CAGR (compound annual growth rate)
The steady yearly growth rate that would take a population from its start value to its end value.
In short
CAGR smooths every year's ups and downs into one constant rate. It answers "if this had grown at a steady pace the whole time, what would that pace have been" — not how it actually grew year to year.
How it's calculated
Take the ratio of the end value to the start value, take the root equal to the number of years between them, then subtract one.
CAGR = (end value ÷ start value)1/years − 1
Typical values
Why it matters here
CAGR is the cleanest way to compare growth across countries, or across periods of different lengths, on the canvas, without one unusually high or low year skewing the comparison. It's closely related to doubling time: the two are different ways of describing the same steady rate.
When the inspector panel shows a growth rate for a country, it is reporting CAGR over the selected time window. This makes comparisons between a country measured over 10 years and one measured over 50 years directly meaningful — the same underlying formula puts them on a common scale. The World Bank's population growth rate series uses the same compound annual growth method for all countries.
CAGR vs. simple average growth
A simple average adds all the annual growth rates and divides by the number of years. CAGR compounds them — it accounts for the fact that growth in one year happens on top of the growth already achieved. Over long periods, the two diverge significantly. A country that grows 50% then shrinks 33% ends up back where it started (net 0%), but a simple average of +50 and −33 gives +8.5%. CAGR gives the correct 0%. For periods longer than a few years, always prefer CAGR.
Frequently asked questions
What is CAGR in population terms?
CAGR — compound annual growth rate — is the constant yearly rate at which a population would have had to grow to get from its starting size to its ending size over a given number of years. It smooths out year-to-year fluctuations and gives a single representative rate for the whole period. The concept is the same one used in finance and ecology for any quantity growing over time — the Our World in Data population growth explainer covers how it applies to countries.
How is CAGR calculated?
CAGR = (end value ÷ start value)^(1/years) − 1. You divide the end population by the start population, raise that ratio to the power of one over the number of years, then subtract one. Multiply by 100 to express as a percentage. Our World in Data publishes annual growth rates for all countries, calculated using this method.
What does CAGR tell me that a raw population change number does not?
Raw change is affected by the length of the period. A country that grew by 20 million over 10 years and one that grew by 20 million over 30 years look the same in absolute terms, but CAGR reveals the first grew roughly three times faster. CAGR enables apples-to-apples comparison across different time windows and countries of different sizes.
How does CAGR relate to doubling time?
Doubling time and CAGR are two ways of describing the same underlying rate. Given a CAGR, you can calculate doubling time using the rule of 70: divide 70 by the CAGR expressed as a percentage. A CAGR of 2% implies a doubling time of about 35 years. They are interchangeable descriptions of the same exponential growth rate.