Average Return Calculator
Compute the arithmetic mean return, the geometric (compound) average return, and the cumulative return from a series of period returns.
Arithmetic Mean
9.00%
Geometric Mean
8.38%
Cumulative Return
62.06%
Summary
Across these 6 periods, the arithmetic average return is 9.00% per period, but the geometric (compound) average is 8.38% — the rate that actually reflects how $100 grew to $162.06, a 62.06% cumulative return.
Best Period
#4: 22.00%
Worst Period
#5: -8.00%
Return by period
What is an Average Return Calculator?
An average return calculator summarizes a series of period-by-period investment returns — annual returns on a stock, fund, or portfolio, for example — into single figures that describe overall performance. Because there are several valid ways to average a series of percentage returns, this calculator reports the three most common ones side by side: the arithmetic mean, the geometric (compound) mean, and the cumulative total return.
The arithmetic mean is the simple average of the returns and is easy to compute, but it systematically overstates true performance for volatile series because it ignores compounding. The geometric mean corrects for this: it is the constant annual rate that would have produced the same ending value as the actual sequence of returns, and it is always less than or equal to the arithmetic mean whenever returns vary.
Growth of $100 Over 6 Periods
Each row applies that period's return to the running balance, showing exactly how compounding — not simple averaging — determines the final result.
| Period | Return | Value of $100 |
|---|---|---|
| 1 | 12.00% | $112.00 |
| 2 | -5.00% | $106.40 |
| 3 | 18.00% | $125.55 |
| 4 | 22.00% | $153.17 |
| 5 | -8.00% | $140.92 |
| 6 | 15.00% | $162.06 |
Arithmetic vs. Geometric Mean Return
Geometric Mean = [(1+r₁)(1+r₂)...(1+rₙ)]^(1/n) − 1
The arithmetic mean answers "what was the average return in a typical period?" The geometric mean answers a different, usually more useful question: "what constant annual rate actually describes how my money grew?" For any series with variability, the geometric mean is strictly lower than the arithmetic mean — the gap grows with volatility, a relationship known as "volatility drag."
Why the Two Averages Can Differ So Much
Consider a two-year sequence of +50% and -50%. The arithmetic mean is 0%, suggesting no change. But $100 growing 50% becomes $150, then losing 50% becomes $75 — a real loss of 25%, which the geometric mean correctly reports as roughly -13.4% per year. This gap is why the arithmetic mean should never be used to describe multi-year investment performance; it is only appropriate for estimating a single typical period's expected return.
Cumulative Return vs. Annualized Return
Cumulative return is the total percentage gain or loss over the entire series, ignoring how many periods it took. It is useful for comparing "how much did I make in total," but says nothing about the rate — a 50% cumulative return over 3 years and the same 50% over 15 years represent very different rates of growth. The geometric mean, expressed per period, is what should be used to compare investments held for different lengths of time.
Limitations of Average Return Metrics
None of these averages account for the timing or size of cash flows into or out of an account — adding or withdrawing money mid-series distorts a simple period-return calculation. For portfolios with deposits and withdrawals, a money-weighted return (internal rate of return) is more accurate than any of the return-only averages shown here. These figures also ignore risk: two series with the same geometric mean can carry very different volatility and drawdown risk.
Example — Your Current Inputs
Across these 6 periods, the arithmetic average return is 9.00% per period, but the geometric (compound) average is 8.38% — the rate that actually reflects how $100 grew to $162.06, a 62.06% cumulative return.
Additional Example — A Volatile Five-Year Fund
A fund returns +30%, -20%, +25%, -10%, and +18% over five years. The arithmetic mean is a healthy 8.6% per year. But compounding those exact returns takes $100 to only about $132.60 — a cumulative return of 32.6%, which annualizes (geometric mean) to roughly 5.8% per year. An investor who only looked at the 8.6% arithmetic average would meaningfully overestimate how their money actually grew.
About These Parameters
- Period Returns
- A list of percentage returns, one per period — typically one per year, but quarterly or monthly returns work identically. Enter negative numbers for loss periods (e.g. -12). At least two periods are required so an average and a growth path can be computed; more periods produce a more reliable picture of the geometric mean.
Frequently Asked Questions
Which average should I actually use?
Use the geometric mean whenever you are describing multi-period investment performance or comparing two investments over time — it is the number that matches your actual account balance. Reserve the arithmetic mean for statistical estimates of a single period's expected return, such as estimating next year's likely return from a history of past years.
Why is the geometric mean always lower?
Mathematically, the geometric mean of a set of positive numbers is always less than or equal to the arithmetic mean (equal only when every return is identical). Financially, this reflects "volatility drag" — losses hurt compounding more than equivalent gains help it, since a loss must be recovered from a smaller base.
Does this account for deposits or withdrawals?
No — this calculator assumes a single lump sum growing (or shrinking) by each period's return with no cash added or removed. If you deposited or withdrew money during the series, a money-weighted return (internal rate of return) would more accurately reflect your personal performance.
Can I use this for monthly or quarterly returns?
Yes — the math is identical regardless of the period length. Just be consistent: if you enter monthly returns, the arithmetic and geometric mean results are per-month figures, not per-year, and would need to be re-annualized separately for a like-for-like comparison with annual figures.