The five limbs, tithi and vara

A Panchang (literally “five limbs”) is the traditional Hindu almanac. For every day it lists five quantities, all calculated from the positions of the Sun and the Moon and from the local time of sunrise. In the tradition, festivals, fasts and the choice of a muhurat are all built on these five numbers. This lesson gives an overview of all five and then explains the first two, tithi and vara.

The five limbs at a glance

• Tithi — the lunar day: each 12° that the Moon gains on the Sun.
• Vara — the weekday, counted from one sunrise to the next.
• Nakshatra — the lunar mansion: which of 27 equal parts of the sidereal zodiac holds the Moon.
• Yoga — the sum of the Sun’s and the Moon’s sidereal longitudes, divided into 27 parts.
• Karana — half a tithi: each 6° that the Moon gains on the Sun.

Notice the pattern. Tithi and karana depend only on the angle between the Moon and the Sun, so they need no ayanamsa (the offset between the tropical and the sidereal zodiac). Nakshatra and yoga use sidereal longitudes, so the choice of ayanamsa affects them. Vara depends on sunrise, so it depends on your place.

Tithi: the Moon’s lead over the Sun

Against the background stars the Moon moves east about 13° a day, while the Sun moves only about 1°. The angle by which the Moon is ahead of the Sun, called its elongation, grows from 0° at new moon to 180° at full moon and on to 360° at the next new moon. Divide that circle into 30 equal parts of 12° and each part is one tithi.

A worked example: if the Moon is 100° ahead of the Sun, 100 ÷ 12 = 8.33. Eight full tithis have passed, so the 9th tithi, Shukla Navami, is running. When the elongation reaches 108°, Navami ends and Dashami begins.

Two fortnights: Shukla and Krishna paksha

The first 15 tithis, while the Moon waxes (0° to 180°), form Shukla paksha, the bright fortnight. They are Pratipada, Dwitiya, Tritiya, Chaturthi, Panchami, Shashthi, Saptami, Ashtami, Navami, Dashami, Ekadashi, Dwadashi, Trayodashi, Chaturdashi and Purnima, the full-moon tithi. The next 15, while the Moon wanes (180° to 360°), form Krishna paksha, the dark fortnight. The names repeat from Pratipada to Chaturdashi, and the 15th is Amavasya, the new-moon tithi.

Purnima and Amavasya are tithis, not instants. The astronomical full moon is the moment the elongation is exactly 180°, and that moment ends the Purnima tithi, which spans 168° to 180°. Likewise Amavasya spans 348° to 360° and ends at the exact new moon.

Why tithis are not 24 hours long

A tithi is defined by angle, not by clock time. The Moon’s speed changes along its elliptical orbit, from roughly 12° to 15° a day, and the Sun’s apparent speed also varies a little through the year. So the time the Moon needs to gain 12° on the Sun changes from tithi to tithi. A tithi can last roughly 20 to 27 hours, averaging a little under 24 hours (a lunar month of about 29.53 days ÷ 30 ≈ 23.6 hours). That is why tithis begin and end at any hour of the day or night.

The tithi itself is a calculation from positions; the meaning attached to each tithi (Ekadashi for fasting, Chaturthi for Ganesha) is tradition. Almanacs that use the old textbook formulas and those that use modern astronomical positions can give tithi end times that differ by minutes or more. The Calendar Reform Committee (1955) urged almanac makers to compute from accurate modern data.

Vara: the weekday and its lord

Vara is the weekday. In the Panchang it runs from one sunrise to the next, not from midnight to midnight as the civil calendar does. So an event at 3 a.m. on a civil Tuesday falls in Monday’s vara, because Tuesday’s sunrise has not yet come. Each vara is named after its lord:

• Ravivara (Sunday) — the Sun
• Somavara (Monday) — the Moon
• Mangalavara (Tuesday) — Mars
• Budhavara (Wednesday) — Mercury
• Guruvara or Brihaspativara (Thursday) — Jupiter
• Shukravara (Friday) — Venus
• Shanivara (Saturday) — Saturn

Where the weekday order comes from: the horas

The classical texts list the seven grahas from the slowest to the fastest: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. The day is divided into 24 horas (hours), and each hora is given to the next graha in this order, cycling round. The first hora at sunrise belongs to the lord of the day.

Start on Sunday: hora 1 is the Sun’s, hora 2 Venus’s, hora 3 Mercury’s, hora 4 the Moon’s, then Saturn, Jupiter, Mars, the Sun again, and so on. Because 24 = 3 × 7 + 3, the 25th hora, the first of the next day, lies three places beyond the Sun in the cycle. It belongs to the Moon, so the next day is Monday. Repeat the step and you get Mars, Mercury, Jupiter, Venus and Saturn: the familiar weekday order.

Many almanacs make the 12 day horas and the 12 night horas unequal, dividing daylight and night separately by 12; others use equal one-hour horas. The sequence of lords is the same either way. What the tradition says about each lord’s day is interpretation, taken up in the muhurat lessons.

The panel below shows today’s five limbs for your place. Look at the tithi and its end time, and at the vara, which follows sunrise rather than midnight.