Percent change measures how much a quantity grew or shrank relative to where it started. OpenStax defines percent increase as the amount of increase as a percent of the original amount, and percent decrease the same way using the amount of decrease. The original value is always the base.
Formula
percent change = (new − original) ÷ original × 100
- new: the value after the change.
- original: the starting value, also the denominator.
Example
Moving from 26 to 36 is an increase of 10, and 10 ÷ 26 = 0.385, a 38.5% increase. A price falling from $3.71 to $3.64 is a decrease of $0.07, and 0.07 ÷ 3.71 = 0.019, a 1.9% decrease.
Common mistakes
- Dividing by the new value. Percent change always divides by the original.
- Expecting a rise and fall of the same percent to cancel. A 20% rise from 100 gives 120, and a 20% fall from 120 gives 96.
The step-by-step method, including reverse percentages, is in the how to calculate a percentage guide, and the percentage calculator computes percent change directly.