CAGR — compound annual growth rate — answers a single question: at what constant yearly rate would your starting value have grown into your ending value? It smooths out a bumpy true history into one number you can compare across investments, business units or revenue lines. It is the rate a mutual fund quotes and the number a startup pitch uses for year-over-year growth.
The formula, plainly
Take the ending value divided by the beginning value, raise it to the power of one over the number of years, and subtract one. If an investment goes from ₹1,000 to ₹2,000 over ten years, the ratio is 2, the tenth root of 2 is about 1.0718, and minus one gives 7.18% — meaning it grew 7.18% per year, compounded, to double in a decade.
cagr = (end / start) ** (1 / years) − 1 1000 → 2000 over 10 years: ratio = 2.0 cagr = 2.0 ** 0.1 − 1 ≈ 0.0718 → 7.18% per year
Why it beats a simple average
A simple average overstates growth whenever the path is volatile. Consider a year of +50% followed by a year of −50%. The arithmetic average is 0%, yet a ₹1,000 investment ends at ₹750 — a real loss of 25%. CAGR reports the true −13.4% per year, because it compounds, and compounding punishes the down years harder than the average can show. Volatility is the entire reason the two numbers diverge.
That compounding is also why CAGR is one of the few growth figures honest enough for comparisons: it lets you line up a lumpy venture, a stable index fund and a property holding on the same yearly scale and ask which one actually grew faster.
What CAGR does not tell you
- Drawdowns: it hides the 30% crash in year four behind the smoothed headline.
- Cash flows: contributions or withdrawals during the period change the true return, and the base formula ignores them.
- Risk: a 7% CAGR from calm index exposure and a 7% CAGR from leveraged bets are not equivalent outcomes.
Use CAGR alongside, not instead of, the raw path. For a single holding with no cash flows it is a fair summary; for an account you added money to monthly, look for money-weighted return instead.
