I have 2 dates, let's say 2010-01-01 and 2020-01-02, and I am interested in calculating the year fraction between them according to the Act/365 time convention.

Would this be just $$ \frac{\text{raw # of days between the dates}}{365} = \frac{3653}{365} = 10 \tfrac{3}{365} $$ or will I have to convert the years normally, and then only apply the convention to the segment which is under a year, resulting in $$ 10+\frac{\text{# of days between Jan 1st and Jan 2nd}}{365} = 10 \tfrac{1}{365}? $$

Additionally, is it correct that if we use Act/Act it will be $10 \frac{1}{366}$ since 2020 is a leap year?

Thank you very much.

  • $\begingroup$ I found a couple of questions on day-count conventions, but did not see this asked explicitly. $\endgroup$
    – gt6989b
    May 9, 2022 at 15:34
  • 1
    $\begingroup$ PDF Page 14f: quant.opengamma.io/…. It is defined as the day difference between d1 and d2 divided by 365 if it is Act/365 fixed. $\endgroup$ May 9, 2022 at 17:51
  • $\begingroup$ Also asked Bloomberg, they are implementing direct difference as well $\endgroup$
    – gt6989b
    May 11, 2022 at 3:08

1 Answer 1


As @Kermittfrog has indicated in the comment, it's the former of your two versions, i.e. Date2 - Date1, divided by 365 (in your case 10.00822). Do note that you did not further specify, and we "assumed" it to be Act/365 fixed

(because there is also the Act/365 Actual convention, which accounts for leap years: 365 in all regular yrs, 366 in leap years --> the very same holds for act/act convention).


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