Ahargana calculations - An easy way

Ahargana is the number of savana (civilian) days elapsed since a defined epoch. In the ancient astronomy texts, the siddhanta, the epoch is referred to the beginning of the current yuga, the onset of the current kalpa etc. In those days since the day-to-day calendar was also based on the same luni-solar calendar with months Chaitra etc. that was followed in the astronomical calculations, the ahargana was calculated in a cumbersome manner based on the same luni-solar calendar that obviously was a sidereal based calendar and had net length more than a tropical year.

Do we really need to do such a complex calculation these days?

No. In the present setup when we're using a tropical calendar with months January, February etc. for civilian use the ahargana calculations can be done based on the same calendar. It sounds easy and we may feel it's simple. But in practice it also poses another challenge as we've to do it manually to align the leap years falling in between and also the days elapsed in the ongoing or the last year of the selected period. Even after following all this we still risk the finer calculation for a longer period as the tropical year length is not exactly 365.2425 days as assumed in the Gregorian calendar. Moreover, the epoch from where the ahargana calculations begin may not necessarily be the year one of the calendar and thus considering the same throughout may not always be right e.g. Feb 18 3102 BC, the popular kaliyuga epoch, would need alignment of Julian and Gregorian calendar.

We cannot even consider the tropical year length as 365.24219 days exactly as per J2000 model since the calendar is not based exactly on this length. We’ve either 365 days or 366 days in a year. Due to all these nuances the ahargana calculation needs a lot of manual intervention somewhere even in the present setup. I’ve seen some people calculating it in an excel sheet writing each day of a particular year one by one and then adding the whole in the end but when I say manually, we needn’t do so much of handiwork either. We can merely write the number of days as 365 for a non-leap year and 366 day for a leap year and then do the month-based calculation for the last year in question.

But even that's not needed as I'm going to rather advise a simple method to calculate the ahargana that would not need so much of calculations. In the modern setup we've an equivalent called JDE that's widely used in astronomical calculations. All we need to do is to find the JDE of the epoch and the JDE of the day up to which we want the ahargana to be calculated and then do the subtraction. For example:

To find ahargana since the kaliyuga date 00:00 hrs Ujjaiyini until January 1, 2000:

JDE on Feb 18, 3102 BC (Julian calendar) = 588465.29

JDE on Jan 1, 2000 AD (Gregorian calendar) = 2451544.29

Ahargana = 1863079 days

One can use a Julian date converter to easily calculate any ahargana thus.

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