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Mathematics — the KP conventions implemented

This page documents exactly what kpastro computes and the formulas behind each layer, so results can be validated against published tables.

The zodiac

  • Everything is sidereal: sidereal = tropical − ayanamsa.
  • Degrees run 0–360 from 0° Aries, normalized to [0, 360) everywhere.
  • Ayanamsa modes:
Mode Swiss Ephemeris id Reference
lahiri SE_SIDM_LAHIRI (1) Chitrapaksha, the Lahiri/IAE 1985 zero point
kp SE_SIDM_KRISHNAMURTI_VP291 (45) Modern KP ayanamsa
kp_old SE_SIDM_KRISHNAMURTI (5) Krishnamurti's original table

In 2026 the Lahiri ayanamsa is ≈ 24.14°.

  • Node: KP traditionally uses the mean node; the true node is available.

Nakshatras and subdivisions

  • 27 nakshatras of 13°20' = 800' each: star_index(lon) = floor(lon / 13.3333).
  • Star-lord of star i is NAKSHATRA_LORDS_BASE[i % 9] (the 9-planet Vimshottari cycle repeats every 9 stars).
  • Sub-lords: each star splits into 9 unequal subdivisions proportional to the Vimshottari years:
sub span (arcmin) = (lord's years / 120) * 800'

The sequence starts at the star-lord and cycles through the Vimshottari order.

  • Sub-sub-lords: the sub is divided again with the same proportion rule, starting from the sub-lord.

  • Pada (quarter): each star is divided into 4 padas of 3°20'.

Vimshottari dasha

Fixed 120-year cycle (1 year = 365.25 days):

Ketu Venus Sun Moon Mars Rahu Jupiter Saturn Mercury
7 20 6 10 7 18 16 19 17

The mahadasha of the birth Moon's star-lord is running at birth. Only the fraction of the star not yet traversed is lived as the balance:

MD_bal = (star_end   − Moon) / star * Y_star * 365.25     # days
AD_bal = (sub_end    − Moon) / star * Y_star * 365.25     # days
PD_bal = (subsub_end − Moon) / star * Y_star * 365.25     # days

where star = 13°20', star_end/sub_end/subsub_end are the ends of the Moon's star/sub/sub-sub, and Y_star is the star-lord's mahadasha years.

Every later full sub-period width:

parent−child period = years(parent) * years(child) / 120 * 365.25  days

current_periods() locates MD, AD and PD by counting days from the birth epoch, with the birth AD/PD balances only applied to the opening periods.

Significators (Nirdeshan)

A planet signifies a house by:

  1. Occupation — it sits in the house.
  2. Sign-lordship — it rules the sign whose cusp begins the house.
  3. Star-lord agency — its (nakshatra) star-lord occupies or owns the house; a planet delivers the results signified by its star-lord.

For judgement, Bhaav Nirdeshan ranks per house (strength tiers):

Tier Meaning
1 Occupant of the house
2 A planet in an occupant's star
3 The cuspal lord
4 A planet in the cuspal lord's star

The sub-lord of a house cusp (cusp_sub_lords) is the final arbiter of that house's matters.

Ruling planets

The ruling planets (RPs) of a moment are the sign / star / sub lords of the ascendant, the same three of the Moon, and the day-lord (weekday). ruling_planets() deduplicates and merges their sources.

The rectification module uses the classic five-lord RP set instead: the day-lord plus the ascendant and Moon sign and star lords only.

Birth-time rectification

The reference KP method (ported from the "timeofbirth" tool, K. P. systems) scores each candidate birth minute against the judged life events. Per house it builds a significator set:

sets[h] = { cusp sub-lord }  ∪  { occupants of h and their star-lords }
                             ∪  { planets aspecting h and their star-lords }

KP aspects are house-based: every planet aspects the 7th house from itself; Mars adds the 4th and 8th, Jupiter the 5th and 9th, Saturn the 3rd and 10th.

For a candidate whose lagna sub-lord is l:

Term Formula
Specificity spec = max(0, min(1, (12 − n) / 9)), n = houses whose set contains l
LSL (per event) 2 per primary house + 1 per secondary house l appears in, × spec
Dasha (per event) 1 / 1 / 0.5 for MD/AD/PD lords in the primary house's set; 0.25 each for a secondary-house hit
RP 1 if l ∈ the five-lord RP set of the analysis moment (optional)
Identity 0.25 when the sibling hint matches house-3 occupancy (optional) 
total = lsl_score + 0.5 * dasha_score + rp_score + identity_score

Dasha lords at an event are anchored to the candidate birth moment and that moment's Moon (the original tool's convention). Events with dasha_score < 1 are strikes (surfaced, not subtracted).

The ranked score curve is converted to a probability distribution with a softmax (temperature = 1.5): p ∝ exp((score − max) / 1.5). The credible interval covers the smallest contiguous span of time holding the target mass (default 75%). Jupiter/Saturn transits at each event date are checked separately as a cross-check (star- or sign-lord of the transit is a significator of the event's primary house).

KP horary — why 249 divisions

  • 27 stars × 9 sub-lords = 243 subs from 0° Aries.
  • Six of the twelve sign boundaries fall inside a sub. They split that sub in two: the sub-lord is unchanged but the sign changes.
  • Result: 243 + 6 = 249 numbered divisions.

A querent's number n (1–249) selects division n; the horary ascendant is the division's midpoint:

asc(n) = (division_start + division_end) / 2

Houses

Placidus cusps come from the Swiss Ephemeris (swe.houses_ex(jd, lat, lon, "P")) and are converted to the sidereal zodiac. House assignment walks counter-clockwise from each cusp to the next, wrapping from cusp 12 to cusp 1 + 360°.

Precision

Situation Accuracy
No data files (default) Moshier ephemeris: planets < 1", Moon ≈ 0.5"
*.se1 files present Full compressed VSOP87 / JPL DE431 Swiss Ephemeris