Average Return Calculator · Practical guide
Arithmetic vs Geometric Average Return
Two ways to average annual returns — and why the geometric one is what your portfolio actually earned.
At a glance
The Short Answer
The arithmetic average is the simple mean of yearly returns; the geometric average (also called CAGR) accounts for compounding and is the rate that actually reproduces your final balance. The geometric average is always lower when returns vary — and the gap widens with volatility.
Interactive tool
Average Return Calculator
Enter your own values, then compare the result with the examples below.
Results
The Classic Example: +50%, Then −50%
Gain 50% one year and lose 50% the next. The arithmetic average is (50 − 50) ÷ 2 = 0%, which suggests you broke even. But $10,000 becomes $15,000, then $7,500 — you lost 25%. The geometric average is (1.5 × 0.5)^(1/2) − 1 = 0.75^(1/2) − 1 ≈ −13.40% per year, which matches reality exactly. Enter 50, -50 in the calculator above to see both figures side by side.
A Five-Year Worked Example
For annual returns of 8%, −2%, 12%, 5%, and 7%:
| Measure | Value | What It Tells You |
|---|---|---|
| Arithmetic average | 6.00% | The typical year's return (30 ÷ 5) |
| Geometric average (CAGR) | 5.90% | The steady rate that compounds to the same result |
| Standard deviation | 4.60% | How widely returns swing around the average |
| Total growth | 1.332x | $10,000 becomes about $13,318 |
When Each Number Matters
Use the geometric average to report performance or compare investments — it is the only average that respects compounding. The arithmetic average still has a job: it is the better estimate of next year's expected return, and it is the input most risk models expect. Reporting an arithmetic average as if it were your growth rate overstates results, and the overstatement grows with volatility.
Frequently Asked Questions
Which return should I quote when comparing investments?
The geometric average (CAGR). It is the rate that, applied every year, takes your starting balance to your ending balance — the arithmetic average usually overstates actual growth.
Why is the geometric return always lower?
Because losses hurt more than equal gains help. A 10% loss needs an 11.1% gain to recover, so volatility drags the compounded result below the simple average.
Can I enter monthly or quarterly returns?
Yes — the math is the same, but the geometric result is then a per-period rate, not an annual one. To annualize monthly CAGR, compute (1 + r)^12 − 1.
Is CAGR the same as geometric average return?
Yes. CAGR is the geometric average computed over a start and end value; this calculator derives the same rate from the year-by-year return series.