Suppose a shop’s annual sales were ₹40 lakh five years ago and are ₹70 lakh now. Sales grew 75% in total, but “75% over five years” is hard to compare with anything else. A steady yearly rate is easier to think about, and that is what CAGR, the compound annual growth rate, provides.
The formula
CAGR = (ending value ÷ starting value)^(1 ÷ number of years) − 1
For the shop: 70 ÷ 40 = 1.75. Raise it to the power 1/5 (0.2) to get about 1.1184. Subtract 1: CAGR is roughly 11.8% a year.
What the number means
CAGR does not say growth was 11.8% every year. It says that if growth had been the same each year, 11.8% is the rate that would take you from the start value to the end value. In practice, some years may have been higher and some lower, or even negative. CAGR smooths the path. For the forward-looking version of the same arithmetic, see an explainer on how a single amount grows with yearly compounding.
A simple check
Start with 100 and grow it 14.87% a year for 5 years: 114.87, 131.95, 151.57, 174.1, 200. So doubling in five years corresponds to a CAGR of about 14.9%. A rough shortcut for doubling time is to divide 72 by the annual rate in percent; at 14.87% that gives about 4.8 years, close to five.
Why not just divide by the number of years?
The simple average of 75% over five years is 15% a year, which overstates the figure. That is because each year’s growth builds on a larger base. CAGR accounts for that compounding.
Where it is useful
- Comparing the revenue trends of two businesses over the same period.
- Looking at salary or price histories across several years.
- Checking population, enrolment or output data in school and college projects.
- Understanding what a target growth rate means over several years.
Where it can mislead
- Only two points are used. Two series with very different paths can have the same CAGR. A company whose profit fell by half and then recovered has the same endpoint CAGR as one that grew smoothly.
- Start and end dates matter. Choosing a weak start year or a strong end year changes the answer a lot. Always say which years you used.
- It is about the past. A historic CAGR describes what happened. It does not predict what comes next.
- It cannot be used when the start or end value is zero or negative.
A series with ups and downs
Take a fictional business with revenue of ₹100 lakh, then ₹150 lakh, then ₹90 lakh, then ₹120 lakh. Yearly growth is +50%, −40% and +33.3%. The simple average of those three is +14.4%, which sounds healthy. But revenue ended at ₹120 lakh, only 20% above the start. The CAGR over three years is (120 ÷ 100)^(1/3) − 1 = 6.3%. The simple average of percentage changes overstates the growth, because the big drop in the middle is applied to a larger base than the later rise.
Real versus nominal CAGR
If revenue grows at a CAGR of 11.8% while prices in the economy rise at 6% a year, the growth in real terms is lower: roughly (1.118 ÷ 1.06) − 1 = 5.5%. For long periods or periods of high inflation, the difference is large. Say whether a stated CAGR is nominal or adjusted.
Choosing the window
A CAGR depends on the start and end years. Look at the same business over two windows. If the three-year CAGR is 6% and the ten-year CAGR is 12%, something changed. Quote the window every time, and where possible show more than one.
Using it for planning
CAGR also works in reverse. If a target is to grow a quantity from 100 to 200 in seven years, the needed yearly rate is 2^(1/7) − 1, about 10.4%. Framing a goal this way tells you what pace is required, without implying it will be achieved.
Doing it in a spreadsheet
Put the starting value in A1, the ending value in B1 and the number of years in C1. The formula is =(B1/A1)^(1/C1)-1, formatted as a percentage. Many spreadsheets also have a built-in rate function that gives the same result.
Limits to keep in mind
- CAGR needs both the start and the end value to be positive.
- It ignores what happened in between, including any cash added or withdrawn along the way. For investments with regular additions, other measures are used.
- A smooth CAGR can hide a volatile path. Always look at the yearly figures too.
Used with care, CAGR is one of the cleanest ways to describe change over time. The care consists of stating the years, the values and whether the figures are adjusted for inflation. With those in place, two people can reproduce the same number, which is the real test of a clear statistic.
To avoid arithmetic slips, a CAGR calculator will work out the yearly growth rate between two values and display the steps. Then try the same numbers by hand once to build the intuition.
The most useful habit is to quote the CAGR together with the start year, the end year and the two values it came from.
