My question is so basic, I'm embarrassed to ask it. (I study computational theory, not economics.) I'm looking at quarterly GDP numbers and growth rates. I've tried to arrive at the BEA's CPGDPAI numbers using the generic formula:

GDP(t)/GDP(t-1) = (1 + r)^t - t-1

Which fails miserably. I'm grateful for some light on this.


So, it's the data, not the math. I was pulling the nominal GDP data off FRED. After plugging in the the GDPC1 data, it was all right as rain. A rookie mistake, but, well, I'm a rookie. Thanks for the answers below.

  • $\begingroup$ Please bear in mind that this is an international site. If you ask a question relating to a particular country, please indicate the country in the title or early in the text. $\endgroup$ – Adam Bailey Mar 20 '20 at 18:42
  • $\begingroup$ Will do. Thanks. $\endgroup$ – user26034 Mar 20 '20 at 23:27


The BEA does use the generic growth formula to calculate percent change of GDP.

The formula used by BEA to calculate the average annual growth is a variant of the compound interest formula:

Formula used by BEA to calculate the average annual growth.


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GDPt is the level of activity in the later period;

GDP0 is the level of activity in the earlier period;

m is the periodicity of the data (for example, 1 for annual data, 4 for quarterly data, or 12 for monthly data); and n is the number of periods between the earlier period and the later period(that is t-0).

This is reported on there website here: https://www.bea.gov/help/faq/463

For internal calculations they may use the difference in logs as the other person had posted.


Normally growth is calculated either as:


Or approximated by:


Within year you can either continue using the above definition or use year on year growth which compares every month quarter with the same quarter previous year.

If you are looking for Fred specifically here is the list of formulas:


The list overlaps with what I written above and also the list shows other changes (which you might be interested to look into)

  • 1
    $\begingroup$ Brilliant. Thank-you. $\endgroup$ – user26034 Mar 20 '20 at 15:42
  • $\begingroup$ @Pascal80 you are welcome if you find my answer helpful please consider accepting it $\endgroup$ – 1muflon1 Mar 20 '20 at 15:44
  • $\begingroup$ Tried voting, but alas, I need to be vested first, or something, before it shows up. Still, you have my vote, and my thanks. $\endgroup$ – user26034 Mar 20 '20 at 16:12
  • $\begingroup$ @Pascal80 no problem you are welcome $\endgroup$ – 1muflon1 Mar 20 '20 at 16:12

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