# CAGR Calculator Calculate the compound annual growth rate between a starting and ending value to measure investment performance over time. --- - **Canonical URL:** https://dothecalculation.com/calculators/cagr-calculator - **Category:** Financial calculators - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology - **Reviewed by:** Dr. Elizabeth Vance, PhD, PhD in Quantitative Finance, London School of Economics (https://dothecalculation.com/about/team/elizabeth-vance) --- ## CAGR Calculator — Compound Annual Growth Rate Compute the smoothed annual rate of return required for an investment to grow from its initial value to its final balance over a set timeline. - Smoothed annual return rate - Total percentage growth metrics - Growth multiplier factors ## What is Compound Annual Growth Rate (CAGR)? Compound Annual Growth Rate (CAGR) is the geometric average rate of return at which an investment grows annually, assuming profits are reinvested (compounded) at the end of each year. CAGR is a highly useful financial metric because it smooths out the volatile, irregular annual returns of an investment, presenting a single annualized rate that represents the investment's overall growth velocity. Unlike a simple average rate of return, CAGR accounts for compounding, making it the industry standard for comparing the performance of different assets or portfolios over identical historical periods. ## How to Use This Calculator Enter the starting value of the investment, its ending value, and the number of years between the two. The calculator solves for the single constant annual growth rate that connects those two points. Use it to compare investments of different sizes and durations on an apples-to-apples annualized basis, rather than looking at raw dollar gains alone. ## Worked Example: $10,000 Growing to $15,000 Over 5 Years Starting value $10,000, ending value $15,000, 5-year period. CAGR: (\(15,000 / 10,000\))^(1/5) − 1 = (1.5)^0.2 − 1 ≈ 8.45%. That 8.45% annualized figure is easy to misread against the raw 50% total gain — the investment did not grow 50% per year, it grew 50% total, which compounds out to roughly 8.45% per year over the 5-year holding period. Checking the math: $10,000 growing at 8.45% annually for 5 years compounds to approximately $10,000 × (1.0845)^5 ≈ $15,000, confirming the rate. ## The Mathematical CAGR Formula To calculate the Compound Annual Growth Rate, apply the geometric growth formula: $$\text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1$$ Where: * \(\text{Ending Value}\) is the final balance of the investment. * \(\text{Beginning Value}\) is the initial principal amount. * \(n\) is the number of years in the investment term (can be fractional). This formula solves for the single constant annual growth rate that connects the beginning and ending values over the specified time horizon. ## CAGR vs. Average Annual Return (AAR) Average Annual Return (AAR) is a simple arithmetic average of annual gains and losses. AAR can be highly misleading because it ignores the mathematical effects of compounding and losses. For example, if an investment of $10,000 gains 100% in year one (value becomes $20,000) and loses 50% in year two (value becomes $10,000), the AAR is \((100\% - 50\%) / 2 = 25\%\). However, you have made zero dollars. The CAGR is \((10,000 / 10,000)^{0.5} - 1 = 0\%\), which accurately reflects the real financial outcome. ## Limitations of CAGR: The Smoothed Reality Trap CAGR is a representational metric. It assumes a steady, constant growth rate over the entire investment term. In reality, assets experience volatility, down years, and rapid climbs. CAGR is best used to summarize long-term trends, but should be paired with standard deviation or maximum drawdown metrics to evaluate risk. ## Related Calculators To factor in cash added or withdrawn along the way (not just start and end values), use the [ROI calculator](/calculators/roi-calculator), or weigh this smoothed growth rate against the asset's volatility with the [risk-adjusted return calculator](/calculators/risk-adjusted-return-calculator). ## Frequently asked questions ### What does CAGR stand for? CAGR stands for Compound Annual Growth Rate. It measures the annualized average growth rate of an investment over a multi-year period. ### What is the formula for CAGR? CAGR = (Ending Value / Beginning Value) ^ (1 / Years) - 1. It calculates the smoothed constant annual rate of return. ### How does CAGR differ from average annual return? Average annual return is a simple arithmetic average of annual returns. CAGR is a geometric average that accounts for compounding and the impact of losses, reflecting the real rate of return. ### Can CAGR be negative? Yes. If the final value of the investment is lower than the initial investment, the CAGR will be negative, indicating an annualized average loss. ### Does CAGR account for portfolio volatility? No. CAGR smooths out annual fluctuations, assuming a constant rate of growth. It does not measure or reflect the risk or volatility of the underlying asset. ### Is CAGR useful for comparing different investments? Yes. CAGR annualized performance, allowing you to compare a 3-year investment directly against a 10-year investment on an equal annual basis. ### Can I calculate CAGR for periods under one year? Yes, but it is less common. You can use fractional years (e.g., 6 months = 0.5 years) in the formula, but annualized short-term returns can distort long-term expectations. ### How do contributions affect CAGR calculations? CAGR assumes a single lump sum is invested at the beginning and grows to the end. It does not easily account for ongoing deposits or withdrawals, which require calculating Internal Rate of Return (IRR). ### What is a good CAGR for a stock portfolio? Historically, a CAGR of 7% to 10% is considered strong for long-term equity portfolios, matching or exceeding historical index averages. ### What is the difference between CAGR and IRR? CAGR measures growth from a single beginning value to an ending value. IRR (Internal Rate of Return) calculates returns for complex cash flows containing multiple recurring contributions or withdrawals. ### Why does a 50% total gain not equal a 50% CAGR? A 50% total gain spread over several years compounds to a much smaller annual rate. CAGR converts the total percentage move into the single constant annual rate that, compounded year after year, would produce the same ending value — so the more years the gain took, the lower the CAGR relative to the total gain. ### Can CAGR be used for business revenue growth, not just investments? Yes. The same formula applies to any starting and ending value over time — company revenue, user counts, real estate prices, or portfolio balances — as long as you have a clean beginning figure, ending figure, and number of years between them. ## Related concepts - **AAR** — Average Annual Return: a simple arithmetic average of annual investment return rates. - **IRR** — Internal Rate of Return: the annualized return rate calculated for portfolios with complex ongoing cash flows. - **Geometric Mean** — The mathematical averaging method used by CAGR to accurately compound multi-period returns. - **Total Return** — The raw percentage gain or loss over the full holding period, before annualizing. ## Related guides - [Compound Interest: Formula, Examples, and Calculator](https://dothecalculation.com/blog/finance/compound-interest-deep-dive) — Learn how compound interest works, calculate growth with monthly deposits, compare assumptions, and avoid common projection mistakes. - [Simple vs Compound Interest: Linear Growth vs Interest on Interest](https://dothecalculation.com/blog/finance/simple-vs-compound-interest) — Compare simple interest and monthly compound interest, learn when each model fits, and use worked examples aligned to the calculators. ## Related calculators - [Compound Interest Calculator](https://dothecalculation.com/calculators/compound-interest-calculator) — Model compound growth of savings or investments with regular deposits, interest rate, and time horizon to project future value. - [Interest Calculator](https://dothecalculation.com/calculators/interest-calculator) — Calculate simple and compound interest scenarios instantly to see how principal, rate, and time affect your total earnings. - [Investment Calculator](https://dothecalculation.com/calculators/investment-calculator) — Project compound growth of your investments with regular contributions, interest rate, and time horizon to estimate future value. - [Savings Calculator](https://dothecalculation.com/calculators/savings-calculator) — Forecast savings account growth and calculate the monthly deposits needed to reach a specific financial goal by a target date. - [Simple Interest Calculator](https://dothecalculation.com/calculators/simple-interest-calculator) — Calculate simple interest, the final amount owed, and total repayment amount based on your principal, rate, and loan term. - [Dividend Calculator](https://dothecalculation.com/calculators/dividend-calculator) — Calculate dividend yield, projected annual income, and future portfolio value with DRIP dividend reinvestment over time. --- _This tool is for educational purposes only. Compounding schedules, investment returns, inflation indices, retirement nest egg timelines, and asset appreciation targets depend on personal budget profiles, tax brackets, market volatility, and macroeconomic policies. Always consult a certified financial planner (CFP) or tax advisor before finalizing long-term investment strategies._ --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/cagr-calculator). Quote freely with attribution and a link to this page._