Compound growth rate connects starting and ending values through a constant rate per period; the period unit determines how the result is interpreted.
A compound growth rate is the constant rate per period that would turn a starting value into an ending value through repeated compounding. It can describe changes in revenue, earnings, an investment value, or another consistently measured quantity.
The period is essential: a monthly rate is not an annual rate. When time is measured in years, the calculation is called the compound annual growth rate, or CAGR. The rate summarizes the endpoints; it does not establish a steady historical path or predict future growth.
For positive beginning value V_0, positive ending value V_n, and n elapsed periods:
This follows by rearranging the compounding relationship:
Use n = 12 for twelve monthly intervals, n = 4 for four quarterly intervals, or n = 1 for one year. Those choices give different period rates for the same endpoint change.
Excel’s RRI(nper, pv, fv) implements the equivalent-rate calculation from a period count and two values. Its result has the same period unit as nper. Microsoft: RRI Function.
Suppose a company’s quarterly revenue rises from $100 million in the first quarter of Year 1 to $121 million in the first quarter of Year 2. There are four quarterly intervals, even though a complete sequence would contain five observations.
The compound quarterly growth rate is:
The total increase is 21%. Because the endpoints are one year apart, the annual compound growth rate is also 21%.
That does not mean revenue increased by exactly 4.88% every quarter. Some intervening quarters could have declined. It also does not mean shareholders earned 21%: revenue, profit, cash flow, and share-price performance are different quantities.
If g_q is a quarterly compound rate, its equivalent annual rate is:
Using the unrounded quarterly rate from the example gives 21%, not the approximately 19.52% obtained by multiplying 4.88% by four.
| Conversion | Calculation |
|---|---|
| Monthly to annual | Compound the monthly growth factor over 12 months |
| Quarterly to annual | Compound the quarterly growth factor over four quarters |
| Annual to monthly | Take the twelfth root of the annual growth factor, then subtract one |
A conversion describes an equivalent rate. Annualizing a short observation window does not show that its growth will persist for a full year.
Inconsistent business data. A revenue comparison should use comparable currencies, reporting periods, and business scope. An acquisition can increase reported revenue without the acquired growth being organic. Comparing a seasonal peak with a trough can also distort interpretation.
Cash added to an investment account. A larger ending balance may reflect deposits rather than investment gains. For accounts with contributions or withdrawals, use a return method that accounts for cash-flow timing, such as time-weighted return or money-weighted return, depending on the question.
Zero and negative bases. A zero starting value causes division by zero. Crossing from a loss to a profit does not produce a conventional compound percentage growth rate. Report the amounts and change directly instead of forcing the result into a growth formula.
A complete loss. From a positive starting value to zero, the endpoint formula reaches its boundary value of -100% per period. This does not reveal when the loss occurred; subsequent percentage changes from a zero base are undefined.
Turning history into a forecast. Extending a historical rate into future periods is an assumption. Changes in capacity, competition, margins, financing, and market conditions may make that assumption unsuitable. Historical investment performance does not guarantee future results. Investor.gov: Reading Fund Performance.
This article explains financial calculations, not guaranteed growth or personalized investment, tax, or business advice.