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What Formulas are Used to Calculate Growth Rates?

Note that because FRED uses levels and rounded data as published by the source, calculations of percentage changes and/or growth rates in some series may not be identical to those in the original releases.

The following formulas are used:

Change:  change formula


Change from Year Ago: change from year ago formula1


Percent Change:  percent change formula1
Percent Change from Year Ago: percent change from year ago formula1


Compounded Annual Rate of Change: compounded annual rate of change formula1


Continuously Compounded Rate of Change: continuously compounded rate of change formula


Continuously Compounded Annual Rate of Change: continuously compounded annual rate of change formula


Natural Log: natural log


x at time period t is the value of series x at time period t.

'n_obs_per_yr' is the number of observations per year. The number of observations per year differs by frequency:

Daily, 260 (no values on weekends)
Annual, 1
Monthly, 12
Quarterly, 4
Biweekly, 26

'ln' represents the natural logarithm.

Posted in Understanding the Data, Frequently Asked Questions
FRED Economic Data | St. Louis Fed

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