How it’s calculated
Percentage change is the difference between the new and original amounts, as a percentage of the original amount. Over several periods, the compound average growth rate is the steady rate that gets from the first value to the last.
Example (OpenStax Prealgebra): fees rose from 26 to 36 per unit. The increase is 10, and 10 ÷ 26 = 38.5%. A fall from 3.71 to 3.64 is a decrease of 0.07 ÷ 3.71 = 1.9%.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 = 25%.
Why isn’t a 20% drop undone by a 20% rise?
Each percentage applies to a different base. 100 down 20% is 80, and 80 up 20% is only 96. You would need a 25% rise to get back to 100.
What is the difference between percentage change and percentage points?
A margin moving from 10% to 12% is a 2 percentage-point rise but a 20% increase in the margin itself.
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Sources
- Prealgebra 2e, 6.2: Solve General Applications of Percent (percent increase and decrease) — OpenStax
- Principles of Finance, 15.1: Risk and Return to an Individual Asset (geometric average return) — OpenStax
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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