Panchaka is a counting test Kalaprakasika (1917, pp. 151–152) gives for the moment of setting out on a journey. Add the numbers of the tithi, the weekday, the star and the rising sign. Add 15 to that total and divide by 9; then do the same with 12, 10, 8 and 4 in place of 15. If any of the five divisions leaves a remainder of 5, the book counts the moment as one to pass over. Any other remainder is clear.
☕ How the count works
Panchaka uses four of the moment's facts and turns each into a number: the tithi, the weekday, the star and the rising sign (lagna). Add the four numbers to get one total. The book then makes five small checks on that total: add 15, divide by 9 and look at the remainder; then add 12 instead, then 10, then 8, then 4. A remainder of 5 in any of the five is the one the book bars.
The book does not say how each limb is numbered for this rule. A rule printed before it, on the same page (p. 151), works an example that counts the tithi within its own fortnight (Panchami is 5), the weekday from Sunday (Friday is 6) and the star from Ashwini (Pushya is 8). This page uses the same counts, and numbers the rising sign from Aries (Aries is 1), which the book also leaves unstated.
Kalaprakasika places panchaka in its chapter on journeys, as a test for the moment of starting. It is plain arithmetic on the panchangam's own limbs, so anyone with the day's panchangam and the rising sign can work it by hand. It builds on the tithi, the weekday and the star, which the limbs series explains.
Nava Panchangam does not use this rule in its day score. This page explains it as the books give it.
The five checks, and the shortcut
- Add 15 to the total, divide by 9: a remainder of 5 is barred
- Add 12 to the total, divide by 9: a remainder of 5 is barred
- Add 10 to the total, divide by 9: a remainder of 5 is barred
- Add 8 to the total, divide by 9: a remainder of 5 is barred
- Add 4 to the total, divide by 9: a remainder of 5 is barred
- The bare total, divided by 9, leaves 1, 2, 4, 6, 8: one of the five checks gives 5
- It leaves 0, 3, 5, 7: none of the five gives 5, so the moment is clear
- This shortcut is our arithmetic on the book's rule, not a line of the book
Frequently Asked Questions
Why is it called panchaka?
Pancha means five. The book runs five checks on one total, with five different numbers added, and each check can give the barred remainder of 5.
Which numbers go into the total?
The tithi, the weekday, the star and the rising sign at the moment of starting. The book does not say how to number them for this rule. This page follows the counts the book uses in an example printed before it: the tithi within its fortnight, the weekday from Sunday, the star from Ashwini; and the sign from Aries.
Is there a quicker way to work it?
Yes. Divide the bare total by 9. If it leaves 1, 2, 4, 6, 8, one of the five checks gives 5; if it leaves 0, 3, 5, 7, none does. That follows from the book's rule by arithmetic; the book itself gives only the five checks.
Is panchaka only for journeys?
In Kalaprakasika it appears in the chapter on journeys, for the moment of setting out. Other books and regional almanacs use similar counts for other events; this page explains only what this book states.
Does Nava Panchangam show panchaka?
No. The app does not compute panchaka. This page explains the book's arithmetic so you can follow it by hand.
Working it through
One worked example, the shortcut, and what this page leaves out.
🔢 A worked example
Take the limbs of the book's own example: Panchami (5), Friday (6 from Sunday) and Pushya (8 from Ashwini). With Taurus rising the total is 21; with Leo rising it is 24. The five checks:
| Rising sign | Total | +15, remainder | +12, remainder | +10, remainder | +8, remainder | +4, remainder | A remainder of 5? |
|---|---|---|---|---|---|---|---|
| Taurus (2) | 21 | 0 | 6 | 4 | 2 | 7 | no |
| Leo (5) | 24 | 3 | 0 | 7 | 5 | 1 | yes |
The book's own example gives no rising sign; the two signs here are this page's example, to show one moment that clears and one that does not.
➗ Why the shortcut works
Adding a number and then dividing by 9 only moves the remainder round the nine places. So a remainder of 5 after adding a number means the bare total had a fixed remainder of its own:
| Number added | The total's remainder (on 9) that gives 5 |
|---|---|
| 15 | 8 |
| 12 | 2 |
| 10 | 4 |
| 8 | 6 |
| 4 | 1 |
The five checks together bar the totals that leave 1, 2, 4, 6, 8 and clear those that leave 0, 3, 5, 7. This is our arithmetic, not a line of the book.
✂️ What this page leaves out
The book names a different trouble for each of the five checks, and for the rule printed above it. This page keeps only the arithmetic and leaves those lines out.