CAGR Calculator

What is CAGR?

Compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning value to its ending value, assuming profits are reinvested at the end of each year. It represents a smoothed annual rate of return, eliminating the effects of volatility.

CAGR is widely used because it provides a single, easily comparable number that describes growth over time. Unlike simple average returns, CAGR accounts for the compounding effect and gives you the true equivalent annual return.

The CAGR formula

$$CAGR = \left(\frac{Ending\ Value}{Beginning\ Value}\right)^{\frac{1}{n}} - 1$$

Where:

• $Ending\ Value$ = Final value of the investment
• $Beginning\ Value$ = Initial value of the investment
• $n$ = Number of years

Example calculation

An investment grows from $10,000 to $25,000 over 5 years:

$$\begin{aligned} CAGR &= \left(\frac{\$25,000}{\$10,000}\right)^{\frac{1}{5}} - 1 \\[0.5em] &= (2.5)^{0.2} - 1 \\[0.5em] &= 1.201 - 1 \\[0.5em] &= 20.1\% \end{aligned}$$

CAGR vs simple average return

Consider an investment with these annual returns: +50%, -30%, +20%

Simple average:

$$\frac{50\% + (-30\%) + 20\%}{3} = 13.3\%$$

CAGR calculation:

• Starting: $100
• After year 1: $150 (+50%)
• After year 2: $105 (-30%)
• After year 3: $126 (+20%)

$$CAGR = \left(\frac{\$126}{\$100}\right)^{\frac{1}{3}} - 1 = 8.0\%$$

The CAGR of 8.0% is much more accurate than the 13.3% simple average because it reflects actual wealth growth.

Why CAGR matters

Smooths volatility

Real investments don't grow steadily. CAGR gives you a single number that represents what the steady growth rate would need to be to achieve the same result.

Enables comparison

CAGR allows you to compare:

• Different investments over different time periods
• Your portfolio vs. market benchmarks
• Business revenue or profit growth
• Any metric that changes over time

Shows compound effect

CAGR inherently accounts for compounding, making it more meaningful than simple arithmetic averages.

CAGR benchmarks

Investment type	Historical CAGR
US Stocks (S&P 500)	~10%
International Stocks	~8%
Bonds	~5-6%
Real Estate	~4-5%
Inflation	~2-3%
Savings Accounts	~1-2%

Note: Historical returns don't guarantee future results.

Practical applications

Investment performance

"My portfolio grew from $50,000 to $85,000 over 7 years."

• CAGR = (85,000/50,000)^(1/7) - 1 = 7.8%

This lets you compare against benchmarks or other investments.

Business growth

"Our revenue grew from $2M to $10M over 5 years."

• CAGR = (10/2)^(1/5) - 1 = 38.0%

This shows consistent growth regardless of year-to-year fluctuations.

Real estate appreciation

"My home value increased from $300,000 to $450,000 over 10 years."

• CAGR = (450,000/300,000)^(1/10) - 1 = 4.1%

Retirement planning

If you need $2M in 25 years starting with $200,000:

• Required CAGR = (2,000,000/200,000)^(1/25) - 1 = 9.6%

Limitations of CAGR

Ignores volatility risk

Two investments can have identical CAGRs but vastly different risk profiles:

• Investment A: Steady 10% annually
• Investment B: +50%, -20%, +30%, -10%, +15% (same CAGR)

Investment B is much riskier despite the same CAGR.

Assumes reinvestment

CAGR assumes all returns are reinvested. If you withdraw funds, actual returns will differ.

Doesn't reflect interim cash flows

CAGR only considers beginning and ending values. It doesn't account for:

• Additional contributions
• Withdrawals
• Dividend income not reinvested

For complex scenarios, use IRR instead.

Historical, not predictive

Past CAGR doesn't predict future returns. Markets, businesses, and economies change.

CAGR vs other metrics

Metric	Use case
CAGR	Smoothed annual growth rate
IRR	Multiple cash flows over time
ROI	Total return regardless of time
Annualized ROI	Same as CAGR
Simple Average	Quick approximation

Reverse CAGR calculation

You can also solve for ending value or years:

Find ending value:

$$Ending\ Value = Beginning\ Value \times (1 + CAGR)^n$$

Find years needed:

$$n = \frac{\ln(Ending\ Value / Beginning\ Value)}{\ln(1 + CAGR)}$$

Example: How long to double at 7% CAGR?

$$n = \frac{\ln(2)}{\ln(1.07)} = 10.2\ years$$

Tips for using CAGR

1. Compare like with like — Use same time periods when possible
2. Consider risk — Don't choose investments based solely on CAGR
3. Check the time frame — Short periods may not be representative
4. Account for fees — Calculate CAGR after all fees
5. Adjust for inflation — Use real CAGR for purchasing power analysis
6. Verify the data — Ensure beginning and ending values are accurate