Compound annual growth rate (CAGR) is the constant annual rate that would turn a starting value into an ending value over a specified period. An arithmetic average adds periodic returns and divides by the number of periods. They answer different questions and can diverge sharply when returns vary.
Calculate it: use the CAGR Calculator for a clean starting value, ending value and time period. Use the ROI Calculator when you need a total holding-period return that includes costs and income.
CAGR connects two values through compounding
The formula is:
CAGR = (ending value ÷ starting value)1 ÷ years − 1
If €10,000 becomes €18,000 after five years, the total return is 80%. CAGR is approximately 12.47% a year. Dividing 80% by five produces 16%, but 16% compounded for five years would produce more than €21,000. It does not describe the observed start-to-end result.
| Measure | Calculation | Result | What it means |
|---|---|---|---|
| Total return | €18,000 ÷ €10,000 − 1 | 80.00% | Full five-year change |
| Simple total-return average | 80% ÷ 5 | 16.00% | Division only; ignores compounding |
| CAGR | (1.8)1/5 − 1 | 12.47% | Constant compounded annual rate |
Arithmetic average can overstate compounded experience
Suppose an investment gains 50% in year one and loses 20% in year two. The arithmetic average is 15%:
(50% − 20%) ÷ 2 = 15%
But €100 becomes €150 and then €120. The two-year CAGR is approximately 9.54%, because the second-year loss applies to the larger balance.
| Stage | Return | Value |
|---|---|---|
| Start | — | €100.00 |
| After year one | +50% | €150.00 |
| After year two | −20% | €120.00 |
| Arithmetic average | 15.00% a year | Does not reproduce €120 |
| CAGR | 9.54% a year | Reproduces €120 after two years |
“Average annual return” can be ambiguous
Some regulated investment reports use “average annual return” to mean an annualized, compounded return. In informal discussion, people may use the same phrase for an arithmetic average of yearly results. Check the formula or methodology instead of relying on the label.
The SEC’s investor guide describes fund performance tables as showing annualized, or average annual, returns for standard periods. FINRA separately warns that dividing a total return by the holding period creates a simple average that does not account for compounding.
When CAGR is useful
- comparing point-to-point growth over periods of different lengths;
- summarising revenue, portfolio or price growth with one annualized figure;
- checking whether a stated annual growth rate reproduces the start and end values; and
- communicating a geometric rate when there are no intermediate cash flows.
What CAGR hides
CAGR uses only the start, end and elapsed time. It does not reveal:
- volatility or the sequence of yearly returns;
- drawdowns experienced during the period;
- deposits or withdrawals;
- whether income was reinvested;
- fees and taxes unless they are already reflected in the values; or
- risk taken to achieve the result.
For an investment account with irregular cash flows, a money-weighted or time-weighted return method may be needed. A point-to-point CAGR calculator cannot infer those cash-flow timings.
Methodology and sources
The examples are original Finance Charts calculations. Values are rounded for display. They assume no intermediate cash flows and do not represent any asset or expected return.
- FINRA — Calculating Your Investment Returns
- US Securities and Exchange Commission — How to Read a Mutual Fund Shareholder Report
- Finance Charts — Methodology
Important: annualizing a historical result makes periods easier to compare. It does not turn that result into a forecast or remove investment risk.