Vedic Panchang
वैदिक पंचांग — पाँच अंगों का दर्शन
Hora Clock
होरा चक्र — Planetary hours from sunrise · Each hora ruled by a planet in cosmic sequence
Current hora ruler
Day ruler (sunrise hora)
24 Hora sequence (D = day, N = night)
Panchang
पंचांग — The five limbs: Tithi · Nakshatra · Yoga · Karana · Vara
Monthly Calendar
मासिक पंचांग — Tithi, Nakshatra & festivals for each day
Ritu — Six Seasons
षड्ऋतु — India's six-fold seasonal cycle linked to solar movement & Ayurveda
How It All Works
गणित शास्त्र — The astronomical science behind every element of this dashboard
Hora — The Origin of Weekday Names
होरा — सप्ताह के दिनों के नामों का मूल

Ravivar, Somvar, Mangalvar — these are not random names. They are calculated using an astrological clock called Hora, documented in texts like the Surya Siddhanta and Brihat Parashara Hora Shastra.

What is a Hora?
In Vedic astrology, the time from one sunrise to the next sunrise is divided into 24 Hora — meaning 24 planetary hours. But these hours are not equal like modern 60-minute hours. They are calculated by:

Day Hora Duration = (Sunset Time − Sunrise Time) ÷ 12
Night Hora Duration = (Next Sunrise − Sunset) ÷ 12

Example: If sunrise = 6:26 AM and sunset = 6:37 PM
Day duration = 12h 11m → Each day hora = ~61 minutes
Night duration = 11h 49m → Each night hora = ~59 minutes

The Cosmic Sequence
Each hora is ruled by a specific planet. These planetary rulers follow a fixed cosmic sequence based on their orbital distance from Earth (as observed in geocentric astronomy):

This order keeps repeating, every single hour, without break.

The Most Important Rule — How Weekdays Are Named:
The planet ruling the first Hora at sunrise decides the weekday name.

1
If sunrise starts with Sun hora, the day becomes Sunday (Ravivar / रविवार).
2
After 24 horas, the sequence has cycled. Since 24 ÷ 7 = 3 remainder 3, the next sunrise automatically shifts 3 planets ahead in the cosmic sequence.
3
3 positions ahead of Sun → Moon. So the next day is Monday (Somvar / सोमवार).
4
3 positions ahead of Moon → Mars. So the next day is Tuesday (Mangalvar / मंगलवार).
5
And the cycle continues — Mercury (Wednesday), Jupiter (Thursday), Venus (Friday), Saturn (Saturday).

The Mathematical Proof:

Sequence: Saturn(0) → Jupiter(1) → Mars(2) → Sun(3) → Venus(4) → Mercury(5) → Moon(6)

24 mod 7 = 3 → Each sunrise shifts +3 positions in the sequence

Sun(3) → +3 = Moon(6) → +3 = Mars(2) → +3 = Mercury(5) → +3 = Jupiter(1) → +3 = Venus(4) → +3 = Saturn(0)
Sunday → Monday → Tuesday → Wednesday → Thursday → Friday → Saturday
DayHindiRulerRuler Hindi1st Hora starts atEnergy
SundayरविवारSunसूर्यSunriseAuthority, vitality, self-expression
MondayसोमवारMoonचन्द्रSunriseMind, emotions, nurturing
TuesdayमंगलवारMarsमंगलSunriseCourage, action, energy
WednesdayबुधवारMercuryबुधSunriseIntellect, communication, trade
ThursdayगुरुवारJupiterगुरुSunriseWisdom, expansion, teaching
Fridayशुक्रवारVenusशुक्रSunriseLove, beauty, creativity
SaturdayशनिवारSaturnशनिSunriseDiscipline, endurance, karma

Each planet carries different energy and vibration. So the planet ruling sunrise influences the overall energy of that day. This is why Shanivar (Saturn's day) is associated with discipline and austerity, while Shukravar (Venus's day) is associated with beauty and devotion.

Next time you hear the name of a weekday — remember: it was calculated thousands of years ago using planetary time science.

Tithi — Angles in Space, Not Dates
तिथि — अंतरिक्ष में कोण, तारीखें नहीं

Ekadashi, Ashtami, Purnima — these are not dates. They are angles in space. And once you understand this, Indian calendars start looking more scientific than modern ones.

The Core Geometry:
The Moon completes a 360° revolution around the Earth in one lunar cycle (~29.5 days). Ancient astronomers mapped this movement with extraordinary precision. They noticed that from one New Moon to the next, the Moon covers 360°.

360° ÷ 30 parts = 12° per part

Each 12° segment is called a Tithi.
Tithi = Angular distance between the Sun and the Moon.

Every 12° shift in the Sun-Moon angle creates a new tithi.

The 30 Tithis — Pure Angular Geometry:

AngleTithiNameHindiSignificance
Amavasyaअमावस्याNew Moon — Sun & Moon aligned
12°S1Pratipadaप्रतिपदाFirst sliver of waxing moon
24°S2Dwitiyaद्वितीया
36°S3Tritiyaतृतीया
48°S4Chaturthiचतुर्थी⚠ Critical tithi
60°S5Panchamiपंचमी
72°S6Shashthiषष्ठी
84°S7Saptamiसप्तमी
96°S8Ashtamiअष्टमी⚠ Critical — near quadrature (90°)
108°S9Navamiनवमी
120°S10Dashamiदशमी
132°S11Ekadashiएकादशी⚠ Critical tithi — fasting prescribed
144°S12Dwadashiद्वादशी
156°S13Trayodashiत्रयोदशी⚠ Critical tithi
168°S14Chaturdashiचतुर्दशी
180°S15Purnimaपूर्णिमाFull Moon — Sun & Moon exactly opposite

After Purnima (180°), the Krishna Paksha (waning phase) begins. The same 15 tithi names repeat from 192° to 360°, completing the cycle back to Amavasya.

Two Pakshas — Two Halves of the Circle:

Shukla Paksha (शुक्ल पक्ष) = Waxing phase = 0° → 180° = Amavasya to Purnima
Krishna Paksha (कृष्ण पक्ष) = Waning phase = 180° → 360° = Purnima back to Amavasya

Critical Tithis — Resonance Points:
Ancient science observed that some lunar angles create instability — similar to resonance in physics. These tithis include:

Chaturthi (48°/228°)
Angular tension — early deviation from alignment
Ashtami (96°/276°)
Near quadrature — Sun & Moon at ~90°, gravitational vectors cross
Ekadashi (132°/312°)
Approaching opposition/conjunction — bodies accelerating toward peak
Trayodashi (156°/336°)
Pre-peak tension — 24° before Purnima/Amavasya

That's why fasting, silence, and restraint were prescribed on these days — not as rituals, but as biological precautions. Tithi is not religion. It is astronomy influencing physiology. The body reacts to these angular positions because gravitational and electromagnetic influences of the Sun-Moon system change measurably at these points.

How This Dashboard Calculates Tithi:

1. Compute Sun's sidereal longitude (using orbital mechanics + Lahiri Ayanamsa correction)
2. Compute Moon's sidereal longitude (including major perturbation terms)
3. Angular difference = (Moon longitude − Sun longitude) mod 360°
4. Tithi number = floor(angular difference ÷ 12°) + 1
5. Tithi 1–15 = Shukla Paksha · Tithi 16–30 = Krishna Paksha
Nakshatra & Rashi — The Moon's Address in the Sky
नक्षत्र एवं राशि — चन्द्रमा का आकाशीय पता

While Tithi measures the angle between Sun and Moon, Nakshatra and Rashi measure where the Moon actually sits in the sky against the backdrop of fixed stars.

Nakshatra — 27 Lunar Mansions:
The ancient astronomers divided the entire 360° ecliptic (the path the Moon travels) into 27 equal segments:

360° ÷ 27 = 13°20' per Nakshatra

Each Nakshatra is a "lunar mansion" — a specific arc of the sky identified by a prominent star or star group within it.

The Moon spends approximately 1 day in each Nakshatra (27 Nakshatras × ~1 day ≈ 27.3 days, the sidereal month).

The 27 Nakshatras beginning from 0° Aries (Mesha) are: Ashwini (0°–13°20'), Bharani (13°20'–26°40'), Krittika (26°40'–40°), and so on through to Revati (346°40'–360°).

Each Nakshatra has a ruling deity, a planetary lord, and specific qualities that influence the day. For example, Pushya (ruled by Saturn, deity Brihaspati) is considered extremely auspicious for new ventures.

Rashi — 12 Zodiac Signs:
The same 360° ecliptic is also divided into 12 equal signs of 30° each:

360° ÷ 12 = 30° per Rashi

Mesha (Aries) 0°–30° · Vrishabha (Taurus) 30°–60° · Mithuna (Gemini) 60°–90°
Karka (Cancer) 90°–120° · Simha (Leo) 120°–150° · Kanya (Virgo) 150°–180°
Tula (Libra) 180°–210° · Vrischika (Scorpio) 210°–240° · Dhanu (Sagittarius) 240°–270°
Makara (Capricorn) 270°–300° · Kumbha (Aquarius) 300°–330° · Meena (Pisces) 330°–360°

Relationship between Nakshatra and Rashi:
Each Rashi (30°) contains exactly 2.25 Nakshatras (30° ÷ 13°20' = 2.25). This creates the beautiful interlocking system you see in the Panchang — the Moon's Rashi tells you its broad zodiac zone, while its Nakshatra gives you a much finer position (4× more precise).

How This Dashboard Calculates Them:

1. Compute Moon's sidereal longitude (degrees from 0° Aries)
2. Nakshatra index = floor(Moon longitude ÷ 13.333°) → gives 0–26 (27 Nakshatras)
3. Rashi index = floor(Moon longitude ÷ 30°) → gives 0–11 (12 Rashis)
4. The Moon moves ~13° per day, so it changes Nakshatra roughly daily and Rashi every ~2.3 days

Ganda Mool Nakshatras: Six specific Nakshatras (Ashwini, Ashlesha, Magha, Jyeshta, Moola, Revati) fall at the junction points of water and fire Rashis. These junctions are considered sensitive — births during Ganda Mool periods traditionally call for special observances.

Panchang — Five Simultaneous Measurements
पंचांग — पाँच अंग (तिथि, नक्षत्र, योग, करण, वार)

The word Panchang comes from Sanskrit: Pancha (पंच = five) + Anga (अंग = limb). It is a system of five simultaneous astronomical measurements taken at any moment, together capturing the complete celestial state.

Think of it as a five-dimensional coordinate system for time:

1
Tithi (तिथि) — Sun-Moon angular distance. Measures the Moon's phase angle relative to the Sun. 30 tithis of 12° each. Determines lunar days, fasting dates, and festival timing. This is the angle between two bodies.
2
Nakshatra (नक्षत्र) — Moon's absolute stellar position. Which of 27 lunar mansions (each 13°20') the Moon occupies against the fixed star background. This is the Moon's address in space.
3
Yoga (योग) — Sum of Sun + Moon longitudes. 27 yogas of 13°20' each. Measures the combined luni-solar energy. When both luminaries are in specific combined positions, the day takes on particular qualities. This is the joint energy signature.
4
Karana (करण) — Half of a Tithi. Each tithi (12°) is split into two karanas (6° each), giving 60 karanas per lunar month. 11 named karanas cycle through. This is a finer sub-division of the lunar angle.
5
Vara (वार) — Weekday from Hora ruler. The planet ruling the first hora at sunrise gives the day its name and dominant planetary energy. This is the solar-planetary clock.
Yoga Calculation:
Yoga = floor((Sun longitude + Moon longitude) mod 360° ÷ 13.333°)

Karana Calculation:
Karana = floor(Sun-Moon angular difference ÷ 6°)
Two karanas per tithi · 60 karanas per lunar month · 11 named types cycling

Every single cell in a Hindu calendar like the one on Prokerala encodes all five of these measurements. The calendar you saw showing "K 5 Panchami, H 19, IN 17, ☆ Swati, ☾ Tula" is simultaneously telling you: the tithi (Panchami = 60° Sun-Moon angle, Krishna Paksha), the Nakshatra (Swati = Moon in the 15th lunar mansion), the Rashi (Tula = Moon in Libra), plus the Hijri and Indian Civil calendar dates — all for the same moment.

This is not a religious calendar. It is a multi-axis astronomical coordinate system for tracking time through celestial mechanics.

Ritu — Six Seasons from Solar Geometry
षड्ऋतु — सूर्य की गति से छह ऋतुएँ

While most of the world uses 4 seasons, the Vedic system recognizes 6 Ritus — a more precise division based on the Sun's movement through zodiac pairs. This system was already documented during the Vedic period in the Jyotisha Vedanga.

The Astronomy:
As the Earth orbits the Sun, the Sun appears to move through the 12 Rashis (zodiac signs) over a year. The six Ritus are defined by pairing adjacent Rashis:

RituHindiEnglishZodiac PairMonthsAnchored To
ShishiraशिशिरLate WinterMakara + KumbhaMagha–PhalgunaStarts at Winter Solstice (Uttarayana)
Vasantaवसन्तSpringMeena + MeshaChaitra–VaisakhaVernal Equinox at midpoint
Grishmaग्रीष्मSummerVrishabha + MithunaJyaistha–AsadhaEnds at Summer Solstice (Dakshinayana)
Varshaवर्षाMonsoonKarka + SimhaShravana–BhadraStarts at Summer Solstice
SharadaशरदAutumnKanya + TulaAshvina–KartikaAutumnal Equinox at midpoint
Hemantaहेमन्तEarly WinterVrischika + DhanuAgrahayana–PaushaEnds at Winter Solstice

Key Astronomical Anchors:

Uttarayana (Winter Solstice, ~Dec 22) → Sun begins northward journey → Shishira begins
Vasant Vishuva (Vernal Equinox, ~Mar 20) → Equal day/night → Midpoint of Vasanta
Dakshinayana (Summer Solstice, ~Jun 21) → Sun begins southward journey → Varsha begins
Sharad Vishuva (Autumnal Equinox, ~Sep 22) → Equal day/night → Midpoint of Sharada

Ayurvedic Connection (Ritucharya):
Each Ritu has a specific Ritucharya — a seasonal regimen prescribed in Ayurveda (documented in Charaka Samhita and Sushruta Samhita). This isn't folklore — it's a systematic approach connecting solar geometry to:

Dosha cycles
Kapha accumulates in Shishira, liquefies in Vasanta. Pitta peaks in Sharada. Vata rises in Varsha.
Digestive fire (Agni)
Strongest in Hemanta/Shishira (cold compresses heat inward), weakest in Varsha (humidity).
Diet
Heavy/warm in winter, light/bitter in spring, sweet/cold in summer, sour/warm in monsoon.
Agriculture
Rabi sowing (Hemanta) → Rabi harvest (Vasanta) → Kharif sowing (Varsha) → Kharif harvest (Sharada).
Vikram Samvat — The Living Calendar
विक्रम संवत् — भारत का सजीव कालगणना तंत्र

The Vikram Samvat is the traditional Hindu calendar era, believed to have been founded by Emperor Vikramaditya in 57 BCE. The current year is Vikram Samvat 2083 (2026 CE), making it one of the oldest continuously-used calendar systems in the world.

Vikram Samvat = Gregorian Year + 57 (approximately)

More precisely: The new year begins at Chaitra Shukla Pratipada (the first day of waxing moon in Chaitra month), which typically falls in March/April. Before this date, the Samvat year is Gregorian + 56; after it, Gregorian + 57.

Why Chaitra Shukla Pratipada?
This is not arbitrary. It marks the first sunrise after Amavasya in Chaitra — the moment when the Sun-Moon angle passes 0° and the first sliver of the new crescent becomes visible. This is celebrated as Gudi Padwa (Maharashtra), Ugadi (Karnataka/Andhra), and Nav Samvatsar across North India.

Luni-Solar Calibration:
The Hindu calendar is luni-solar — months follow the Moon (synodic month ≈ 29.5 days), but the year stays aligned with the Sun (tropical year ≈ 365.25 days). This creates a mismatch:

12 lunar months = 12 × 29.5 = 354 days
1 solar year = 365.25 days
Deficit = ~11 days per year

Solution: Every ~2.7 years, an Adhik Mas (intercalary month) is inserted.
This keeps festivals like Holi, Diwali, and Navratri in their correct seasons — unlike a pure lunar calendar (e.g., Islamic) where months drift through seasons over a 33-year cycle.

The 12 Hindu Months:
Each month runs from one Purnima to the next (Purnimant system, used in North India) or one Amavasya to the next (Amant system, used in South/West India). The months are named after the Nakshatra in which the Full Moon falls:

Chaitra
Full Moon near Chitra Nakshatra (Mar–Apr)
Vaisakha
Full Moon near Vishaka Nakshatra (Apr–May)
Jyaistha
Full Moon near Jyeshta Nakshatra (May–Jun)
Asadha
Full Moon near Purva/Uttara Ashadha (Jun–Jul)
Shravana
Full Moon near Shravana Nakshatra (Jul–Aug)
Bhadra
Full Moon near Purva/Uttara Bhadrapada (Aug–Sep)
Ashvina
Full Moon near Ashwini Nakshatra (Sep–Oct)
Kartika
Full Moon near Krittika Nakshatra (Oct–Nov)
Agrahayana
Full Moon near Mrigashirsha Nakshatra (Nov–Dec)
Pausha
Full Moon near Pushya Nakshatra (Dec–Jan)
Magha
Full Moon near Magha Nakshatra (Jan–Feb)
Phalguna
Full Moon near Purva/Uttara Phalguni (Feb–Mar)

This is why the Prokerala calendar you saw shows "Phalguna 2082 – Chaitra 2083" for March 2026 — the month of March straddles the end of one Hindu month and the beginning of another, with the Hindu new year falling on March 19.

The Vikram Samvat is not just a dating system — it is a living astronomical framework that synchronizes lunar phases, solar seasons, stellar positions, and planetary hours into a single coherent system of timekeeping.