Calculation methodology

Calculation profiles

A calculation profile is the complete set of methodological choices. Profiles are versioned; saved reports record the profile, its version and the engine version. You can choose a profile in your account settings or with the location selector.

Ayanamsa

Sidereal (nirayana) longitudes are apparent tropical longitudes minus the ayanamsa. Each ayanamsa is defined by its value at a reference epoch and carried forward with the IAU 2006 general precession in longitude (Capitaine et al. 2003). For “true” definitions, nutation in longitude is added so that the result is on the same apparent frame as the planetary positions.

Sunrise, sunset and moonrise

Sunrise and sunset are the moments when the upper limb of the Sun touches the horizon, with standard atmospheric refraction, as used by modern drik Panchangs (the profile setting is shown above). Moonrise and moonset use the setting shown in each profile; the built-in profiles use the centre of the Moon's disc on the geometric horizon without refraction, which matches the convention of widely used Panchang publishers. Positions are topocentric for the selected coordinates and elevation. The Hindu day (vara) runs from one sunrise to the next, so an instant before sunrise belongs to the previous weekday.

Positions of the Sun, Moon and planets come from NASA/JPL's DE440 ephemeris (public domain), the same planetary ephemeris NASA uses for spacecraft navigation; checked against JPL Horizons to within 0.5 arcsecond. Time scales, precession, IAU 2000B nutation, sidereal time and sunrise and moonrise come from Astronomy Engine (MIT licence) by Don Cross. Rahu and Ketu use the mean or true lunar node (Meeus, Astronomical Algorithms, ch. 47) according to the profile.

Tithi, Nakshatra, Yoga and Karana

The five limbs are found by searching for the exact moments at which these quantities cross their division boundaries, so every start and end time is an actual crossing, not an interpolation from sunrise values.

• Tithi = ⌊(Moon − Sun) / 12°⌋ + 1, using the Moon–Sun elongation (30 tithis; 1–15 Shukla, 16–30 Krishna; 30 = Amavasya).

• Nakshatra = ⌊sidereal Moon / 13°20′⌋ + 1 (27 nakshatras); pada = quarters of 3°20′.

• Yoga = ⌊(sidereal Sun + sidereal Moon) mod 360° / 13°20′⌋ + 1 (27 yogas).

• Karana = half-tithi of 6° elongation (60 per lunar month): the first half of Shukla Pratipada is Kimstughna, then the seven movable karanas (Bava … Vishti) repeat eight times, and the last three halves are Shakuni, Chatushpada and Naga. Vishti karana is Bhadra.

• Lunar month: an Amanta month runs from new moon to new moon and is named after the sidereal sign occupied by the Sun at the new moon that begins it (Meena → Chaitra, Mesha → Vaishakha, …). If the Sun does not change sign during the lunation the month is Adhik; if it changes sign twice, one month name is skipped (Kshaya). Purnimanta names are derived by assigning the Krishna paksha to the following month.

• Samvat: Vikram and Shaka years change at the start of Chaitra. The 60-year Samvatsara name uses the South Indian cycle reckoned with the Shaka era.

Day divisions and named periods

These periods are fixed traditional fractions of the local day (sunrise to sunset) or night (sunset to next sunrise). Because day length changes through the year and with latitude, their clock times change every day.

Day and night are each divided into eight equal parts. The seven choghadiyas follow the order Udveg (Sun), Char (Venus), Labh (Mercury), Amrit (Moon), Kaal (Saturn), Shubh (Jupiter), Rog (Mars). The day starts with the weekday lord's choghadiya and advances one step; the night starts five steps after it and advances five steps each period.

Hora: 12 equal parts of daytime and 12 of night (so a hora is not a clock hour). The first hora of the day belongs to the weekday lord and the sequence follows the Chaldean order Sun, Venus, Mercury, Moon, Saturn, Jupiter, Mars.

Brahma Muhurat

14th of the 15 muhurtas of the preceding night: from two night-muhurtas before sunrise to one night-muhurta before sunrise.

Pratah Sandhya

From 1.5 night-muhurtas before sunrise until sunrise.

Abhijit Muhurat

8th of the 15 day muhurtas (around local midday).

Vijaya Muhurat

11th of the 15 day muhurtas.

Madhyahna

3rd of 5 equal parts of daytime.

Aparahna

4th of 5 equal parts of daytime.

Sayahna Sandhya

From sunset until 1.5 night-muhurtas after sunset.

Pradosh Kaal

From sunset for one fifth of the night (6 ghatis of a 30-ghati night).

Nishita Kaal

8th of the 15 night muhurtas (around local midnight).

Varjyam

Varjyam (Nakshatra Tyajyam): a window of 4 ghatis (of 60) inside each nakshatra, starting at a nakshatra-specific ghati, scaled to the nakshatra's actual duration.

Festivals and vrat rules

Festival and vrat definitions are data, not fixed Gregorian dates. Each defines a lunar month (in Amanta numbering), paksha, tithi and the part of the day (kaal) that the tithi must cover — for example Madhyahna for Ram Navami, Pradosh for Diwali, Nishita for Janmashtami, Aparahna for Shraddha and moonrise for Sankashti Chaturthi (kaal vyapti). The engine finds the tithi interval and checks which civil day's kaal it covers.

• If the tithi covers the kaal on two consecutive days, each definition states the tie-break: the first day, the second day (optionally only if the overlap reaches a minimum, e.g. one ghati for Diwali), or the day with the larger overlap.
• If the tithi covers the kaal on no day (a kshaya tithi), the day on which the tithi prevails longest is used, and a note is shown.
• Where a definition requires it (Holika Dahan, Raksha Bandhan), Bhadra (Vishti karana) is removed from the observance window; for Raksha Bandhan, if Bhadra leaves no usable time and the Purnima prevails at the next sunrise long enough, the next morning is used. Otherwise, if Bhadra covers the whole window, the time after Bhadra ends is given, until the tithi ends but not beyond midnight (Nishita).
• Sankrantis are the sidereal solar ingresses; if the ingress is after local sunset, the observance is on the next day.
• Ekadashi: the Smarta rule observes the day on which Ekadashi prevails at sunrise (the first such day if two). The Vaishnava rule moves the fast to the next day if Dashami still prevails at Arunodaya (96 minutes before sunrise). The built-in profiles use the Smarta rule. If Dwadashi ends before the sunrise that follows the chosen day, the Smarta fast is kept on the previous day and the later day is shown as the optional Gauna Ekadashi.
• Parana (breaking the fast) is on the next day after sunrise and not during Hari Vasara (the first quarter of Dwadashi), preferably within Pratahkal (the first fifth of daytime) and before Dwadashi ends; if Hari Vasara extends beyond Pratahkal, Parana is given after Madhyahna.
• Annual festivals are observed in the regular (Nija) month, not in an Adhik month, unless the definition says otherwise.
• Every decision (tie-break, fallback, Bhadra exclusion) is recorded with the result so that it can be explained. Definitions are editable by administrators and every change is audit-logged.

Muhurat rules

A Muhurat purpose is a data-driven rule set built from reusable checks: allowed or avoided tithis, nakshatras, weekdays and yogas, lunar months, lagna, Chaturmas, Kharmas, Adhik Maas, combustion (asta) of Jupiter and Venus, Rahu Kaal, Yamaganda, Gulika, Dur Muhurat, Varjyam, Bhadra, Panchak, Disha Shool for travel, and personal Tara bala and Chandra bala when birth details are supplied. “Required” rules exclude a window; “preferred” rules only add warnings shown with the result.

Rule sets are compiled from Muhurta Chintamani selections as commonly cited by modern Panchangs. Each rule goes through the platform's Jyotish review, an automated (AI) review against the classical texts and published Panchangs, recorded rule by rule with its sources; a Muhurat whose rules have not all passed it is marked “Beta” on its page. A Muhurat shown here is a traditional guideline, not a guarantee of any outcome.

Jyotish (Kundli)

Kundli charts use sidereal positions with the profile's ayanamsa and whole-sign houses from the Lagna (ascendant). Rahu and Ketu use the mean or true node according to the profile. Vimshottari dasha starts from the lord of the natal Moon's nakshatra, with the balance in proportion to the unfinished part of that nakshatra; the year length is taken from the profile. Doshas (Manglik and others) are reported with the exact rule applied, the variants recognised by different traditions and commonly cited cancellations, without fear-based wording.

Divisional charts (vargas) available

D1, D2, D3, D4, D7, D9, D10, D12, D16, D20, D24, D27, D30, D40, D45, D60

Vimshottari dasha years

Ketu 7 → Venus (Shukra) 20 → Sun (Surya) 6 → Moon (Chandra) 10 → Mars (Mangal) 7 → Rahu 18 → Jupiter (Guru) 16 → Saturn (Shani) 19 → Mercury (Budh) 17 = 120

Validation

The calculation engine is tested against independently published results. Test expectations are taken from the publisher and are never adjusted to match the engine.

• Sunrise and sunset from the U.S. Naval Observatory (8 places, 24 dates), with Rahu Kaal and the other day periods derived from them; tithi end times printed by the Rashtriya Panchang of the India Meteorological Department (2024–2027); Sun and Moon positions from NASA/JPL Horizons.
• Smarta Ekadashi dates as printed by the Rashtriya Panchang (2024–2027), and Vaishnava fast days, Mahadwadashis and Parana times from ISKCON's GCal calendars (147 fasts).
• Festival dates in the Government of India holiday orders (2024–2027), State Government holiday lists and the Rashtriya Panchang, for example Diwali, Holika Dahan, Janmashtami, Raksha Bandhan, Makar Sankranti and Navratri.
• Lahiri ayanamsa values from Swiss-Ephemeris-based tables (Jagannatha Hora): 1 January 2000 00:00 UT = 23°51′12″ and 1 January 2025 = 24°12′23″.
• The Lahiri (calibrated) ayanamsa is an empirical adjustment (the standard value plus about 22″, without nutation) towards the timings of popular North Indian almanacs; it is not an official definition. The Sun ingress times printed by the Rashtriya Panchang agree with the standard Lahiri within a minute and come 4–12 minutes before the calibrated variant's (2024–2027).

Agreement with one publisher does not make another publisher wrong: Panchangs legitimately differ in ayanamsa, sunrise definition and festival conventions.

See the yearly public accuracy report: our festival dates against the official lists

Data sources and software

• Place names, coordinates, elevation and time zones: GeoNames (geonames.org), licensed under Creative Commons Attribution 4.0 (CC BY 4.0).
• Time zones and daylight-saving rules: the IANA time zone database as provided by the runtime.
• Astronomical positions: NASA/JPL DE440 ephemeris (public domain) and Astronomy Engine (MIT licence).
• Traditional rules: editorial summaries of classical works such as Muhurta Chintamani, Nirnaya Sindhu, Dharma Sindhu and Brihat Parashara Hora Shastra, as applied by modern drik Panchangs.

Reference values from published almanacs are used only to check our own calculations; Udyog Jyotish is not affiliated with their publishers or with any temple trust.

Known limitations

• At polar latitudes, on days when the Sun does not rise or set, sunrise-based periods (Rahu Kaal, Choghadiya, Hora, muhurtas) cannot be defined and are not shown; tithi and nakshatra are given for the civil day.
• Regional festival conventions differ (for example Tamil, Kerala, Bengali and Odia solar-calendar rules, and local tie-break customs). The rules used are stated with each result; your local Panchang or family tradition may differ.
• Moon illumination is approximated from the Moon–Sun elongation, (1 − cos elongation) / 2, and can differ slightly from precise physical illumination.
• Two Samvatsara names are shown: the North Indian one (Jupiter or Barhaspatya cycle after the Surya Siddhanta, the name current at Mesha Sankranti, with an occasional skipped name) and the South Indian one (60-year cycle reckoned with the Shaka era). The moment the Jupiter cycle changes can differ by a few hours between Panchangs.
• Differences of a minute or two from other Panchangs are normal and arise from ayanamsa variants, sunrise definitions, coordinates and elevation.
• Interpretations of Muhurat, doshas, Rashifal and Vastu are traditional guidance, not predictions or guarantees.