent change because it would divide by zero. For a negative starting value, the change is divided by its absolute value so that a move upward still shows as positive. For finance such as losses, interpret those results carefully.
Percent change in everyday life
Use it for price increases, a change in your weight or score, website traffic or an investment statement. When the numbers are small to begin with, a big percentage can be a tiny absolute change. Going from 2 to 4 is a 100 percent increase but only 2 more.
Assumptions and limits
- The old value cannot be zero in change mode.
- In difference mode the two values cannot add up to zero.
- Results are shown to up to 6 decimal places.
Frequently asked questions
How do I calculate percent increase?
Subtract the old value from the new, divide by the old value and multiply by 100.
Why is a 50 percent drop followed by a 50 percent rise not break-even?
The second change applies to a smaller number. 100 falls to 50, then rises 50 percent to 75, not back to 100.
How is this related to a pay raise?
A raise is a percent increase. The pay raise calculator works from salary figures.