Calculating percent changes : U.S. Bureau of Labor Statistics

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Bureau of Labor Statistics > Consumer Price Index > Publications > Factsheets

Calculating percent changes

One-month percent changes

Movements of an index from one month to another are usually expressed as percent changes rather than as changes in the index value, because index value changes are affected by the level of the index in relation to its base period, while percent changes are not. To find the percent change, you first subtract the earlier index value from the later one, then divide that difference by the earlier index value, and finally multiply the result by 100. Table 1 shows an example of a CPI one-month change between November 2021 and December 2021 using the CPI-U U.S. city average series for all items, not seasonally adjusted. You can find full historical data for this series in our online database.

Table 1, 1-month percent change in CPI-U U.S. city average series for all items
Quantity	Representation	Value
Index value, December 2021		278.802
Index value, November 2021		277.948
Difference in index values	278.802 - 277.948	0.854
Ratio of difference to earlier index value	0.854 / 277.948	0.003
Ratio multiplied by 100	.003 * 100	0.3

Twelve-month percent changes

To arrive at a percent change over an entire year, the beginning and ending periods of a CPI series must always be the same month, such as December 2021 and December 2022. Note: A calculation using January and December data would result in an 11-month change, not a 12- month or year-over-year change. Table 2 shows an example 12-month change in the CPI-U U.S. city average series for all items from December 2021 to December 2022.

Table 2, 12-month percent change in CPI-U U.S. city average series for all items
Quantity	Representation	Value
Index value, December 2022		296.797
Index value, December 2021		278.802
Difference in index values	296.797 - 278.802	17.995
Ratio of difference to earlier index value	17.995 / 278.802	0.065
Ratio multiplied by 100	.065 * 100	6.5

There are two critical points to remember when calculating percent changes:

Always use the same reference base period for all calculations. If the earlier data point uses the 1982-84=100 base, the later data point must also use that base.
An over-the-year percent change, such as December 2021 to December 2022, is not equal to the sum of the over-the-month changes between those two time periods.

Annual average percent changes

Annual averages are the sum of the 12 monthly data points (i.e. index values), divided by 12. As an example, the calculation of the annual average for the CPI-U U.S. city average series for all items is shown in table 3. Annual averages represent an average index for a given year, not a particular month. An annual average percent change should not be confused with the over the year percent change, such as the calculation of the December-to-December change mentioned in the previous section.

Table 3, annual average of the CPI-U U.S. city average series for all items
Quantity	Value
Index value, January 2021	261.582
Index value, February 2021	263.014
Index value, March 2021	264.877
Index value, April 2021	267.054
Index value, May 2021	269.195
Index value, June 2021	271.696
Index value, July 2021	273.003
Index value, August 2021	273.567
Index value, September 2021	274.310
Index value, October 2021	276.589
Index value, November 2021	277.948
Index value, December 2021	278.802
Sum of index values for 2021	3251.637
Sum of index values for 2021, divided by 12	270.970

A December-to-December percent change is unlikely to be the same as the change in the annual average percent change between the same two years. The annual average percent change between 2021 and 2022 for the CPI-U U.S. city average series for all items is presented in table 4 as an example. Users should take care to examine the data with which the CPI is being compared to determine whether the annual average or 12- month percent change is more appropriate for their purposes.

Table 4, annual average percent change in CPI-U U.S. city average series for all items
Quantity	Representation	Value
Annual average index value, December 2022		292.655
Annual average index value, December 2021		270.970
Difference in index values	292.655 - 270.970	21.685
Ratio of difference to earlier index value	21.685 / 270.970	0.080
Ratio multiplied by 100	.080 * 100	8.0

In addition, users should note that, for an index series that is published every other month, such as those for many metropolitan areas, the annual average is based on 12 months of data. Many food and energy prices are collected for the off-cycle months, and the unpublished off-cycle indexes are carried forward from the previous month and used in the annual average.

Last modified date: February 9, 2023