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I'm wondering how the monthly inflation rate is calculated from the consumer price index?

Here you can find the monthly CPI data from 1913 - 2016: https://fred.stlouisfed.org/series/CPIAUCNS

From this data I want to calculate the inflation like it is presented on this website: http://www.usinflationcalculator.com/inflation/historical-inflation-rates/

I already calculated it by this formula:

((i/l)-1)*100 = inflation rate

i = CPI value of the current month
l = CPI value from 12 month ago

But I'm wondering if this is correct and if this is the usual way to do it? Wouldn't it better to consider the average inflation of the past 12 month instead of considering just the difference from 12 month ago till current?

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    In January, assume you have $100. In December, assume you have $115. If you want to know how much the value of your account changed over the year, do you care whether you earned the $15 on Dec 30 vs on Jan 2nd? No - only the net change matters, if you simply want to know the % change during the year.
    – Grade 'Eh' Bacon
    Nov 16, 2016 at 20:41

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That is the correct way

You could, if you wanted, calculate it over any period of time, you just need to label it appropriately. Typically, people care about the annualized inflation number so that it can be compared to ones investment returns. E.g. My investments grew 10% this year, but inflation was 3%, so my investments only effectively grew by 7%.

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