Average Return Calculator
Average a series of yearly investment returns the right way. Paste your returns to get the arithmetic mean, the geometric mean (what you actually earned per year), and cumulative growth — or switch modes to compute CAGR from a starting and ending value.
📈 Put your average return to work
Compare platformsArithmetic vs geometric: why they differ
The arithmetic mean adds your returns and divides by the count. The geometric mean multiplies the growth factors and takes the nth root — it answers “what constant yearly return would have produced the same ending balance?” Because a loss shrinks the base your next gain works on, the geometric mean is always at or below the arithmetic mean, and the gap widens with volatility. A fund advertising a 7% “average return” computed arithmetically may have compounded meaningfully less.
Rule of thumb: geometric ≈ arithmetic − half the variance of returns. Two portfolios with the same arithmetic average can end up in very different places if one is much bumpier.
How it’s calculated
Arithmetic mean = Σri ÷ n. Geometric mean = (Π(1 + ri))1/n − 1. Cumulative return = Π(1 + ri) − 1. In CAGR mode: CAGR = (end ÷ start)1/years − 1, and cumulative = end ÷ start − 1. Each return is treated as one full year.
Assumes a single lump sum with no deposits, withdrawals, fees, or taxes along the way. Estimates only — not investment advice.
Worked example
Five years of returns — +12%, −8%, +15%, +6%, +10% — have an arithmetic mean of 7.00%, but the geometric mean is 6.68%: the loss year drags real compounding below the simple average. Cumulative growth is 38.17%, so $10,000 becomes $13,817. In CAGR mode, growing $10,000 to $16,000 over 6 years works out to 8.15% a year.
Common mistakes
- Projecting future balances with the arithmetic mean — it overstates compounding whenever returns vary.
- Averaging percentages across different-sized accounts or periods as if they were equal-weighted years.
- Forgetting that a −50% year needs +100%, not +50%, to break even.
- Mixing pre-fee and post-fee return figures in the same list.
Where it is used
- Translating a fund fact sheet’s yearly returns into what an investor actually compounded.
- Comparing two volatile assets fairly over the same period.
- Turning a “my account doubled in 9 years” claim into an annual rate.
- Homework and CFA-style practice on time-weighted returns.
Frequently asked questions
Why is the geometric mean lower than the arithmetic mean?
Because losses hurt more than equal gains help. A +50% year followed by a −50% year averages 0% arithmetically, but your money is actually down 25% — a geometric mean of about −13.4% per year. The gap between the two means grows with volatility, and the geometric mean is what your balance actually experiences.
Which average should I use?
Use the geometric mean (or CAGR) to describe what an investment actually earned per year, and to project a balance forward. The arithmetic mean is only appropriate as the expected value of a single, independent year — using it for multi-year growth overstates results.
Is CAGR the same as geometric mean return?
Essentially yes. CAGR is computed from just the start and end values over a number of years, while a geometric mean is computed from the yearly returns in between — if the returns multiply to the same total growth, both give the same annualized figure.
How do I enter a losing year?
Type it with a minus sign, like -8. The calculator turns each entry into a growth factor (1 plus the return), multiplies them, and takes the nth root, so negative years are handled exactly.
Does this account for deposits and withdrawals?
No — it assumes one lump sum riding through the returns. If you added or removed money along the way, your personal (money-weighted) return differs from the fund’s time-weighted return; an IRR calculation handles that case.