CAGR (compound annual growth rate)

Also called: CAGR, compound annual growth rate, average annual growth

The steady yearly growth that turns a start value into an end value over n years: (end ÷ start)^(1/n) − 1. 100,000 → 275,589 over 20 years is a CAGR of 5.2%.

CAGR answers: what constant yearly growth would take the start value to the end value?

$CAGR = \left(\frac{V_n}{V_0}\right)^{1/n} - 1$

The power 1/n is the n-th root: it finds the factor that, multiplied by itself n times, gives the total growth. In a spreadsheet: =(end/start)^(1/n)-1.

Dividing the total growth by the number of years overstates it, because it ignores compounding. And when yearly returns swing, CAGR is lower than their simple average: a loss needs a bigger gain to recover (−28% needs +38.9%).

Example

Klasna Club grew from 400 to 900 members in 4 years.

Total growth: 900 ÷ 400 = 2.25.
CAGR = 2.25^(1/4) − 1 = √1.5 − 1 ≈ 22.47%.
The shortcut 125% ÷ 4 = 31.25% would compound to 1.3125⁴ ≈ 2.97, far more than 2.25.

Common mistakes

Dividing total growth by years. +40% over 3 years is 11.87% a year, not 13.3%.
Averaging yearly returns. +300% then −75% averages +112.5% but ends where it started.
Annual ≠ 12 × monthly. 2% a month is 26.8% a year; 5% monthly churn is about 46% a year, not 60%.

Learn it in the course

Compounding · Growth factors, why −50% then +50% loses a quarter, (1 + r)ⁿ, simple vs compound interest, CAGR with a fractional power, and monthly ↔ yearly rates and churn.