Use CAGR = (EV/BV)^(1/n) − 1.
Finance comparison
CAGR vs Geometric Mean: Same Formula, Different Inputs
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.
Short answer
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.
Same growth story, two input formats
CAGR and geometric mean produce identical results when the inputs describe the same growth path.
Example input $1,000 to $1,750 over 5 years
CAGR = (1,750/1,000)^(1/5) − 1 = 11.84%. GM of five identical 11.84% factors = 1.1184 ✓.
CAGR = 11.84% 11.84%
Equiv. GM factor = 1.1184 1.1184
Side-by-side comparison
Use this table when you need a fast, practical distinction before choosing a calculator.
| Feature | Option A | Option B |
|---|---|---|
| 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. |
CAGR or GM: choose by input format
The data you already have determines which form to use.
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.
Examples that make the choice clear
When CAGR and GM give identical results
$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.
When GM is more natural
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% ✓.
Common mistakes
These are the errors most likely to make the correct formula return a misleading answer.
Using CAGR when cash flows occurred mid-period
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.
Entering raw percentage returns into the GM formula without converting
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.
Treating CAGR as a forecast
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.
Frequently asked questions
Is CAGR a geometric mean?
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).
Can geometric mean replace CAGR?
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.
Should I use CAGR or XIRR for SIP investments?
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.