# CAGR Formula: How to Calculate Compound Annual Growth Rate Published: 2026-03-01 Author: Warren Team URL: https://www.heywarren.com/blog/cagr-formula --- CAGR is the single most useful rate-of-return metric in finance — it tells you the smoothed annual growth rate of any investment or business metric, stripping out year-to-year volatility to show what consistent compounding would have produced the same result. Here's the formula, how to calculate it in Excel, and how to use it correctly. ## What Is CAGR? CAGR stands for **Compound Annual Growth Rate** — the [rate of return](/blog/calculating-rates-of-return) that would take an initial value to an ending value if the growth occurred consistently at the same rate, compounded annually. CAGR doesn't tell you what actually happened each year — it tells you the equivalent annual growth rate as if growth were perfectly smooth. **Why CAGR matters**: When someone says "the S&P 500 returned 10% per year historically," they mean its long-run CAGR is approximately 10%. In reality, individual years ranged from +37% to −37%. CAGR gives you the single "steady-state" equivalent. ## The CAGR Formula **CAGR = (Ending Value / Beginning Value)^(1/N) − 1** ![Three-step process to calculate CAGR from any starting and ending value over N years.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20660%20125%22%20width%3D%22660%22%20height%3D%22125%22%20role%3D%22img%22%3E%3Ctitle%3EFlow%20diagram%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%2230%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22115%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EEnd%20%C3%B7%20Start%3C%2Ftext%3E%3Ctext%20x%3D%22115%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EDivide%20values%3C%2Ftext%3E%3Cline%20x1%3D%22205%22%20y1%3D%2262.5%22%20x2%3D%22237%22%20y2%3D%2262.5%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cpolygon%20points%3D%22244%2C62.5%20235%2C57.5%20235%2C67.5%22%20fill%3D%22%2364748b%22%2F%3E%3Crect%20x%3D%22245%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22330%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3ERaise%20to%201%2FN%3C%2Ftext%3E%3Ctext%20x%3D%22330%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EN%20%3D%20years%3C%2Ftext%3E%3Cline%20x1%3D%22420%22%20y1%3D%2262.5%22%20x2%3D%22452%22%20y2%3D%2262.5%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cpolygon%20points%3D%22459%2C62.5%20450%2C57.5%20450%2C67.5%22%20fill%3D%22%2364748b%22%2F%3E%3Crect%20x%3D%22460%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22545%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3ESubtract%201%3C%2Ftext%3E%3Ctext%20x%3D%22545%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3E%3D%20CAGR%20%25%3C%2Ftext%3E%3C%2Fsvg%3E) *Three-step process to calculate CAGR from any starting and ending value over N years.* Where: - **Ending Value**: Value at the end of the period - **Beginning Value**: Value at the beginning of the period - **N**: Number of years **Example 1 — Investment return**: - Portfolio value in 2019: $100,000 - Portfolio value in 2024: $162,890 - N: 5 years **CAGR = ($162,890 / $100,000)^(1/5) − 1** = (1.6289)^0.2 − 1 = 1.10 − 1 = **10.0% per year** **Example 2 — Business revenue growth**: - 2020 revenue: $5 million - 2024 revenue: $9.77 million - N: 4 years **CAGR = ($9.77M / $5M)^(1/4) − 1** = (1.954)^0.25 − 1 = 1.18 − 1 = **18% per year** ## How to Calculate CAGR in Excel Excel has a dedicated CAGR formula using the `RATE` function, or you can use the power operator directly: ### Method 1: Power Operator ```excel = (Ending_Value / Beginning_Value) ^ (1 / Years) - 1 ``` With values in cells: ```excel = (B2 / B1) ^ (1 / A2) - 1 ``` Where B1 = beginning value, B2 = ending value, A2 = number of years. Format the result as a percentage. ### Method 2: POWER Function ```excel = POWER(Ending_Value / Beginning_Value, 1 / Years) - 1 ``` ### Method 3: RRI Function (Dedicated CAGR) Excel's `RRI` function is designed specifically for this calculation: ```excel = RRI(nper, pv, fv) ``` Where: - `nper` = number of periods (years) - `pv` = present value (beginning value) - `fv` = future value (ending value) **Example**: `=RRI(5, 100000, 162890)` returns **10%** ### Method 4: Using Dates (More Precise) For partial years or when you want to use actual dates: ```excel = (B2/B1)^(1/((date2-date1)/365)) - 1 ``` Replace `date2-date1` with the number of days between the dates, then divide by 365 to convert to years. ## CAGR with Annual Data: Excel Step-by-Step If you have a column of annual values (say, 6 years of revenue data from C2:C7): ```excel = (C7/C2)^(1/(ROWS(C2:C7)-1)) - 1 ``` The `ROWS()-1` gives you the number of intervals (5 intervals between 6 data points = 5 years of growth). ## Common CAGR Mistakes **Mistake 1: Counting periods incorrectly** If you have values for Year 0 through Year 5, there are 5 periods of growth — not 6. N = number of intervals, not number of data points. Year 0: $100 Year 1: $110 Year 2: $121 Year 3: $133 Year 4: $146 Year 5: $161 CAGR = (161/100)^(1/5) − 1 = 10%. ✓ Five intervals between 6 data points. **Mistake 2: Using CAGR without noting volatility** Two investments with the same CAGR can have dramatically different risk profiles: - Investment A: +10%, +10%, +10%, +10%, +10% → CAGR 10% - Investment B: +50%, −30%, +50%, −30%, +50% → CAGR ≈ 10% (roughly) Same CAGR, very different experience. Always report standard deviation or max drawdown alongside CAGR. **Mistake 3: Short time periods** CAGR of 50% over 1 year is just the 1-year return — not meaningful compounding. CAGR becomes meaningful over 3+ years and most useful over 5+ years. **Mistake 4: Choosing start/end points selectively** CAGR is highly sensitive to start and end points. A stock that went from $100 to $50 over 5 years then back to $90 in year 7 has a negative 7-year CAGR but was technically profitable if you look only at years 5–7. Always use consistent, relevant time horizons. ## CAGR in Practice: Investment Analysis **Stock return evaluation**: "Stock XYZ had a 10-year CAGR of 15%" means if you held for 10 years, your money compounded at 15% annually on average. **Business revenue analysis**: "Revenue grew at a 25% CAGR from 2018 to 2024" tells you the company grew rapidly — from $100M in 2018 to approximately $375M in 2024. **Portfolio benchmark comparison**: Compare your portfolio CAGR to the S&P 500 CAGR over the same period. If the index returned 11% CAGR and your portfolio returned 9%, you underperformed by 2% annually — which compounds significantly over time. **Dividend growth**: A company that grew its dividend from $1.00 to $1.85 over 6 years has a dividend CAGR of (1.85/1.00)^(1/6) − 1 ≈ **10.8%**. This is a key metric for dividend growth investors. ## The Power of Compounding: CAGR Table Why CAGR matters: a seemingly small difference in annual growth rate dramatically changes ending wealth over time. ![A 4-percentage-point CAGR difference grows $100,000 to $1,006,000 at 8% versus $2,996,000 at 12% over 30 years.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20800%20210%22%20width%3D%22800%22%20height%3D%22210%22%20role%3D%22img%22%3E%3Ctitle%3EComparison%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Ctext%20x%3D%22230%22%20y%3D%2257.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3E8%25%20CAGR%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%2225%22%20width%3D%22151.1014686248331%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22403.1014686248331%22%20y%3D%2257.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%232563eb%22%3E%241.0M%3C%2Ftext%3E%3Ctext%20x%3D%22230%22%20y%3D%22152.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3E12%25%20CAGR%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%22120%22%20width%3D%22450%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%237c3aed%22%2F%3E%3Ctext%20x%3D%22702%22%20y%3D%22152.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%237c3aed%22%3E%243.0M%3C%2Ftext%3E%3C%2Fsvg%3E) *A 4-percentage-point CAGR difference grows $100,000 to $1,006,000 at 8% versus $2,996,000 at 12% over 30 years.* | Initial Amount | CAGR | 10 Years | 20 Years | 30 Years | |---|---|---|---|---| | $100,000 | 5% | $163,000 | $265,000 | $432,000 | | $100,000 | 8% | $216,000 | $466,000 | $1,006,000 | | $100,000 | 10% | $259,000 | $673,000 | $1,745,000 | | $100,000 | 12% | $311,000 | $965,000 | $2,996,000 | | $100,000 | 15% | $405,000 | $1,637,000 | $6,622,000 | The difference between 8% and 12% CAGR over 30 years: $2,996,000 vs. $1,006,000 — nearly 3x as much wealth from just 4 percentage points of additional annual return. ## CAGR vs. Average Annual Return These are NOT the same: ![After +50% then −50%, arithmetic average shows 0% but CAGR correctly shows −13.4% loss.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20800%20210%22%20width%3D%22800%22%20height%3D%22210%22%20role%3D%22img%22%3E%3Ctitle%3EComparison%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Ctext%20x%3D%22230%22%20y%3D%2257.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EArithmetic%20Avg%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%2225%22%20width%3D%226%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22258%22%20y%3D%2257.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%232563eb%22%3E%250%3C%2Ftext%3E%3Ctext%20x%3D%22230%22%20y%3D%22152.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3ECAGR%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%22120%22%20width%3D%22450%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%237c3aed%22%2F%3E%3Ctext%20x%3D%22702%22%20y%3D%22152.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%237c3aed%22%3E%25-13%3C%2Ftext%3E%3C%2Fsvg%3E) *After +50% then −50%, arithmetic average shows 0% but CAGR correctly shows −13.4% loss.* **Arithmetic average return**: Sum of annual returns / number of years **CAGR (geometric mean return)**: Accounts for compounding **Why they differ**: Year 1: +50%, Year 2: −50% - Arithmetic average: (50% − 50%) / 2 = **0%** (breakeven) - CAGR: (1.5 × 0.5)^0.5 − 1 = 0.75^0.5 − 1 = 0.866 − 1 = **−13.4%** A +50% followed by −50% does NOT break even. $100 → $150 → $75. You lost 25% over 2 years — CAGR correctly captures this as −13.4%. Arithmetic average overstates compound growth for volatile assets. **Always use CAGR (geometric return) for investment performance analysis.** ## Authoritative Sources For deeper background and primary-source data on this topic, the following authoritative sources are useful starting points: - [IRS](https://www.irs.gov/) - [SEC](https://www.sec.gov/) ## Conclusion CAGR is the essential tool for converting multi-period data into a single, comparable growth rate. The formula — (End/Start)^(1/N) − 1 — is simple to calculate manually or in Excel using the RRI function, power operator, or POWER function. Understanding CAGR's limitations (point-in-time sensitivity, volatility blindness) and distinguishing it from arithmetic average returns helps you use it correctly. When evaluating investments, businesses, or financial plans, CAGR is the standard language for expressing compound growth. For related financial metrics and analysis, see our guides on [year-over-year analysis](/blog/year-over-year), [TTM meaning](/blog/ttm-meaning), and [return on equity (ROE)](/blog/return-on-equity). Warren at [heywarren.com](https://heywarren.com) automatically calculates CAGR, ROE, and dozens of other performance metrics for any stock in your watchlist. --- ## Related Reading **More from Warren**: - [EPS Formula: How to Calculate Earnings Per Share and Why It Matters](/blog/eps-formula) - [Return on Equity (ROE): Formula, Calculation, and What It Reveals About a Business](/blog/return-on-equity) - [Cox-Ingersoll-Ross (CIR) Model: The Interest Rate Model Explained](/blog/cox-ingersoll-ross) **Authoritative sources**: - [SEC EDGAR — Company Filings](https://www.sec.gov/edgar/searchedgar/companysearch) - [Federal Reserve Economic Data (FRED)](https://fred.stlouisfed.org/) - [Bureau of Labor Statistics — Data Tools](https://www.bls.gov/data/)