Math & Statistics

Growth Rate and CAGR Calculator

Turns a series into period-on-period change, cumulative change and a compound growth rate.

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How to use this tool

  1. Paste the series in order, one value per period, oldest first.
  2. Select Calculate.
  3. Take the compound rate from the summary — it is the figure that survives being checked.
  4. Scan the period-on-period column for the one period that is carrying the whole trend.

What growth rate does

Paste the series in order, one value per period, and every period gets its change on the previous value and its change on the first. The compound rate across the whole series is calculated from the two ends, which is what CAGR is — a constant rate that would have produced the same finish from the same start, not an average of the steps along the way.

The simple average of the period changes is shown next to the compound rate, and it is almost always the larger of the two. That gap widens with volatility, which is why a volatile series quoted at its arithmetic mean growth looks better than it was. When the series starts or ends at or below zero no compound rate exists, and the page says so instead of printing a number.

Frequently asked questions

CAGR is the constant rate that would have taken you from the first value to the last over the same number of periods. The average of the period-on-period changes is nearly always higher, and the gap widens with volatility. CAGR is the figure that reconciles with the actual endpoints, which is why it is the one to quote.

Because a compound rate needs both ends to be positive. A series that starts at or below zero, or ends there, has no constant multiplier that connects them — the mathematics gives a complex number or an infinity. The page says so rather than printing something that looks like an answer.

Only for how you describe the result. The calculation is the same whether your rows are days, months or years; the compound figure is per period. Label it correctly when you quote it, because a monthly rate read as an annual one is out by more than an order of magnitude.