How to calculate CAGR (and when not to use it)

How to calculate CAGR: divide the end value by the start value, raise the result to the power of 1 ÷ years, and subtract 1. CAGR (compound annual growth rate) is the single steady yearly rate that would take the start value to the end value. It smooths out the ups and downs so that different investments, or different businesses, can be compared.

The CAGR formula

CAGR = (End value ÷ Start value)^{1 ÷ years} − 1

Years can be a decimal. Two and a half years is 2.5.

Worked example

You invested ₹1,00,000 and it is worth ₹2,50,000 after 7 years.

1. End ÷ Start = 2,50,000 ÷ 1,00,000 = 2.5
2. 2.5^1/7 = 1.1399
3. 1.1399 − 1 = 0.1399, so CAGR = 13.99%

The total (absolute) return is 150%, but that ignores time. CAGR spreads it over 7 years. At 13.99% a year, money doubles in about 5.3 years.

The same formula works for a business. Sales of ₹50 lakh growing to ₹80 lakh in 4 years is a CAGR of about 12.47%.

Why CAGR is not the average return

The average of −50% and +50% is 0%, yet you lost ₹25,000. The CAGR is about −13.4% a year, which matches what happened to the money.

When not to use CAGR

• Money added or taken out along the way (SIPs, top-ups, withdrawals). Use XIRR. See how SIP returns are calculated.
• Very short periods. A 20% rise in three months turns into a huge yearly figure that means little.
• Judging risk. Two investments with the same CAGR can have very different falls along the way.

How to use the CAGR calculator

1. Enter the start and end values.
2. Enter the years between them (decimals are fine).
3. Read the CAGR, the absolute return and the doubling time.

For a simple change between two numbers without time, use the percentage calculator.