Reference

How a panchangam is computed: the astronomical and tabular traditions

Two ways of producing a panchangam — one from tables handed down in verse, one from the actual positions of the sun and moon. What separates them, why they now differ by days in places, and which one this site uses.

Every panchangam is an answer to one question: where are the sun and the moon right now? There are two traditions of answering it, and the difference between them is the reason two printed panchangams on the same shelf can place a festival on different days.

The tabular tradition

The older approach, still followed in the vakya tradition of Tamil Nadu and parts of Kerala, works from tables. Mean motions for the sun and moon were established centuries ago and encoded in memorable verse — vakya means 'sentence' — so that a practitioner could reproduce a position anywhere, with no instrument and no reference library. As a piece of engineering for a world without printing, it is remarkable.

Its weakness is inherent to the design. Mean motions ignore the fact that neither the moon nor the earth moves at a constant speed, and the constants were fixed against observations made a long time ago. Small errors accumulate. Over a millennium and a half they have grown to the point where a vakya panchangam and an astronomically computed one can differ by a day on a tithi boundary, and occasionally more.

The astronomical tradition

The other approach computes the true position of the sun and moon for the exact instant in question, using an ephemeris. This is what modern almanacs do, what observatories do for planning, and what the Rashtriya Panchang — India's official calendar — has done since 1957.

It is not a Western import onto an Indian tradition. Indian astronomy has computed true positions from corrections to mean motion since Aryabhata, and the Surya Siddhanta contains exactly this kind of correction. What has changed is the precision of the underlying series, not the intent.

This site uses the astronomical method throughout. Positions come from established ephemeris series evaluated for the moment being asked about rather than interpolated from a daily table, and the moment a tithi, nakshatra, yoga or karana ends is found by root-finding on the underlying angle — which is why our end times are given to the minute rather than the quarter hour.

Ayanamsa: the number that decides where the zodiac starts

Modern ephemerides give positions measured from the vernal equinox — the tropical, or sayana, frame. Indian astronomy measures from the fixed stars — the sidereal, or nirayana, frame. The two frames coincided once, around the fifth century CE, and have been drifting apart ever since at roughly fifty arc-seconds a year because of the precession of the equinoxes.

The offset between them is the ayanamsa, and it is currently a little over twenty-four degrees. Every sidereal position in a panchangam is a tropical position minus the ayanamsa, so the value chosen matters directly.

Other values are in use — Raman and Krishnamurti are the most common alternatives — and they differ from Lahiri by a fraction of a degree. That is small, but the moon covers a fraction of a degree in a couple of minutes, so a different ayanamsa can move a nakshatra boundary by enough to put it on the other side of sunrise. If your panchangam uses one of these, expect occasional differences of exactly that kind.

What we compute, and how

• Tithi — the moon's elongation from the sun, divided into thirty parts of twelve degrees.
• Nakshatra — the moon's sidereal longitude, divided into twenty-seven parts of 13°20′.
• Yoga — the sum of the sun's and moon's sidereal longitudes, divided into twenty-seven parts.
• Karana — half a tithi, six degrees of elongation.
• Sunrise and sunset — the moment the sun's upper limb meets a level horizon, including standard atmospheric refraction, at a zenith distance of 90°50′.
• The kalams — eighths of the daylight period, assigned by weekday.
• Abhijit muhurta — centred on solar noon, the midpoint of the daylight period.

Sunrise deserves a note of its own, because it does more work than any other number on the page. It starts the panchangam day; it decides which tithi the day is named for; and it is one end of the interval from which every kalam is derived. We compute it iteratively, re-evaluating the sun's declination at the estimated moment of the event rather than at noon, which keeps it accurate to a few seconds rather than a minute.

Why the same site can show different times to different people

Because it should. A panchangam computed for a point four hundred kilometres away is a panchangam computed for a different sunrise. Every page here is computed for a specific latitude, longitude and time zone; we detect your zone when the page loads and use the nearest city we cover, and you can set it exactly from the header.

For readers in cities that observe daylight saving, the offset is resolved for the particular date being shown rather than assumed to be fixed — otherwise half the year would be an hour out.

Where we still defer to tradition

Computation gets you the sky. It does not get you the calendar, because a festival is a tithi rule plus a regional custom, and customs differ legitimately. Vinayaka Chaviti, Deepavali and Sankranti are all observed on different days by different communities in the same year, and no formula resolves that — it is not a computational question.

So our festival dates come from validated data reviewed against published panchangams rather than from a formula alone, and where two dates are in common use we say so on the page instead of quietly picking one. Being transparent and occasionally disagreeing with your panchangam is better than being vague and always seeming right.

Every timing referenced in these guides is computed astronomically for the city you select and cross-referenced against the traditional panchangams in common use. How we compute