CAGR Calculator — the annual rate your growth implies

How it works

One inversion: compound growth says end = start × (1+r)^y, so the implied rate is r = (end/start)^(1/y) − 1. Compounding the answer back for y years reproduces the ending value to the cent — the round trip the tests assert. Total growth (end/start − 1) and the dollar gain sit beside it for scale. The time-dilution sweep is the page's lesson: the same start and end reached over 2, 5, 10, or 20 years shows the identical total growth dissolving into very different annual rates — which is precisely the comparison plain ROI cannot make. CAGR is an average in the geometric sense: real paths wobble around it, but any path with those endpoints has that CAGR.

Worked example

Both anchors are the published growth pairs read backwards. The default: $3,000 grew to $3,932.39 in four years (LibreTexts' compound example), so the implied rate is (3932.39/3000)^(1/4) − 1 = 7.00% — the rate the textbook used, recovered exactly. The preset: Sophia's $200 bond reaching $530.77 over 30 years implies about 3.31% a year — the effective annual rate of its published 3.28%-compounded-semiannually terms, which is exactly what an annualizing measure should return.

Frequently asked questions

What is CAGR?

The constant yearly growth rate connecting a start value to an end value over a period — the smoothed rate, not the actual year-by-year path. It answers "how fast, per year" where total growth answers "how much, overall", and the two convert exactly through the years.

Why use CAGR instead of a simple average of yearly returns?

Because arithmetic averages overstate compound growth: +50% then −50% averages 0% but leaves you down 25%. CAGR is the geometric answer — the rate that actually reproduces the endpoints when compounded — so it is the number that matches what the money did.

How do I compare investments held for different lengths of time?

That is CAGR's job: convert each to its implied annual rate and compare those. The sweep on this page shows why totals mislead — the same doubling is 41% a year over two years and under 4% over twenty.

Can CAGR be negative?

Yes — an ending value below the start gives a negative rate, and a total loss is exactly −100% a year in the limit. Declines annualize the same way gains do: the rate that compounds the start down to the end.

What does CAGR hide?

The path: volatility, interim highs and lows, and any cash added or removed along the way. It treats the journey as smooth and the endpoints as the whole story — for money with deposits and withdrawals in between, a money-weighted measure is the honest tool.

How does CAGR relate to compounding frequency?

CAGR always speaks in effective annual terms, whatever compounding produced the endpoints — Sophia's semiannual 3.28% bond recovers as its 3.31% effective annual rate here. That makes CAGRs comparable across instruments that compound differently.

How accurate is this, and what does it exclude?

The inversion is exact for the two values and the span you enter. It excludes interim cash flows (use IRR-style tools for those), taxes and fees unless your endpoints already net them, and inflation — subtracting an inflation assumption gives the real rate, which the inflation calculator can supply.