CAGR Calculator

Compound annual growth rate is the single constant rate that would carry a beginning value to an ending value over a given number of years:

$\text{CAGR} = \left(\frac{V_{\text{end}}}{V_{\text{begin}}}\right)^{\frac{1}{n}} - 1$

• $V_{\text{begin}}$ — the value at the start
• $V_{\text{end}}$ — the value at the end
• $n$ — the number of years between the two observations, not the number of data points

It is the inverse of compounding: where $V_{\text{end}} = V_{\text{begin}}(1+r)^n$ solves forward for a value, CAGR solves backward for the rate. That makes it a smoothed figure — it describes the endpoints only and says nothing about the path between them. Two series with wildly different volatility can share a CAGR.

The same relation answers three other questions:

$V_{\text{end}} = V_{\text{begin}}(1+r)^n, \qquad V_{\text{begin}} = \frac{V_{\text{end}}}{(1+r)^n}, \qquad n = \frac{\ln(V_{\text{end}}/V_{\text{begin}})}{\ln(1+r)}$

The last one uses logarithms because $n$ sits in the exponent; any log base works as long as both are the same.

For a non-whole horizon, put the years in as a decimal: 42 months is $n = 3.5$.

CAGR is not the arithmetic mean of yearly returns. The arithmetic mean adds and divides; CAGR multiplies and takes a root, which is a geometric mean of the growth factors:

$1 + \text{CAGR} = \sqrt[n]{(1+r_1)(1+r_2)\cdots(1+r_n)}$

Whenever the yearly returns vary, the geometric mean is strictly below the arithmetic mean, and the gap widens with volatility. Only CAGR reproduces the actual ending value.

• Counting data points instead of intervals: values for 2018 through 2024 span $n = 6$ years, not 7.
• Averaging the annual percentages: use the geometric mean, or the CAGR will not reproduce the ending value.
• Applying CAGR to a series that crosses zero or goes negative: the ratio $V_{\text{end}}/V_{\text{begin}}$ must be positive, or the root is undefined.
• Forgetting to subtract 1: the root gives the growth factor; CAGR is that factor minus 1.
• Comparing CAGRs over different horizons: a 3-year and a 10-year CAGR are not like-for-like.
• Reading CAGR as a forecast: it is a description of two observed endpoints, nothing more.