Average Return Calculator
Enter several years of annual returns to compute the arithmetic mean, geometric mean (CAGR) and cumulative total return.
Input Data
Results
At a glance:There are two common averages: the arithmetic mean is the simple average of yearly returns and overstates long-run compounding; the geometric mean (CAGR) accounts for compounding and volatility and reflects the real average annual growth, usually lower. The wider the gap, the more volatile the returns.
Formula
Yearly returns rᵢ (decimal), n years.
Arithmetic = (r₁+…+rₙ) ÷ n.
Cumulative factor = (1+r₁)×(1+r₂)×…×(1+rₙ).
Geometric (CAGR) = factor^(1/n) − 1.
Cumulative return = factor − 1.
How to Use
- Enter consecutive yearly returns (positive for gains, negative for losses).
- Compare the arithmetic and geometric (CAGR) means.
- Cumulative return shows total growth over the n years.
FAQ
Why is geometric mean usually lower than arithmetic?
Arithmetic mean ignores the non-linearity of compounding: after a gain then a loss (or high volatility), the real ending value grows less than the average of the yearly returns. E.g. +50% then −50% averages 0% arithmetically, but capital actually shrinks 25% (1.5×0.5=0.75). Geometric mean reflects this true average growth, so use it to judge long-term performance.
When to use arithmetic vs geometric?
Use arithmetic mean to forecast a 'typical yearly return' (e.g. historical mean assumption); use geometric mean (CAGR) to review actual compounded growth over a past period. Together they reveal volatility — a wider gap means higher risk.
Will entering a loss break the calculator?
No. A 10% drop is entered as -10; the tool uses (1 − 0.10)=0.9 in the factor. If a single year dropped more than -100% the factor hits zero and geometric mean is undefined; in practice a single year cannot fall over 100%.
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References
Content review: Calculatorism Finance Team. Results for educational reference only; investing involves risk.