CAGR Calculator

How to use the CAGR calculator

1. Enter the initial value: what the investment, revenue figure or other quantity was worth at the start of the first period.
2. Enter the end value: what it was worth at the end of the last period.
3. Enter the number of periods, usually years, as a whole number of at least 1.

The calculator returns the CAGR as a percentage and the total growth, which is simply the end value minus the initial value. A negative CAGR means the value shrank. The initial value cannot be zero, because growth from nothing has no rate.

Understanding CAGR

The compound annual growth rate answers a simple question: at what constant yearly rate would the starting value have to grow to land exactly on the end value? Real investments rarely move in a straight line, so the CAGR is a smoothed figure that hides the ups and downs along the way and keeps only the start, the finish and the elapsed time.

That makes it a convenient yardstick for comparing things that grew over different spans, such as a fund against a benchmark, a company's revenue against its rivals, or a website's traffic over three years against five. It is a geometric average, which is the correct way to average growth that compounds.

The CAGR formula

CAGR = (end value ÷ initial value)^{1 ÷ periods} − 1Multiply the result by 100 to express it as a percentage.

The formula rearranges to answer related questions. To project an end value from a known growth rate, and to find how many periods a target takes:

end value = initial value × (1 + CAGR)^periods

periods = ln(end value ÷ initial value) ÷ ln(1 + CAGR)

For example, at a steady 9% a year it takes ln(3) ÷ ln(1.09) = 12.75 years for money to triple, and $8,000 growing at 7.5% for six years becomes 8,000 × 1.075⁶ = $12,346.41.

Worked examples

Growth. An investment grows from $1,000 to $2,500 over 5 years. The ratio is 2.5, and 2.5^1/5 = 1.20112, so the CAGR is 20.112%. Total growth is $1,500. As a check, 1,000 × 1.20112⁵ comes back to $2,500.

Decline. A holding falls from $2,500 to $1,000 over the same 5 years. The ratio is 0.4, and 0.4^1/5 = 0.83255, so the CAGR is −16.745% and total growth is −$1,500.

How long to double. The growth rate needed to double an amount depends only on the time allowed:

CAGR versus the average return

Averaging yearly returns the ordinary way overstates what an investor actually earned, because gains and losses compound on a changing base. Take three years of +10%, +30% and −20%. The arithmetic mean is (10 + 30 − 20) ÷ 3 = 6.667% a year. But the money multiplied by 1.10 × 1.30 × 0.80 = 1.144, and 1.144^1/3 − 1 = 4.586%. The CAGR is the figure that reproduces the real end balance.

A starker case: a value that rises 50% and then falls 50% has an arithmetic average change of 0%, yet $100 became $150 and then $75. Over those two periods the CAGR is 0.75^1/2 − 1 = −13.397% a year.

Limitations of CAGR

• It ignores the path. Two investments with the same start, end and period have the same CAGR even if one was far more volatile. Compare risk separately.
• It is sensitive to the dates you choose. Starting at a market low or ending at a peak can flatter a result. Check several windows.
• It assumes no cash flows in between. Deposits, withdrawals and dividends that were not reinvested distort it. For uneven cash flows use the IRR calculator or the XIRR calculator.
• It is backward-looking. A historical CAGR is not a forecast.
• This calculator takes whole periods only. A fractional number of periods is rejected, so express the span as a whole number of periods, for example 18 monthly periods rather than 1.5 years.

To judge whether a growth rate is worth the money tied up, compare it with the cost of capital using the WACC calculator, or discount projected cash flows with the NPV calculator. A compounding projection with regular deposits is on the compound interest calculator.

CAGR figures describe the past and are not investment advice or a promise of future returns. See the disclaimer.