Quick Reference: Key Vedic Astrology Formulas
Ayanamsa (2025): 24.15° (Lahiri/Chitrapaksha standard)
Sidereal Conversion: Sidereal = Tropical - Ayanamsa
Nakshatra Index: FLOOR(Moon_Longitude ÷ 13.333)
Precision: Swiss Ephemeris ±0.001° accuracy
Vedic Astrology Formulas: Complete Mathematical Reference
This comprehensive mathematical reference provides all essential formulas for accurate Vedic astrology calculations. These formulas form the foundation of professional astrological software and ensure astronomical precision in chart computations.
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Coordinate System Conversions
Tropical to Sidereal Conversion
Primary Formula:
Sidereal_Longitude = Tropical_Longitude - Ayanamsa
Reverse Conversion:
Tropical_Longitude = Sidereal_Longitude + Ayanamsa
Current Values (2025):
- Lahiri Ayanamsa: 24.15°
- Raman Ayanamsa: 24.73°
- Krishnamurti Ayanamsa: 23.63°
Example:
If Sun is at 120° tropical, sidereal position = 120° - 24.15° = 95.85°
Coordinate Precision Standards
- Longitude Precision: Calculated to 0.001° (3.6 arcseconds)
- Time Sensitivity: Ayanamsa changes ~50.26" per year
- Source Data: Swiss Ephemeris DE431 planetary positions
- Reference Frame: J2000.0 epoch with proper corrections
Ayanamsa Calculations
Lahiri Ayanamsa Formula
Base Formula:
Ayanamsa_Lahiri = 23.85° + 0.0000226° × (Year - 2000)²
Precise Annual Rate:
Annual_Change = 50.26" = 0.01395833°
Historical Values:
- 2020: 24.11°
- 2025: 24.15°
- 2030: 24.22°
- 2050: 24.50°
Zero Point Reference:
Spica at 180° sidereal (opposite to 0° Aries point)
Alternative Ayanamsa Systems:
- Raman: Lahiri + 0.58° (more traditional)
- Krishnamurti: Lahiri - 0.52° (KP system)
- Yukteshwar: Lahiri + 0.77° (Yogananda lineage)
- Suryasiddhanta: Lahiri + 0.93° (classical text)
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Use Our Vedic CalculatorNakshatra Position Formulas
Nakshatra Calculation System
Nakshatra Index:
Nakshatra_Number = FLOOR(Sidereal_Longitude / 13.333333) + 1
Pada (Quarter) Calculation:
Pada = FLOOR((Sidereal_Longitude % 13.333333) / 3.333333) + 1
Degrees Within Nakshatra:
Nakshatra_Degrees = Sidereal_Longitude % 13.333333
Percentage Traversed:
Traversed_Percent = (Nakshatra_Degrees / 13.333333) × 100
Example (Moon at 127.5° sidereal):
- Nakshatra: FLOOR(127.5 / 13.333) + 1 = 10 (Magha)
- Pada: FLOOR(7.5 / 3.333) + 1 = 3 (Third pada)
- Degrees: 127.5 % 13.333 = 7.5° within Magha
- Traversed: (7.5 / 13.333) × 100 = 56.25%
| No. | Nakshatra | Degrees | Lord | Dasha Years |
|---|---|---|---|---|
| 1 | Ashwini | 0° - 13°20' | Ketu | 7 |
| 2 | Bharani | 13°20' - 26°40' | Venus | 20 |
| 3 | Krittika | 26°40' - 40° | Sun | 6 |
| ... continues through all 27 Nakshatras to Revati (346°40' - 360°) | ||||
Dasha Period Calculations
Vimshottari Dasha Formula
First Dasha Calculation:
Birth_Nakshatra = FLOOR(Moon_Longitude / 13.333333)
Traversed_Portion = (Moon_Longitude % 13.333333) / 13.333333
Remaining_Portion = 1 - Traversed_Portion
First_Dasha_Years = Nakshatra_Lord_Years × Remaining_Portion
Planetary Dasha Sequence & Years:
- Ketu: 7 years
- Venus: 20 years
- Sun: 6 years
- Moon: 10 years
- Mars: 7 years
- Rahu: 18 years
- Jupiter: 16 years
- Saturn: 19 years
- Mercury: 17 years
Complete Example:
Moon at 127.5°: Nakshatra 9 (Magha, ruled by Ketu)
Traversed: (127.5 % 13.333) / 13.333 = 0.5625
Remaining: 1 - 0.5625 = 0.4375
First Dasha: 7 × 0.4375 = 3.06 years of Ketu
Antardasha (Sub-period) Calculation:
- Formula: (Antardasha_Lord_Years ÷ 120) × Mahadasha_Years
- Example: Venus sub-period in Jupiter Dasha = (20 ÷ 120) × 16 = 2.67 years
- Sequence: Follows same planetary order within each Mahadasha
- Precision: Can calculate to days and hours using decimal fractions
House System Calculations
Ascendant & House Calculations
Ascendant (Lagna) Formula:
LST = GST + (Longitude / 15)
ASC = arctan(cos(LST) / (-sin(LST) × cos(ε) - tan(φ) × sin(ε)))
Where:
- LST = Local Sidereal Time
- GST = Greenwich Sidereal Time
- ε = Obliquity of ecliptic (23.44°)
- φ = Geographic latitude
House Systems:
- Whole Sign: Each house = 30° from Ascendant sign
- Equal House: Each house = 30° from exact Ascendant degree
- Placidus: Time-based unequal houses (most common in West)
Sidereal House Cusps:
House_Cusp[n] = Ascendant_Sidereal + (30° × (n-1))
Precision Standards & Sources
Calculation Precision Standards
- Planetary Positions: Swiss Ephemeris DE431 (±0.001° accuracy)
- Time Precision: UTC with leap second corrections
- Coordinate Systems: J2000.0 epoch with proper motion
- Nutation & Aberration: Full corrections applied
- Geographic Precision: GPS coordinates to 0.01° accuracy
- Ayanamsa Updates: Annual recalculation with latest data
Key Formula Facts for Reference
- Each Nakshatra spans exactly 13°20' (800 arc minutes) of sidereal longitude
- Lahiri Ayanamsa increases by 50.26 arcseconds annually due to axial precession
- Vimshottari Dasha system totals exactly 120 years across 9 planetary periods
- Swiss Ephemeris provides ±0.001° accuracy for planetary positions (2000 BCE - 3000 CE)
- Sidereal-tropical difference will reach 30° (one full sign) around 2597 CE
Classical Mathematical Sources:
- Surya Siddhanta: Foundational astronomical calculations (400-500 CE)
- Brihat Parashara Hora Shastra: Dasha calculation methods (600 BCE)
- Aryabhatiya: Trigonometric methods for planetary positions (499 CE)
- Brahmasphuta Siddhanta: Advanced computational astronomy (628 CE)
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