Hindu Panchanga

The Hindu calendar, ordered by the Panchanga, is lunisolar: its months follow the moon while the year is kept in step with the sun by an added intercalary month roughly every three years, giving years of about 354 to 384 days. Its reckoning varies by region and era, the Vikram Samvat, counted from 57 BCE, and the Shaka era, from 78 CE, are the most common. The Panchanga, meaning the five limbs, is the traditional almanac that gives for each day its five essentials: the lunar day (tithi), the weekday, the lunar mansion (nakshatra), the Sun-Moon combination (yoga), and the half-day (karana). From these an astrologer determines auspicious times and the dates of festivals. These are the features of the Hindu calendar tradition, which regulates the vast cycle of religious observance across the Indian subcontinent.

Where the added month falls, and whether a lunar day is skipped or doubled, is governed by the rule that each of the twelve solar months, marked by the sun's entry into a zodiacal sign (samkranti), should ordinarily contain one lunar month; a lunar month that contains no samkranti is intercalary and termed adhika, while, more rarely, a solar month spanning two lunar new moons causes a lunar month to be omitted, termed kshaya. The two principal eras in civil and religious use differ in origin: the Vikram Samvat, beginning 57 BCE, is traditionally associated with King Vikramaditya of Ujjain, while the Shaka era, beginning 78 CE, is linked to the Kushan or Satavahana rulers and was adopted as India's official civil calendar alongside the Gregorian calendar in 1957.

Every calendar in the world solves the same arithmetic problem, and there are only three solutions. A lunation is about 29.53 days and a tropical year about 365.2422 days, and the second is not a whole multiple of the first. A calendar can therefore follow the Moon and let its year drift against the sun, follow the sun and let its months lose contact with the Moon, or follow both and insert an extra month at intervals to keep them together.

The Hindu calendars take the third path, and they add something the others do not have. A Panchanga is not primarily a list of dates but a table of five limbs, and only one of those five is the lunar day. The others are the weekday, the nakshatra the Moon occupies, the yoga computed from the combined longitudes of Sun and Moon, and the karana, which is half a tithi. A day is therefore described by five simultaneous positions rather than by a single number.

The tithi itself is unlike a day in any other system. It is the time the Moon takes to gain twelve degrees of longitude on the Sun, so it varies in length with the actual motion of both bodies, and it does not align with the civil day. A tithi can be skipped or repeated in a given civil month, which is a feature of the definition and not an irregularity.

There is no single Hindu calendar. Regional systems differ in whether the month begins at the new or the full moon, in whether the year is reckoned from a solar or a lunar starting point, and in which era they count from, so two Panchangas printed in different parts of India can give different month names for the same day.