Annualized growth versus total return
Total return answers how much value changed overall. CAGR answers which constant annual rate would create the same endpoints. Starting, ending and period used are shown so the implied endpoint or time is visible in reverse modes.
For the total percentage gain or loss over the full holding period, use the ROI Calculator instead of interpreting an annualized rate as a total return.
The formula
Starting and ending are positive values measured on the same basis. Years is the elapsed holding period, including decimal years. The formula returns a decimal rate; multiply by 100 to express it as a percentage. The inverse formulas rearrange the same annual compounding relationship. Time solving needs a nonzero rate and endpoints with a matching growth or decline direction.
Worked example
Growing from 10,000 to 20,000 over five years produces a CAGR of about 14.87%, even if actual yearly returns were uneven.
How to use this calculator
- Choose the annual growth rate, ending value, starting value or time period to calculate.
- Enter the three visible values on the same measurement basis. An entered annual rate is used only in inverse modes; entries are retained when modes change.
- Read the live annualized rate, total change and values used. Intermediate deposits and withdrawals require a cash-flow return method.
Why holding time changes the comparison
Doubling a value over five years gives about 14.87% annualized growth; doubling it over ten years gives about 7.18%. Both have a 100% total return, but the longer period spreads that change over more years. Compare CAGR figures only after checking that each period and endpoint is measured consistently.
Contributions can disguise the investment return
An account can grow because its investments gained value or because you deposited more money. CAGR treats the full endpoint change as growth, so intermediate deposits and withdrawals distort that interpretation. A cash-flow return calculation is needed when the amounts and dates of those transactions matter.
Work backward from a supplied annual rate
Choose Ending value to apply a supplied constant annual rate to a known starting value and period. For example, 10,000 at 10% for five years gives 16,105.10. Starting value reverses that relationship: 16,105.10 at the same rate and period implies 10,000. These are arithmetic scenarios, not predictions of annual market performance.
Choose Time period when both endpoints and a nonzero annual rate are known. Growing 100 to 121 at 10% takes two years; declining 100 to 81 at −10% also takes two years. A zero rate cannot identify a unique time, and a growth rate cannot connect declining endpoints over a positive period. Implied endpoints and periods must remain within this calculator’s original positive-value and time bounds.
Assumptions & limitations
What this calculation assumes
- Positive starting and ending values.
- The time period can include decimal years.
- No intermediate cash flows.
What to keep in mind
- It does not show volatility or drawdowns.
- It is not an arithmetic average of yearly returns.
- Negative or zero endpoints are unsupported.
- Inverse input rates range from −99.9999% to 10,000%; supported implied periods range from 0.000001 to 200 years.
Common questions
Can CAGR be negative?
Yes, when the ending value is below the starting value.
Is CAGR the same as total return?
No. CAGR annualizes; total return covers the whole period.
Why can’t the start be zero?
The formula divides by the starting value and takes a root.
Can I solve the start or end value instead?
Yes. Choose the missing value and enter an annual rate and period. The same compounding relationship is rearranged, with no intermediate contributions or withdrawals.
Sources & further reading
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