Geometric Mean Calculator Interactive tool
CAGR (compound annual growth rate) is the single annual rate that connects a beginning value to an ending value as if growth were perfectly smooth each year. Formula: CAGR = (EV / BV)^(1/n) − 1. Example: $1,000 growing to $1,750 over 5 years → CAGR = (1,750/1,000)^(0.20) − 1 = 11.84% per year. This calculator returns CAGR, total return %, and the ending value multiple.
Geometric mean of annual growth
CAGR (compound annual growth rate) is the single annual rate that connects a beginning value to an ending value as if growth were perfectly smooth each year. Formula: CAGR = (EV / BV)^(1/n) − 1. Example: $1,000 growing to $1,750 over 5 years → CAGR = (1,750/1,000)^(0.20) − 1 = 11.84% per year. This calculator returns CAGR, total return %, and the ending value multiple.
CAGR is the most widely used annualized growth metric precisely because it is a single comparable number — but that simplicity is also its limitation.
Each year’s growth multiplier is (1 + return). CAGR is the nth root of the product of all n multipliers, minus 1. For returns 6%, −35%, 10%: multipliers = 1.06, 0.65, 1.10. Product = 0.7579. GM = 0.7579^(1/3) = 0.9144. CAGR = −8.56%/yr. This is the only average that correctly reproduces the ending value.
Divide 72 by the CAGR percentage to estimate years to double. At 11.84%: 72 / 11.84 = 6.1 years. At 7%: doubles in 10.3 years. At 12%: doubles in 6 years. This is an approximation — exact calculation: years = ln(2) / ln(1 + CAGR).
Two portfolios can reach $1,750 from $1,000 in 5 years (CAGR = 11.84%) via completely different paths. Portfolio A: steady +11.84% each year. Portfolio B: +6%, +8%, −35%, +10%, +68%. Both end at $1,750 but Portfolio B hit a $650 low in Year 3. CAGR is silent on this difference. Always pair CAGR with maximum drawdown or annual return spread.
Each row shows the inputs and whether CAGR is the right metric or whether a different calculation is more accurate.
| Situation | Input | Best next move | Why |
|---|---|---|---|
| Lump-sum portfolio: $1,000 → $1,750 over 5 years | BV = $1,000, EV = $1,750, n = 5 | CAGR = 11.84%/yr ✓ | Single start, single end, no interim flows. CAGR is the exact and correct metric. |
| SIP investment: $500/month for 3 years, final value $22,000 | 36 dated contributions + final value | Use XIRR — not CAGR | CAGR would use only the first and last values, ignoring the 35 intermediate contributions and their timing. |
| Company revenue: $500k (2020) → $2.1M (2025) | BV = 500,000, EV = 2,100,000, n = 5 | CAGR = (2,100/500)^(0.20) − 1 = 33.2%/yr | CAGR converts 5-year revenue growth into a single annual rate for investor presentations. |
| Volatile fund: returns 6%, 8%, −35%, 10%, 40% | AM = 5.8%, but actual ending value = $1,166 from $1,000 | CAGR = ($1,166/$1,000)^(0.20) − 1 = 3.1%/yr | AM = 5.8% implies $1,000 → $1,330 — wrong. Only CAGR reproduces the $1,166 ending value. |
Confirm you have a single lump-sum beginning value and a single ending value with no interim deposits or withdrawals. If deposits or withdrawals occurred, use the XIRR calculator instead.
Enter beginning value (BV): the portfolio, revenue, or metric value at the start of the period.
Enter ending value (EV): the same metric at the end of the period. Both must be positive — CAGR is undefined for zero or negative beginning values.
Enter years (n): use decimal years for partial periods (e.g., 2.5 for 30 months). The formula applies the same way.
Read CAGR as the annual compounding rate. Verify by mentally checking: BV × (1 + CAGR)^n should equal EV.
BV = $1,000 | EV = $1,750 | n = 5 years | Total return = 75%
CAGR = (1,750/1,000)^(1/5) − 1 = 1.75^0.20 − 1 = 11.84%/yr. Year-by-year: $1,000 → $1,118 → $1,250 → $1,398 → $1,564 → $1,750. Arithmetic mean of 5 identical years of 11.84% = 11.84% (same, because all years are identical in this smooth scenario).
CAGR = 11.84%/yr. Total return = 75%. Ending multiple = 1.75×. At this rate, the investment doubles in 6.1 years (Rule of 72: 72 / 11.84 ≈ 6.1).
CAGR smooths the path. If the actual yearly returns were 6%, 8%, −35%, 10%, 40%, the CAGR is still 11.84% — but the year with −35% meant the portfolio dropped to $650 before recovering. CAGR alone does not warn you about that drop.
CAGR is the correct metric for annualizing start-to-end growth. It produces the wrong answer when cash flows are irregular, when you need to understand risk, or when you want the total gain rather than the pace.
| Method | Best for | Watch for | Example |
|---|---|---|---|
| CAGR | Comparing growth pace across investments or businesses with different time spans and different sizes. | Hides volatility and ignores interim cash flows. Two portfolios with identical CAGR can have completely different risk paths. | $1,000 → $1,750 over 5 years: CAGR = 11.84%/yr. Revenue $500k → $2.1M over 5 years: CAGR = 33.2%/yr. |
| Total return | Showing the absolute gain or loss over the full period, regardless of duration. | Does not adjust for time. A 75% gain in 1 year and a 75% gain in 10 years look the same. | $1,000 → $1,750 = 75% total return. $1,000 → $2,500 over 10 years = 150% total return (CAGR = 9.60%). |
| XIRR | Investments with multiple dated cash flows: SIP contributions, dividends, partial withdrawals, final portfolio value. | Requires at least one negative (invested) and one positive (received) cash flow. Results differ from CAGR when timing is uneven. | Invest $1,000 Jan 2021, $500 Jun 2022, receive $1,850 Jan 2024: XIRR ≈ 8.59% vs CAGR = 12.2% (CAGR ignores the extra deposit). |
| Arithmetic mean of annual returns | Quick rough comparison — acceptable only when returns are small and volatility is low. | Always overstates the true compounding rate. Returns 50%, −50%: AM = 0% (implying no change) but actual loss = 25%. | Annual returns 6%, 8%, −35%, 10%, 40%. AM = 5.8%. CAGR = 3.1%. The $1,000 portfolio is worth $1,166, not $1,330. |
Each bar is BV × 1.1184^year. Year 5 value = $1,000 × 1.1184^5 = $1,750. This is the smoothed path CAGR describes — real portfolios may dip far below any of these bars mid-period.
CAGR = (EV/BV)^(1/n) − 1. For $1,000 → $1,750 over 5 years: (1750/1000)^(0.20) − 1 = 11.84%. Verify: 1000 × 1.1184^5 = 1,750 ✓.
EV ÷ BV = 1,750 ÷ 1,000 = 1.75 (the total growth multiple).
Raise 1.75 to the power of 1/n: 1.75^(1/5) = 1.75^0.20 = 1.1184.
Subtract 1: 1.1184 − 1 = 0.1184 = 11.84% per year.
BV × (1 + CAGR)^n = 1,000 × 1.1184^5 = 1,750 ✓. If it does not match, check for rounding.
Investment returns compound: a 50% gain followed by a 50% loss does not break even. It leaves you with 75 cents per dollar ($1 × 1.5 × 0.5 = $0.75). The arithmetic mean of 50% and −50% = 0% (implying no change), which is wrong. CAGR = (0.75)^(1/2) − 1 = −13.4%, correctly reporting a loss. This is why CAGR uses the geometric mean formula: (EV/BV)^(1/n) − 1 instead of summing and dividing.
CAGR requires exactly one beginning value, one ending value, and one time span — no interim cash flows. Use it for: company revenue 2020–2025 ($500k → $2.1M → CAGR = 33.2%/yr), stock index growth, and market-size projections. Use XIRR instead when: monthly SIP contributions add up (investing $500/month changes the cost basis), dividends were reinvested on specific dates, or mid-period withdrawals occurred. XIRR solves for the rate r where Σ (CFᵢ / (1+r)^(dᵢ/365)) = 0 across all dated cash flows.
CAGR is simple enough that the mistakes are usually conceptual rather than arithmetic.
If you invested $1,000 initially and added $500 a year later, CAGR on the final value treats the whole balance as if it came from the initial $1,000. The correct metric is XIRR, which discounts each dated cash flow separately.
CAGR describes the past (or an assumed scenario). A mutual fund showing 5-year CAGR of 15% is not promising 15% next year. Performance past is not performance future. Label historical CAGR as 'historical' and scenario CAGR as 'projected'.
For returns 6%, 8%, −35%, 10%, 40%: AM = 5.8% but CAGR = 3.1%. If a fund report shows 'average annual return = 5.8%', the actual compound growth is lower. Request the geometric mean (CAGR) for apples-to-apples portfolio comparison.
No. Two portfolios can share the same CAGR but have completely different risk profiles. Example: Portfolio A grows smoothly at 11.84%/yr; Portfolio B drops 35% in Year 3 then recovers. Both land at $1,750 from $1,000 after 5 years (CAGR = 11.84%), but Portfolio B required surviving a $650 low. Always pair CAGR with maximum drawdown or annual standard deviation.
Yes, when EV < BV. Example: $10,000 declining to $6,500 over 3 years → CAGR = (6,500/10,000)^(1/3) − 1 = 0.65^0.333 − 1 = −13.6%/yr. This means the asset lost an average of 13.6% per year, compounded.
Context determines 'good'. S&P 500 historical CAGR (1957–2024): approximately 10.5%/yr nominal, 7–8%/yr real (inflation-adjusted). A diversified equity portfolio at 8–12%/yr CAGR is typical. A startup at 40%+/yr CAGR revenue is high-growth. Always compare CAGR against a relevant benchmark, not an absolute number.
Yes. CAGR is the standard metric for revenue, user counts, market size, and any single-stream business metric. Example: revenue $400k (2021) → $1.2M (2024) → CAGR = (1,200/400)^(1/3) − 1 = 44.2%/yr. This is directly comparable to a competitor’s revenue CAGR, regardless of absolute size.
The exponent (1/n) is the inverse of compounding for n years. Compounding applies a rate n times: BV × (1+r)^n = EV. Solving for r: r = (EV/BV)^(1/n) − 1. The exponent undoes the compounding to find the equivalent single-year rate.
No. CAGR summarizes a historical period or a projected scenario. Using a 5-year historical CAGR to predict the next 5 years assumes the same growth conditions persist — which markets rarely guarantee. Use CAGR for comparison and planning, not as a prediction.