CAGR Calculator

CAGR (compound annual growth rate) is the one steady yearly rate that would take an investment from its starting value to its ending value over the same time, with each year's growth added on top of the last. Real investments go up and down; CAGR smooths that into a single number you can compare across shares, funds, property or a business's sales.

The formula

CAGR = (end value ÷ start value)^(1 ÷ years) − 1
end value = start value × (1 + CAGR)^years
start value needed = end value ÷ (1 + CAGR)^years
years = log(end value ÷ start value) ÷ log(1 + CAGR)
absolute return = (end value ÷ start value − 1) × 100%
simple average a year = absolute return ÷ years
real CAGR = (1 + CAGR) ÷ (1 + inflation) − 1

Write rates as decimals in the formulas: 20% is 0.20. Years can include part of a year: 2 years 6 months is 2.5. Between two dates, whole years are counted on the calendar and the part-year is the days left ÷ the days in that year.

Worked example

You invested 10,000 and five years later it is worth 25,000. The value grew 25,000 ÷ 10,000 = 2.5 times. Spread over five years, that is 2.5^1/5 = 1.2011 a year, so the CAGR is 1.2011 − 1 = 20.11% a year. Check: 10,000 × 1.2011⁵ = 25,000. The absolute return is 150%, and the simple average is 150% ÷ 5 = 30% a year, which overstates the real growth because it ignores compounding. At 20.11% a year, money doubles in about log 2 ÷ log 1.2011 = 3.78 years.

Other questions use the same sum turned around. 10,000 growing at 12% a year for 5 years ends at 10,000 × 1.12⁵ = 17,623.42. To reach 25,000 at 12% you would need log 2.5 ÷ log 1.12 = 8.09 years, or 25,000 ÷ 1.12⁵ = 14,185.67 invested today to get there in 5 years.

Real and after-tax CAGR

If inflation was 6% a year over the same five years, the real CAGR is 1.2011 ÷ 1.06 − 1 = 13.31% a year, and 25,000 then is worth 25,000 ÷ 1.06⁵ = 18,681 in today's money. With 20% tax on the 15,000 gain (3,000), you keep 22,000, an after-tax CAGR of (22,000 ÷ 10,000)^1/5 − 1 = 17.08%. Tax rules differ by country and by how long you held the investment, so enter the rate that applies to you.

CAGR vs the average of yearly returns

Yearly returns of 12%, −5%, 20%, 8% and 15% average 10% a year, but 10,000 grows to 10,000 × 1.12 × 0.95 × 1.20 × 1.08 × 1.15 = 15,857.86. That is a CAGR of 1.5858^1/5 − 1 = 9.66%. The simple average is always at least as high as the CAGR; the gap (here 0.34 points) grows the more the returns swing. A +50% year followed by a −50% year averages 0% but leaves you 25% down.

XIRR: when you add or take out money

CAGR only works for one amount in and one amount out. If you invested at different times, as with a SIP, top-ups or withdrawals, use XIRR. It finds the yearly rate at which every deposit, grown to today, minus every withdrawal, grown to today, equals what the investment is worth now. There is no direct formula, so the calculator guesses a rate and improves it with Newton's method until the sums balance. Like spreadsheet XIRR, it counts time as days ÷ 365.

Example: 10,000 in on 1 Jan 2021, 5,000 in on 1 Jan 2022, 3,000 out on 1 Jul 2023, 5,000 in on 1 Jan 2024, and worth 25,000 on 1 Jan 2026. You put in 20,000 and got back 28,000 in all, a gain of 8,000 (40%), but the money was invested for different lengths of time. The XIRR is 9.33% a year.

Doubling time

Doubling time = log 2 ÷ log(1 + CAGR). The rule of 72 is a quick shortcut: 72 ÷ the rate.

CAGR describes the past; it does not promise future returns, and it hides how bumpy the ride was. Dividends or interest you took out are not in the end value, so add them with XIRR (as withdrawals) for a total return. Results are before fees unless your end value is after fees.