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The Five Limbs of Panchanga: Inputs and Formulas

Compare tithi, vara, nakshatra, nitya yoga and karana. A numerical example explains Sun–Moon difference, longitude sum and local-day boundaries.

Names and related terms
Panchanga limbs

Editorially reviewed: · Reviewed by OpenFate · Editorial Methodology

Overview

The five limbs of Panchanga are tithi, vara, nakshatra, yoga and karana. Tithi and karana use the Moon–Sun longitude difference; nakshatra uses the Moon’s sidereal longitude; nitya yoga uses the sidereal Sun–Moon sum. Vara follows the stated weekday/day-boundary convention.

At a glance

Tithi / karana
12° /6° divisions of normalized Moon minus Sun
Nakshatra
13°20′ divisions of the Moon’s sidereal longitude
Nitya yoga
13°20′ divisions of normalized sidereal Sun plus Moon
Vara
Weekday with a declared local-day boundary

Which angle belongs to which limb?

Let Δ = (Moon − Sun) modulo 360°. Tithi number is floor(Δ / 12°) + 1; the half-tithi ordinal is floor(Δ / 6°) + 1. Karana names follow their own repeating/fixed sequence, so sixty half-intervals are not sixty different names.

For the 27-part scheme, nakshatra is floor(Moon / (13°20′)) + 1 and nitya yoga is floor(((Sun + Moon) modulo 360°) / (13°20′)) + 1, using specified sidereal longitudes. This calendar yoga is not a natal planetary-combination yoga. Weekday cannot be derived from these angles alone.

One synthetic Sun–Moon pair

Take sidereal Sun 40° and Moon 65°. Their difference 25° gives tithi 3, the waxing third. The Moon is in nakshatra 5, Mrigashira. Their sum 105° gives nitya yoga 8, Dhriti. The half-tithi ordinal is 5, which is Taitula in Rao’s karana sequence.

Vara still needs a dated local-day context; no weekday is inferred from those two longitudes. A common ayanamsa subtraction cancels in the difference, but not in the sum or Moon position. That is why not every limb responds identically to a changed sidereal convention.

How are the boundaries assigned?

Use lower-inclusive, upper-exclusive angle intervals and normalize a full 360° back to 0°. At an exact 6° boundary a new half-tithi begins; at 12° the second tithi begins. Keep precision until after locating the interval.

Rao names seven repeating karanas and four fixed ones; the first half of the waxing first tithi is Kimstughna, not Bava. Sunrise sampling and real change times require separate calculations. This arithmetic explanation neither verifies live product output nor rates a day’s success.

Sources and editorial basis

  1. P. V. R. Narasimha Rao: Vedic Astrology — An Integrated Approach
    §1.3.6/Table 2, printed pp. 10–11; §1.3.8.1, pp. 12–13; §1.3.9/Table 5, pp. 15–16; §§1.3.10–1.3.12, pp. 17–18: nakshatra, tithi, nitya yoga, karana, weekday and Panchanga. Sun40°/Moon65° is an original worked example, with half-open notation made explicit.A named practitioner’s introduction to Jyotish. Used for terminology and a stated method, not universal school agreement or scientific validation. The added March 18, 2010 note describes changed views; it does not establish a fully revised 2010 edition.
  2. OpenFate Editorial Methodology
    OpenFate Editorial Methodology, stable sections #editorial-principles, #editorial-workflow, #editorial-ai, and #editorial-context. Used for the calculation/interpretation and evidence-boundary policy.OpenFate separates deterministic chart calculation, traditional interpretation, and modern editorial explanation.
  3. Swiss Ephemeris Programmer’s Manual: Time, Sidereal Modes and Houses
    Swiss Ephemeris Programmer’s Manual, §12.1 swe_set_sid_mode (including Lahiri modes) and §12.2 ayanamsa functions; §15 house calculation. The page’s rounded arithmetic examples are original teaching inputs, not ephemeris outputs.Primary software documentation for numerical time and position calculations. Sidereal modes, including named Lahiri variants, are explicit settings. The manual does not validate astrological interpretations.
  4. IANA Time Zone Database
    IANA tz database theory.html, “Scope of the tz database” and “Accuracy of the tz database”; historical limitations, especially before 1970. This source does not verify an individual birth record.The maintained source for current and historical civil-time offsets and daylight-saving transitions; it provides timekeeping facts, not astrological interpretation.
  5. OpenFate Vedic implementation: local source review, 2026-09-08
    Read-only local source review: app/modules/vedic/interpretation/forecastFacts.ts module contract and prompt/chat/en.ts §11 prohibit invented transits and use frozen Vimshottari intervals; logic/types.ts records unavailable transit factors; logic/policy.ts lists D1/D2/D6/D9/D10/D24, not D4 or D20. This does not verify deployed screens or demonstrate Panchanga, Muhurta or Sade Sati outputs.An editorial review of local policy and calculation source files, not an independently accessible publication or proof of the deployed version. Implementation limitations and discrepancies remain separate from traditional arithmetic.
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