What this calculates
Enter a starting value, an ending value and the number of years between them, and this finds the compound annual growth rate - the steady yearly rate that joins the two - along with the absolute return over the whole period and the gain in money. The growth curve shows the steady path that rate describes.
The formula
CAGR
CAGR = (ending ÷ starting)^(1 ÷ years) − 1Absolute return
Absolute return = (ending ÷ starting − 1) × 100The period can include part-years: two and a half years is 2.5. There is no rate for a starting value of zero, which would divide by zero, nor for a period of zero.
CAGR is the reverse of growing a lumpsum: that takes a rate and finds the ending value; this takes the ending value and finds the rate.
Worked example
At a steady 14.87% a year, ₹1,00,000 is about ₹1,14,870 after the first year and doubles by the fifth.
When to use it, and the mistakes to avoid
Use it to compare investments held for different lengths of time, to turn a total return into a yearly one, and to check what rate a growth figure really works out to.
The mistakes that cost the most:
- Dividing the absolute return by the years. 100% over five years is not 20% a year; the CAGR is about 14.87%, because growth compounds.
- Averaging the yearly returns. +50% then −50% averages 0%, but the money ends at ₹75,000 from ₹1,00,000 — a CAGR of about −13.40%.
- Forgetting that a fall needs a bigger rise to recover. A 50% fall needs a 100% rise to get back to where it started.
- Reading CAGR as a smooth ride. It is one rate joining two ends; the real value may have swung widely along the way.
- Comparing periods of different lengths by total return. 60% over four years (12.47% a year) beats 100% over ten years (7.18% a year). Compare CAGRs instead.
FAQ
What is CAGR?
The compound annual growth rate: the one steady yearly rate that would take a starting value to an ending value over a number of years. It smooths out the ups and downs in between, so different investments over different periods can be compared on the same footing.
How is CAGR calculated?
Divide the ending value by the starting value, take the root for the number of years, and subtract one: CAGR = (ending ÷ starting)^(1 ÷ years) − 1. ₹1,00,000 growing to ₹2,00,000 in five years is 2^(1/5) − 1, about 14.87% a year.
What is the difference between CAGR and absolute return?
Absolute return is the total change over the whole period; CAGR is the yearly rate. ₹1,00,000 to ₹2,00,000 is a 100% absolute return, but over five years that is a CAGR of about 14.87% - not 20% a year, because each year's growth builds on the last.
Can CAGR be negative?
Yes. If the ending value is below the start, the rate is negative: ₹1,00,000 falling to ₹50,000 over three years is a CAGR of about −20.63% a year. A value that falls to zero is −100%.
Why is CAGR different from the average of yearly returns?
Because returns compound. A year of +50% followed by a year of −50% averages 0%, but ₹1,00,000 becomes ₹1,50,000 and then ₹75,000 - a CAGR of about −13.40% a year. CAGR follows the money; a simple average does not.
Does CAGR show how risky an investment was?
No. It joins the two ends with one smooth rate and says nothing about the swings in between. Two investments with the same CAGR can have had very different journeys.