Panchang - Calculation and importance of Karana in Panchang

A karana is half of a tithi in duration. A karana is the time required for the angular distance between the sun and the moon to increase in steps of 6° starting from 0°.

Shukla Paksha

Karana Calculations for Shukla Paksha Tithi (Full Moon Phase)

तिथिर्द्विध्नी द्विकोना च शुक्लपक्षे सदा बुधै:।

शेषांङ्के सप्तभिर्भागस्तिथ्यादौ करणं मतम्॥

              

                            Multiply a Tithi by 2 and after substracting 2, divide it by 7. The resultant number will be identical to the Karana of the 1st half of the day counted from Bava, while succeeding Karana will rule the second half of the day.

Example: Suppose you wish to fond out the ruling Karana on the 12th ( Dwadashi) Tithi of Krishna Paksha

Multiply Tithi by 2 --- 12*2=24

divide the sum by 7

we get 3 as a remainder

so counting from Bava we get Taitil as 3rd Karana which will rule the 1st half of that particular day.


Krishna Paksha

But calculation of Karan in Krishna Paksha is little different

कृष्णपक्षे तिथिर्द्विघ्नी मुनिभिर्भाग माहरेत 

शेषांगकेन बवाद्यम च तीथ्यादौ करणम विदुः||१||  

Multiply the Tithi (The new phase moon) by 2 and divide the sum by 7, the remainder number will denote the name of the Karana prevailing in the first half of the Tithi when counted from Bava Karana. The succeeding karana will occur in the second half of the day.

Another Formula for calculating Karana:

 (Longitude of Moon) - (Longitude of Sun)

  6

Quotient tells the number of Karna passed

30 tithis so 30 * 2 = 60 karnas

But There are eleven karanas in total.

A  tithi consist of 12° of Longitudinal difference between Sun and Moon at particular point of time and Karana being half of Tithi will be formed with 6° longitudinal difference between luminaries.
As such there will be two Karana in one Tithi. These two Karana will operate at tendem in a day.
In all there are 11 Karanas which rotates in a certain specific pattern in 30 Tithis ( 15 of Krishna paksha and 15 of Shukala Paksha) in a lunar month. The pattern is like this 
Seven Movable Karana appear 8 times reflecting total of 56 /karanas out of 60 in a lunar month. The remaining 4 are called fixed Karanas and appear only once in this duration of one lunar month under a fixed scheme of things.

Krishna Paksha starts with Bava Karana while Kinstughana will be 1st Karana of the Shukala Paksha

Of the eleven karanas, four are fixed and occurs only once in a cycle. The remaining 7 karanas repeat eight times to cover the remaining 56 steps.

Bava, Balava, Kaulava, Taitila, Gara, Vanij, Visti, Shakuni, Chatushpada, Naga and Kinstughna

Highlighted ones occur only once a month

They start with Bava on the second half of the first tithi and repeat themselves in the same order eight times in a lunar month. The four fixed Karanas start with the 2^nd half of the 14th day of the Krishna paksha, Amavasya and the first half of the 1^st Tithi of the Shukla Paksha. The first karana in Shukla Paksha is always the fixed Kintughna. The fixed karanas do not repeat themselves.