CAGR Calculator

When to use it

CAGR answers a comparison question, not a prediction one: what steady yearly rate would turn the starting value into the ending value? It is the fair way to put two investments side by side when they ran for different lengths of time, collapsing the good and bad years into one number.

Typical uses: comparing a fund held for seven years with one held for four, describing revenue growth between two annual accounts, or checking whether savings beat inflation. Years can be fractional — 2.5 is right for thirty months — and the values need not be money.

How the maths works

CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1, printed as a percentage per year. Both values must be positive, since the tool takes their ratio and then its root. Total growth is reported too: ending ÷ starting − 1, so 10,000 to 16,000 shows 60% overall, the figure the yearly rate reproduces.

Because the exponent is one over the number of years, the result is sensitive to what counts as a year. Months and years are not interchangeable: 60% over five years is 9.86% a year, but over sixty months it is 0.79% a month.

A worked example

A portfolio goes from 10,000 to 16,000 in five years. What steady rate is that?

1. Form the ratio: 16,000 ÷ 10,000 = 1.6.
2. Take the fifth root of 1.6.
3. In logs: ln 1.6 = 0.4700, ÷ 5 = 0.0940, e^0.0940 = 1.0986.
4. Subtract 1 and read it as a rate: 9.86% per year.
5. Check: 1.0986^5 = 1.6003, or 16,003 — a rounding cent.

Rates from the same tool

The first two rows make the point: 50% over eight years is barely half the rate of 60% over five.

Common mistakes

• Averaging the yearly percentages. The mean of +40%, −10% and +5% is not the growth rate; compounding works on the balance, so only the geometric mean reproduces the end.
• Using it as a forecast. CAGR describes the past, says nothing about the next five years, and hides any crash inside the period.
• Comparing windows of different lengths. A 9.86% five-year rate and a 9.86% ten-year rate describe different achievements; always quote the period.
• Feeding it a zero. The ratio cannot be formed, so the tool asks for values above zero; a total loss has no CAGR.

Keep exploring

• Compound Interest Calculator — project an amount forward at a rate you choose.
• ROI Calculator — total return as a percentage, without time weighting.
• Inflation Calculator — the rate that erodes the purchasing power of the same money.
• Guide: CAGR and Inflation Explained.