Average Return Calculator — CAGR & Returns
Work out your investment's CAGR, cumulative return, arithmetic mean, geometric mean, and volatility — from a simple start/end value, or from a year-by-year list of actual annual returns.
Average Return Calculator
CAGR · Arithmetic & Geometric Mean · Volatility
INVESTMENT VALUES
Additional cash flows are shown for context only — the CAGR math above assumes a clean start/end value with no interim deposits or withdrawals, so keep this honest by leaving it at $0 unless you just want a note-to-self.
CAGR (Compound Annual Growth Rate)
9.19%
7 years · Growth
85.00%
Cumulative Return
$10,000
Starting Value
$18,500
Ending Value
9.19%
CAGR
9.19%
Arithmetic Mean
9.19%
Geometric Mean
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Volatility (σ)
⚖️ Arithmetic vs Geometric Mean — Why It Matters
Arithmetic Mean (Simple Average)
Formula: Sum of returns ÷ n
9.19%
$10K grows to $18,500
Geometric Mean (Compound Average)
Formula: (Π(1+r))^(1/n) − 1
9.19%
$10K grows to $18,500
Geometric mean equals arithmetic mean — this happens when every annual return is identical (no volatility).
Growth of $10,000
Year-by-Year Breakdown
| Period | Annual Return | Opening Value | Gain/Loss | Closing Value |
|---|---|---|---|---|
| Period 1 | 9.19% | $10,000 | +$919 | $10,919 |
| Period 2 | 9.19% | $10,919 | +$1,003 | $11,922 |
| Period 3 | 9.19% | $11,922 | +$1,095 | $13,017 |
| Period 4 | 9.19% | $13,017 | +$1,196 | $14,212 |
| Period 5 | 9.19% | $14,212 | +$1,306 | $15,518 |
| Period 6 | 9.19% | $15,518 | +$1,426 | $16,944 |
| Period 7 | 9.19% | $16,944 | +$1,556 | $18,500 |
CAGR vs Arithmetic vs Geometric Mean
These three numbers can describe the exact same investment and still tell very different stories. Knowing which one you're looking at — and which one actually matches how your money grew — keeps you from over- or under-estimating real performance. For the mechanics behind compounding itself, see our investment calculator and compound interest calculator.
| Measure | Formula | Best Used For | Limitation |
|---|---|---|---|
| CAGR | (End/Start)^(1/years) − 1 | Comparing overall multi-year performance across investments | Smooths away every year-to-year swing |
| Arithmetic Mean | Sum of returns ÷ n | A rough, easy-to-explain 'typical year' figure | Overstates true compound growth whenever returns vary |
| Geometric Mean | (Π(1+r))^(1/n) − 1 | The actual compound growth rate you experienced | A bit more work to compute by hand |
| Total Return | (End − Start) ÷ Start | A simple gain/loss headline number | Not annualized — can't compare across different time spans |
Why Geometric Mean Is Always Less Than (or Equal to) Arithmetic Mean
The classic illustration: an investment gains 50% in year one and loses 50% in year two. The arithmetic mean is (50% − 50%) ÷ 2 = 0%, which sounds like you broke even. But $1 → $1.50 → $0.75 — the geometric mean works out to roughly −13.4% a year, because you actually lost a quarter of your money. This gap, often called variance drag, grows with volatility — a bumpier ride needs a higher average return just to compound to the same place as a smoother one.
Historical Average Returns by Asset Class
| Asset Class | Arithmetic Mean | Geometric Mean (CAGR) | Volatility (σ) |
|---|---|---|---|
| US Stocks (S&P 500) | 11.5% | 10.0% | 15-20% |
| US Bonds (10-yr Treasury) | 5.0% | 4.8% | ~8% |
| 60/40 Portfolio | 8.5% | 7.9% | 10-12% |
| International Stocks | 9.5% | 8.0% | 17-20% |
| Real Estate (REITs) | 10% | 8.8% | 14-18% |
| Cash (T-Bills) | 3.3% | 3.3% | ~3% |
Illustrative long-run averages — actual results vary by period measured.
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