The Kali Epoch and Ahargana: Part 6: Utilising Julian Day Number to determine Ahargana

  1. Julian Day (JDy): Julian day is the continuous count of days since the beginning of the Julian Period used primarily by astronomers. (Wikipedia)
  2. Julian Day Number (JDN): The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar), a date at which three multi-year cycles started and which preceded any historical dates. For example, the Julian day number for the day starting at 12:00 UT on January 1, 2000, was 2,451,545. (Wikipedia)
  3. Julian Date (JD): The Julian date (JD) of any instant is the Julian day number for the preceding noon in Greenwich Mean Time plus the fraction of the day since that instant. Julian dates are expressed as a Julian day number with a decimal fraction added. For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2,456,293.520833. (Wikipedia)

The Julian Day Number is a widely used concept to keep a continuous count of the days elapsed starting at 12:00 on Jan 1, 4713 as per proleptic Julian Calendar. This is mapped to Nov 24, 4714 BC as per proleptic Gregorian Calendar. If we are able to find out the Julian Day Number at the beginning of Kali Yuga and on any date for which Ahargana needs to be found, the difference between the two JDN will give the Ahargana.

The way to determine the Julian Date Number for any date DD/MM/YYYY in Gregorian Calendar is as follows

JDN = DD + TRUNC((153 * MM +2)/5) + 365 * YYYY + TRUNC (YYYY/4) -TRUNC(YYYY/100) + TRUNC(YYYY/400) - 32045

The Trunc Function removes the Decimal places (remainder) and retains the quotient after a division.

Substituting the values of Start of Kali yuga i.e., 22 Jan -3101, we arrive at the JDN 5,88,465. This is the value at 12:00 UT on 22nd Jan -3101.

To keep track of the time, Julian Date can be used. Before that we need to convert the time under consideration into UT and Determine the JD Time.

JD Time (JDT) = Hour + Minutes / 60 + Seconds / 3600
Julian Date (JD) = ROUND(JDN + (JDT - 12) / 24, 3)

The formula of Julian Date gives the value with 3 decimal places precision. 12 is minus off from the time, to compensation for the difference between the Modern clock (12:00 midnight) and the Julian Date (12:00 noon).

Once the Julian Date is known, the weekday can be found using the following formula

Julian Date Weekday (JDW) = Remainder (JDN / 7) + 1. Here 1=Monday, 2=Tuesday, 3=Wednesday, 4=Thursday, 5=Friday, 6=Saturday, 0/7=Sunday.

6am Local Mean Sunrise Time at Ujjain

For the purpose of Ahargana computation, the location chosen is Ujjain and the Sunrise time chosen is 6am LMT. The day whose start (6am) precedes the moment of Chaitra Shukla Pratipada will be furnish the first day of the year. This is in alignment with Varahamihira’s proposition that year 427 started on Monday, although on that day, the Chaitra Shukla Pratipada started in the evening after 7pm (in Ujjain LMT).

The Kali yuga started at 6:37:11 LMT, in Ujjain on 22nd Jan -3101 (3102 BC) as per Proleptic Gregorian Calendar (Feb 17 as per Proleptic Julian Calendar). The Kali Ahargana Number (KAN) started at 6am LMT Ujjain on that day (preceding 6am). Following the convention of Julian Date, we can assign that as Zero (0). This coincides with JDN 5,88,465 and JD 5,88,464.54.

From this we can establish that

Kali Ahargana Number (KAN) = JDN - 588465

Kali Ahargana Date (KAD) = JD - 588464.54

This means that we arrive at the Kali Ahargana Number (KAN) by just dropping the Decimal Places.

And, to Arrive at the Kali Ahargana Date (KAD), we find out the hours elapsed (in decimals) on that day from 6am LMT Ujjain and divide that by 24.

Deriving Weekday from Kali Ahargana Date

There are two methods of arriving at the weekday

Method 1:

Weekday = Remainder(KAD / 7)

4=Monday, 5=Tuesday, 6=Wednesday, 0/7=Thursday, 1=Friday, 2=Saturday, 3=Sunday.

Method 2:

Weekday = Remainder[ Remainder(KAD / 7) + 4 ] / 7

1=Monday, 2=Tuesday, 3=Wednesday, 4=Thursday, 5=Friday, 6=Saturday, 0/7=Sunday.


Find the KAD and KAN for 23rd March 505 at 19:45 LMT Ujjain i.e., the start of Varahamihira Epoch.

JDN = DD + TRUNC((153 * MM +2)/5) + 365 * YYYY + TRUNC (YYYY/4) -TRUNC(YYYY/100) + TRUNC(YYYY/400) - 32045

= 23 + TRUNC((153 * 3 + 2)/5) + 365 * 505 + TRUNC(505/4) -TRUNC(505/100) + TRUNC(505/400) - 32045 = 19,05,589
KAN = JDN - 5,88,465 = 19,05,589 - 5,88,465 = 13,17,124

KAD = KAN + [(19 + 45/60) - 6]/24 = 13,17,124 + [19.75 - 6]/24 = 13,17,124.573

Weekday = Remainder (13,17,124 / 7) = 4. This is as per method 1. Here 4= Monday. Thus the Varahamihira Epoch started on Monday.

Find the KAD and KAN for today 24 Jan 2016 at 6am LMT Ujjain

JDN = DD + TRUNC((153 * MM +2)/5) + 365 * YYYY + TRUNC (YYYY/4) -TRUNC(YYYY/100) + TRUNC(YYYY/400) - 32045

= 24 + TRUNC((153 * 1 + 2)/5) + 365 * 2016 + TRUNC(2016/4) -TRUNC(2016/100) + TRUNC(2016/400) - 32045 = 24,57,412
KAN = JDN - 5,88,465 = 24,57,412 - 5,88,465 = 18,68,947

KAD = Same as KAN at 6am LMT Ujjain.

Weekday = Remainder (18,68,947 / 7) = 3. This is as per method 1. Here 3= Sunday. This is verified to be correct.


Since JDN is a widely used concept, we can use this as a means to compute the Kali Ahargana Number (KAN) and the Kali Ahargana Date (KAD). The Kali Ahargana number (KAN) at 6am LMT at Ujjain, the seat of the Kalapurusha can be derived by subtracting 5,88,465 from the Julian Date Number (JDN). The Kali Ahargana Date (KAD) can be arrived by adding the hours elapsed from 6am LMT at Ujjain to the Kali Ahargana Number (KAN).

This is my recommended approach to determine the Kali Ahargana, the continuous day count from the start of Kali yuga on 22nd Jan 3102 BC.

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