Compound Annual Growth Rate (CAGR) Calculator

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Initial Value

Final Value

Number of Years

Results

Compound Annual Growth Rate (CAGR)

14.87%

per year

Initial Value	1,000
Final Value	2,000
Total Growth	100%

What is CAGR?

The Compound Annual Growth Rate (CAGR) measures the smoothed annual rate at which an investment or quantity grows from a starting value to an ending value over a set number of years. Unlike a simple average, it accounts for compounding, giving a single "as if it grew steadily" rate that is ideal for comparing different investments or time periods.

CAGR represents the smooth annual rate that connects the initial and final values over \(n\) years.

How to use this calculator

Enter the initial value, the final value, and the number of years between them. The calculator returns the annualized CAGR as a percentage, along with the total cumulative growth over the whole period.

The formula explained

CAGR is found with $$r = \left( \frac{V_{\text{final}}}{V_{\text{initial}}} \right)^{\frac{1}{n}} - 1,$$ where \(n\) is the number of years. Multiply by 100 to express it as a percentage. The total growth is simply \(\frac{V_{\text{final}}}{V_{\text{initial}}} - 1\), ignoring the time dimension.

The CAGR formula: divide final by initial value, take the \(n\)-th root, then subtract one.

Worked example

Suppose an investment grows from 1,000 to 2,000 over 5 years. The ratio is 2.0, and \(2.0^{1/5} \approx 1.148698\). Subtracting 1 gives \(0.148698\), so the CAGR is about 14.87% per year. The total growth is 100% over the period.

FAQ

Can the final value be smaller than the initial value? Yes — a decline produces a negative CAGR, indicating the value shrank on average each year.

What if the number of years is less than one? Fractional years work; the exponent \(1/n\) simply annualizes the partial-period growth.

Why use CAGR instead of total growth? CAGR normalizes for time, letting you compare investments held for different durations on an equal footing.