Hindi months are calculated according to the Panchang by combining the movement of the Sun and the Moon
Hindi months are calculated on the basis of the Panchang, which mainly depends on the lunar-solar system. This system keeps track of time by combining the movement of the Sun and the Moon. There are two major Samvats prevalent in the Hindi Panchang - Vikram Samvat and Shak Samvat, on the basis of which months are calculated. In the Hindi calendar, months are based on the phases of the moon. A lunar month is counted from Amavasya to the next Amavasya or from Purnima to the next Purnima. It is approximately 29.5 days.
Samvat year is calculated based on the movement of the Sun. It is adjusted on the basis of Sankranti i.e. change of Sun's zodiac sign. Dates are counted on the basis of the angular difference between the Moon and the Sun. A date varies by a difference of about 12 degrees.
The time of waxing of the moon in Shukla Paksha is from Ekam to Poornima whereas the time of waning of the moon in Krishna Paksha is from the next day of Poornima to Amavasya.
Chaitra March-April, Vaishakh April-May, Jyeshtha May-June, Aashad June-July, Shravan July-August, Bhadrapad August-September, Ashwin September-October, Kartik October-November, Margashirsha November-December, Paush December-January, Magh January-February, Phalguna February-March. These months do not match the English dates exactly because the lunar month is shorter. Therefore, an extra month is added every 2-3 years so that the lunar and solar year remain balanced.
When the difference between the lunar month and the solar month increases, an extra month is added, called Adhik Maas. It is usually a repetition of a month, such as Adhik Aashadha. This process is decided based on Surya Sankranti. Time is also calculated based on the 27 Nakshatras.
Calculation of Hindi months is a complex but systematic system, which balances the movement of the Moon and the Sun. The easiest way to understand this is to look at the local Panchang, as it explains the Tithi, Paksha and Sankranti.
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