Compound Growth Rate Calculator
Solve for the constant per-period growth rate that takes a starting value to an ending value over a number of periods.
How it works
rate = (ending / beginning)^(1 / periods) − 1 · expressed as a percentage per period
The compound (geometric) growth rate is the single constant rate that, applied every period, turns the starting value into the ending value. It answers "what steady rate would produce this overall change?" — smoothing out the bumps along the way. Because compounding multiplies rather than adds, the maths uses the nth root of the total ratio, not a simple average of period-by-period changes.
Worked example
A value that grows from 100 to 200 over 10 periods has a total ratio of 2. The compound rate is 2^(1/10) − 1 ≈ 0.07177, or about 7.18% per period — noticeably below the 10% you would get by naively dividing the 100% total change by 10 periods.
Frequently asked questions
How is this different from a simple average growth rate?
A simple average adds up per-period changes and divides, ignoring compounding. The compound rate accounts for growth building on prior growth, which is why it is lower than the naive total-change-over-periods figure and is the correct rate for anything that compounds.
Does the unit matter — years, months, days?
No. The rate is "per period" in whatever unit you counted periods. Ten yearly periods give an annual rate; ten monthly periods give a monthly rate. Just keep the period consistent.
What if the ending value is smaller than the beginning?
Then the ratio is below 1 and the rate comes out negative, representing a compound rate of decline. The formula handles shrinkage and growth the same way.
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Educational math tool, not financial advice.