Geometric Mean Calculator Finance comparison
CAGR and geometric mean are the same mathematical operation applied to different input formats. CAGR = (EV/BV)^(1/n) − 1 takes a beginning value, ending value, and years. Geometric mean takes n period-by-period growth factors and returns their nth root. For annual returns 6%, −35%, 10%: convert to factors (1.06, 0.65, 1.10), GM = 0.9144 → CAGR = −8.56%/yr — the only rate that reproduces the actual ending value.
CAGR is the specific finance form of geometric mean for start-to-end growth. Use CAGR when you have beginning value, ending value, and years. Use geometric mean directly when you already have the period-by-period growth factors or ratios. When money moves on specific dates instead, XIRR is the correct metric.
CAGR and geometric mean produce identical results when the inputs describe the same growth path.
CAGR = (1,750/1,000)^(1/5) − 1 = 11.84%. GM of five identical 11.84% factors = 1.1184 ✓.
Check the input type and formula side by side before calculating.
| Method | Geometric mean applied to start-and-end values | Broader method for n factors or ratios |
|---|---|---|
| Formula | (EV / BV)^(1/n) − 1 | (x₁ × x₂ × ⋯ × xₙ)^(1/n) |
| Input format | Beginning value, ending value, number of years. | A list of n positive factors, ratios, or values. |
| Finance use | Portfolio growth, revenue, users, market size — one start and one end. | Period-by-period return factors, normalized ratios, index relatives. |
| When they are identical | CAGR from $1,000 → $1,750 in 5 yrs = 11.84%. | GM of five identical 1.1184 factors = 1.1184 → 11.84%. Same result. |
| When they differ | CAGR ignores interim deposits or withdrawals. | GM accepts any n positive factors — it is not limited to start-and-end pairs. |
This is the clearest way to see that CAGR and geometric mean are one calculation. The two columns start from different data and converge at step three.
Situation: A $25,000 portfolio returns +22%, −13%, +18%, and +26% over four years, ending at $39,452.24.
| Step-by-step: how to use this calculator correctly | CAGR route | Geometric mean route |
|---|---|---|
| 1. What you start with | Two endpoints: $25,000 and $39,452.24, over four years. | Four yearly returns: +22%, −13%, +18%, +26%. |
| 2. Normalize the input | Growth multiple = 39,452.24 / 25,000 = 1.578090 | Convert to factors: 1.22, 0.87, 1.18, 1.26 |
| 3. Collapse to one number | The ratio already is the product of the four factors. | Product = 1.22 × 0.87 × 1.18 × 1.26 = 1.578090 |
| 4. Take the nth root | 1.578090^(1/4) = 1.120813 | 1.578090^(1/4) = 1.120813 |
| 5. Read the rate | 12.08% per year | 12.08% per year |
The two columns meet at step three and are character-for-character identical after it. CAGR is not a different or more precise formula — it is the geometric mean with the product handed to you as a ratio of endpoints. Choose between them based on which data you happen to have.
Because the two are the same operation, they share the same blind spots. These are the three worth knowing.
Each assumes the only cash flows are at the start and the end. Add a $5,000 top-up in year three and neither number describes your return any more — you need XIRR, which weights every flow by its own date.
Two portfolios can both post 12.08% per year while one drifts smoothly upward and the other falls 40% in year two before recovering. This figure is a summary of endpoints, not of risk. Pair it with standard deviation or maximum drawdown before comparing funds.
Annualizing a three-month 8% gain to 1.08^4 − 1 = 36.05% assumes that quarter repeats four times running. Over windows shorter than a year, annualizing amplifies noise rather than clarifying it — report the raw period return instead.
The data you already have determines which form to use.
Use CAGR = (EV/BV)^(1/n) − 1.
Use GM = (product of factors)^(1/n). Convert % returns to factors first.
Use XIRR — neither CAGR nor GM handles interim dated flows.
CAGR implies a GM factor of (1 + CAGR). GM of factors implies CAGR = GM_factor − 1.
$1,000 portfolio grows to $1,750 in 5 years. CAGR = (1,750/1,000)^(1/5) − 1 = 11.84%. Alternatively: multiply the five yearly factors 1.1184^5 = 1.75 → GM of those five factors = 1.1184 → 11.84%. Same answer from different inputs.
You have actual annual returns: 6%, −35%, 10%. Convert to factors: 1.06, 0.65, 1.10. GM = (1.06×0.65×1.10)^(1/3) = 0.7579^(1/3) = 0.9144. Annual return = −8.56%. This is the CAGR from $1,000 to $757.90 in 3 years: (757.9/1000)^(1/3) − 1 = −8.56% ✓.
Company revenue went from $480,000 in 2019 to $1.35M in 2025, six years apart, with no year-by-year figures published. CAGR = (1,350,000 / 480,000)^(1/6) − 1 = 2.8125^(1/6) − 1 = 18.81% per year. Geometric mean is unavailable here because the period-by-period factors were never disclosed.
A fund reports +14%, +9%, −22%, and +31% but never publishes its NAV. Factors 1.14, 1.09, 0.78, 1.31 multiply to 1.26968868, so GM = 1.06151 → 6.15% per year. Without a starting balance CAGR cannot be computed at all, yet geometric mean delivers exactly the rate CAGR would have returned.
A correct calculation can still mislead when the method or input type is wrong.
If $500 was added in Year 2, CAGR on the final value treats all capital as if it compounded from Year 0. Use XIRR, which discounts each cash flow to its actual date.
GM of 6%, −35%, 10% as percentages = (6 × −35 × 10)^(1/3) — undefined (negative product). Convert to factors: 1.06, 0.65, 1.10 → GM = 0.9144 → −8.56%/yr.
CAGR describes a past period or an assumed scenario. A fund's 5-year CAGR of 15% does not predict 15% next year. Label historical CAGR as historical.
Yes. CAGR = (EV/BV)^(1/n) − 1 is algebraically identical to GM(annual growth factors) − 1. For $1,000 → $1,750 over 5 years: CAGR = 11.84%. If you had the five actual yearly factors and took their GM, you would get the same 11.84% (or the actual return path, which differs from the smooth CAGR assumption).
Yes, when you have the period-by-period growth factors. GM of the factors minus 1 = CAGR. If you only have beginning and ending values, CAGR is the more direct formula.
Use XIRR. CAGR requires exactly one beginning value and one ending value. A SIP with monthly contributions has 12+ beginning dates per year — each contribution has a different time in the market. XIRR handles this by discounting each flow to its actual date.
They come from different fields. Geometric mean is the statistical name for the product-root average of any set of positive values. CAGR is the finance name for that same average applied to money across years. The vocabulary differs; the arithmetic does not.
Yes. If the ending value is below the beginning value, the ratio is less than 1, so its root is also less than 1 and subtracting 1 leaves a negative rate. A $10,000 position falling to $6,500 over three years gives (0.65)^(1/3) − 1 = −13.38% per year.
Yes. Every factor must cover the same span — all annual, all quarterly, or all monthly. Mixing a quarterly factor in with annual ones silently treats three months as a full year. When your periods genuinely differ in length, use XIRR rather than forcing them into one geometric mean.