Computing Ahargaṇa from Western dates

Ahargaṇa literally means ‘set of days’. It is essentially the number of days that have passed on the specified date, from a fixed point in time. The ahargaṇa is an important number and appears in several calculations related to finding the locations of the planets in the sky.

The traditional procedure to find ahargaṇa is based on working with the date in the Indian calendar. This date is composed of solar years, but lunar months and days. Adding these two together involves converting solar years to lunar, and adding up the months and days. In the end the result is converted from lunar to civil days (sāvanadina - sunrise to sunrise). The process, although straightforward, is time consuming and can become error prone. It also expects knowledge of the calendar of that year (to know the intercalary months).

Modern dates, on the other hand, are largely based on civil dates, with additional days added to different months to make it in line with solar years. Hence, solar years are converted to civil days in a predictable manner. When trying to find the ahargaṇa of a day where the Western date is known, it is therefore easier to directly convert to civil days rather than first finding the Indian date and then doing the steps mentioned above.

The following procedure would be used:

1. Choose a starting date when the ahargaṇa is already known (e.g. 1-1-1900)

2. Take the number of years passed since that date and multiply by 365; add to the above result

3. Find the number of leap years passed since that date (every 4th year is a leap year; every 100th year isn’t; but every 400th year is); add that to the previous result

The result is the ahargaṇa. This can be computed from the beginning of the kalpa, the kaliyuga, or any other chosen date.

Example: Finding the ahargaṇa for 1st August, 2020

1. Choose a starting date: 1-1-1900

2. Ahargaṇa on this date: 1826556 (from the beginning of kaliyuga)

3. Number of years passed: 120

4. Multiply by 365: 43800

5. Add to previous result: 1870356

6. Number of leap years passed:

7. Years divisible by 4: 31

8. Reduce years divisible by 100: 2

9. Add years divisible by 400: 1

10. Final result: 1870386

Final ahargaṇa: 1870386.