CAGR Calculator
Calculate Compound Annual Growth Rate (CAGR) from beginning value, ending value, and time period. Measure smoothed annual investment returns.
Formula
CAGR = (Ending Value / Beginning Value)^(1/n) - 1
Where Ending Value is the final investment value, Beginning Value is the initial investment value, and n is the number of years. This formula calculates the constant annual rate of return that would be needed to grow the beginning value to the ending value over the specified period, assuming compound growth.
Worked Examples
Example 1: Stock Portfolio CAGR Analysis
Problem: Your stock portfolio grew from $50,000 to $145,000 over 8 years. What is the CAGR?
Solution: CAGR = (Ending Value / Beginning Value)^(1/years) - 1\nCAGR = ($145,000 / $50,000)^(1/8) - 1\nCAGR = (2.9)^(0.125) - 1\nCAGR = 1.1423 - 1 = 0.1423\nCAGR = 14.23%\n\nTotal Return = ($145,000 - $50,000) / $50,000 = 190%\nSimple Average = 190% / 8 = 23.75% (overstates actual growth)\nDoubling time at this CAGR = 72 / 14.23 = 5.06 years
Result: CAGR: 14.23% | Total Return: 190% | Growth Multiple: 2.9x
Example 2: Required CAGR to Reach Financial Goal
Problem: You have $75,000 saved and want to reach $500,000 in 12 years. What CAGR is needed?
Solution: Required CAGR = (Target / Current)^(1/years) - 1\nCAGR = ($500,000 / $75,000)^(1/12) - 1\nCAGR = (6.667)^(0.0833) - 1\nCAGR = 1.1713 - 1 = 0.1713\nCAGR = 17.13%\n\nThis requires 17.13% annual compounded growth\nHistorical S&P 500 CAGR is ~10%, so this goal is aggressive\nAlternative: reduce target or increase time horizon
Result: Required CAGR: 17.13% | Growth Multiple Needed: 6.67x | Assessment: Aggressive target
Frequently Asked Questions
What is CAGR and why is it important for investors?
CAGR stands for Compound Annual Growth Rate, which measures the constant annual rate of return that would be required for an investment to grow from its beginning value to its ending value over a specified period, assuming profits are reinvested at the end of each year. Unlike simple average returns, CAGR accounts for the compounding effect and provides a smoothed annual rate that eliminates the volatility of year-to-year performance. This makes it the standard metric for comparing investment performance across different time periods, asset classes, and investment strategies. CAGR is particularly valuable because it tells you exactly what equivalent steady growth rate would produce the same final result as the actual volatile path your investment took.
How is CAGR calculated and what is the formula?
The CAGR formula is CAGR = (Ending Value / Beginning Value)^(1/n) - 1, where n is the number of years. The calculation takes three inputs: the starting value of the investment, the ending value, and the total time period. First, divide the ending value by the beginning value to get the total growth multiple. Then raise that multiple to the power of 1 divided by the number of years, which effectively distributes the total growth evenly across each year. Finally, subtract 1 to convert from a growth factor to a growth rate. For example, if $10,000 grows to $25,000 over 7 years: CAGR = (25000/10000)^(1/7) - 1 = 2.5^0.1429 - 1 = 1.1399 - 1 = 13.99%. This means the investment grew at an equivalent steady rate of about 14% per year.
What is the difference between CAGR and average annual return?
The simple average annual return adds up each year individual returns and divides by the number of years, while CAGR accounts for compounding. These can produce significantly different results. Consider an investment that goes up 100% in year 1 (from $100 to $200) and then drops 50% in year 2 (from $200 to $100). The simple average return is (100% + -50%) / 2 = 25%, suggesting strong performance. But CAGR = ($100/$100)^(1/2) - 1 = 0%, correctly showing that you ended up exactly where you started. CAGR always provides the more accurate representation of actual investment performance because it reflects what actually happened to your money, accounting for the mathematical asymmetry where losses require larger gains to recover.
What is a good CAGR for different types of investments?
Historical benchmarks provide useful context for evaluating CAGR. The S&P 500 has delivered a CAGR of approximately 10% to 11% over the past 50 years in nominal terms, or about 7% after adjusting for inflation. Individual top-performing stocks can achieve CAGRs of 15% to 25% over extended periods, though this level of outperformance is rare and difficult to sustain. Real estate investments typically produce CAGRs of 4% to 8% depending on the market and whether rental income is included. Government bonds have historically delivered 3% to 5% CAGR. Any CAGR consistently above 15% over a decade or more would be considered exceptional by professional investment standards, while anything above 20% sustained for that long would place you among the greatest investors in history.
Can CAGR be misleading and what are its limitations?
While CAGR is extremely useful, it has notable limitations that investors should understand. First, CAGR completely ignores the path taken between the start and end dates, smoothing over what might be extreme volatility. An investment that steadily grows 10% annually looks identical in CAGR to one that drops 80% and then recovers spectacularly. Second, CAGR is highly sensitive to the choice of start and end dates. Cherry-picking favorable dates can make a poor investment look excellent or vice versa. Third, CAGR does not account for cash flows during the period, meaning investments with additional contributions or withdrawals need a different metric called Internal Rate of Return (IRR). Finally, CAGR represents past performance and does not predict or guarantee future returns, despite being commonly used for forward projections.
How does CAGR relate to the Rule of 72?
CAGR and the Rule of 72 are complementary tools for investment analysis. Once you know your CAGR, you can quickly estimate the doubling time by dividing 72 by the CAGR percentage. If your portfolio has achieved a 12% CAGR, it doubles approximately every 72/12 = 6 years. Conversely, if you know your money doubled in a certain period, you can estimate the CAGR. Money that doubled in 5 years had an approximate CAGR of 72/5 = 14.4%. The Rule of 72 also helps project forward: at a 9% CAGR, your investment would double roughly every 8 years, quadruple in 16 years, and grow 8-fold in 24 years. This mental math shortcut makes CAGR far more intuitive and actionable for financial planning discussions.