CAGR Calculator

How to use the CAGR calculator

Enter the value at the start of the period, the value at the end, and how many years separate them. The tool returns the compound annual growth rate, the growth multiple, the total growth across the whole period, and the simple annual rate for contrast.

It also shows a check line: the start value grown at the reported rate for the years given, which lands back on the end value. That round trip is the definition of CAGR, and seeing it close is the fastest way to confirm the inputs are what you meant.

The simple annual rate sits next to the CAGR because the two answer different questions. Eighty percent over five years divided by five gives 16 percent, but growing at 16 percent a year compounding would end at $21,003 rather than $18,000. Simple division ignores that each year grows on a base the previous year already enlarged.

A start value of zero or below returns an explanation rather than a number. There is no percentage rate that grows nothing into something, and a negative start makes the ratio meaningless rather than merely awkward, so the tool says which rule was broken instead of producing a quiet NaN.

That worked pair is the reason to be careful with a CAGR quoted on its own. It is a true statement about two end points and a genuinely useful summary, and it is silent about everything that happened in between, including a year that lost a quarter of the value.

Why CAGR hides the whole path

CAGR is defined by two points, so any path joining those points produces the same rate. That is the point of a smoothed figure and it is also the risk of one. The two series below both start at $10,000, both end at $15,624 after five years, and both therefore report a CAGR of 9.33 percent.

The two lines meet at the beginning and the end and nowhere else. Year two is the worst of it: the real holding is worth $10,500 while the smoothed line reads $11,954, a difference of $1,454 on a $10,000 start. Anyone who needed the money in year two experienced nothing like 9.33 percent a year.

CAGR against the simple annual rate

The simple annual rate is total growth divided by years. It is easier to work out and it is wrong for anything that compounds, because it treats every year as growing on the original base rather than on the base the previous year left behind. The gap widens with both the growth and the length of the period.

One case runs the other way. Over a period shorter than a year the CAGR is larger than the simple rate, because annualising a part year compounds it upward: $100 to $121 in six months is a CAGR of 46.41 percent against a simple annual rate of 42 percent. The reference table below carries both figures for every pair.

The formula, worked line by line

CAGR asks one question: what constant annual rate, applied every year without variation, would have carried the start value to the end value over this period. Dividing end by start gives the growth multiple, taking the root of that multiple by the number of years gives the yearly factor, and subtracting one turns the factor into a rate.

Writing the root as an exponent of 1 divided by years is what lets the formula take part years without any special handling. It also means the whole thing inverts cleanly: raise one plus the rate back to the power of the years and the start value returns to the end value, which is the check line the tool shows.

multiple = end ÷ start
CAGR     = multiple^(1 ÷ years) − 1
check    = start × (1 + CAGR)^years   →   end
total growth  = (multiple − 1) × 100
simple annual = total growth ÷ years
years to double = ln(2) ÷ ln(1 + CAGR)      (only when CAGR > 0)

Why zero and negative start values are refused

A growth multiple is a ratio, and a ratio needs a base to be a ratio of. With a start of zero there is no multiple at all, and every end value would need an infinite rate. With a negative start the multiple flips sign, so the root either has no real value or has one that means nothing financially.

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