How does the Hindu Panchang calendar system work?

The Hindu Panchang is a lunisolar calendar that tracks five key elements daily (pancha = five, anga = limbs): Tithi (lunar day — there are 30 tithis in a lunar month, 15 in the bright half and 15 in the dark half), Vara (weekday — named after the seven planets: Ravi/Sun, Soma/Moon, Mangal/Mars, etc.), Nakshatra (lunar mansion — 27 nakshatras through which the Moon passes, each spanning 13.33 degrees), Yoga (angular relationship between Sun and Moon — 27 yogas combining auspicious/inauspicious qualities), and Karana (half a tithi — 11 types, used for fine-tuning muhurat). Hindu months begin at different points depending on the regional tradition: Amanta system (months end on Amavasya — used in Gujarat, Maharashtra, South India) and Purnimanta system (months end on Purnima — used in North India, Bihar, UP). The year typically begins in Chaitra (March-April) in the Vikram Samvat or Shaka Samvat systems. Pitrupaksha always falls in the Krishna Paksha (dark fortnight) of Ashwin month (September-October). The Panchang is essential for determining auspicious timing (muhurat) for all Hindu rites including weddings, Griha Pravesh, Pind Daan, and Shradh.