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Compound annual growth rate: what it means

The constant yearly growth rate that would take a figure from its starting value to its end value over a period. Different from simply dividing total growth by the number of years.

The compound annual growth rate (sometimes called CAGR or the average annual growth rate) is the steady yearly rate that would turn a starting value into an end value over a given number of years. It is calculated as (end value divided by start value) raised to the power of one divided by the number of years, minus one.

Worked example

A hypothetical budget rises from £100 million to £150 million over five years. Total growth is 50%, but the compound annual rate is about 8.4% a year, not 10%, because each year's growth builds on the last.

Why it matters when checking a claim

  • Dividing total growth by the number of years overstates the yearly rate.
  • Over long periods, small differences in annual rates add up to large differences in levels.
  • The OBR and ONS often quote average annual growth rates; check whether they are compound and whether they are in real terms.

Also searched as: CAGR, average annual growth rate, annualised growth rate, compound growth

Official definitions: Office for Budget Responsibility: Economic and fiscal outlook · ONS: GDP quarterly national accounts

Questions that use this term

Related terms

  • Year-on-year change: The change between a figure for one period and the same period twelve months earlier, such as March this year compared with March last year.
  • Real terms: A figure adjusted to remove the effect of inflation, so amounts from different years can be compared by what they would buy rather than their face value.
  • Index number: A number that shows how a value compares with a chosen reference period set to 100. An index of 110 means 10% higher than the reference period.
  • Percentage point: The arithmetic difference between two percentages. A rise from 4% to 5% is one percentage point, but a 25% increase in the rate.

More measuring change over time terms: Real terms · Cash terms · Percentage point · Year-on-year change · Quarter-on-quarter change · Rolling average · Index number · Base year · Seasonally adjusted · Base effect · Discontinuity (break in series).