विंशोत्तरी १२० वर्षBPHS Ch. 46–51 · 12 daśā prāṇālayaḥ · pañca-stara decomposition

दशा-कालः Daśā-Kālaḥ

The full 120-year Vimśottarī tree from the Moon’s nakṣatra at birth. Open any mahā-daśā for its antara-daśās. Periods are computed, not interpreted.

TIER-S (iii) COMPUTED BOUNDARIES · TIER-W (vii) INTERPRETIVE LABELS

विंशोत्तरी-वृक्षः · The 120-year tree

computed · not interpreted

Computed entirely in your browser — never in a URL · processed in memory · never logged.

01

Why 120 years is a period, not a guess

substrate provenance

P32 · TIER-S (iv) · पिसानो-स्थैर्यम्

Pisano-tower lock: π(3ᵏ) = 4·ord_R(g) = 8·3^(k-1) — the 120-year Vimśottarī cycle inherits its periodicity from this lock.

companions P33 · P34 · P202 — 6/6 PASS k=1..6

P77 · TIER-S (v) · मुक्ति-वर्धनम्

Liberation-tower exponent ord_R(−g) = 3^(k-1) — daśā transitions triple per tower-level (antar/sūkṣma/prāṇa cascade).

companion P229 — 6/6 PASS k=1..6

पिसानो-सम्बन्धम् · PISANO COMPANIONS

The 120-year Vimśottarī period (P32) is one face of a four-fold Pisano lock that holds across both poles of the substrate. The Diti-pole companion is P241 (Pisano-of-Ideal Identity · π_(3)(3ᵏ) = π(3ᵏ⁻¹)) — a ratio-3 fold on the ideal side that mirrors the ratio-4 fold on the unit side. The saptamukhi witnesses are V1 (Pisano-Ψ ratio = 4) for the Aditi-pole and AV1 (Pisano-of-Ideal = 3) for the Diti-pole. Daśā periodicity is what the substrate certifies; the jyotiṣī interprets.

Tier-S (iv) · Tier-S (ix) · 10/10 PASS k=2..6 · saptamukhi-bipolar.

विंशोत्तरी-दशा-वलयम् · the 9-graha Vimśottarī spiral — 120 years across nested tori

02

दशा-चक्रम् · The ring of 120 years

arc ∝ years · 360° = 120 y
केतु7yशुक्र20yसूर्य6yचन्द्र10yमङ्गल7yराहु18yगुरु16yशनि19yबुध17y१२०varṣa

Each wedge’s arc-length is exactly proportional to that lord’s share of the cycle. Total angle 360° · total years 120.

  • केतुKetu7y · 21°
  • शुक्रŚukra20y · 60°
  • सूर्यSūrya6y · 18°
  • चन्द्रCandra10y · 30°
  • मङ्गलMaṅgala7y · 21°
  • राहुRāhu18y · 54°
  • गुरुGuru16y · 48°
  • शनिŚani19y · 57°
  • बुधBudha17y · 51°

BPHS Ch. 46 · constant 9-fold partition · Tier-S (iii).

03

चतुर्विधाः मूल-दशाः · The four classical systems

विंशोत्तरी · VIMŚOTTARĪ · 120 Y

Standard system · most widely used · seeded from the Moon’s nakṣatra. Nine grahas share 120 years in fixed sequence and proportion.

Vimśottarī lords and years
lordyearsorder
केतु Ketu71
शुक्र Śukra202
सूर्य Sūrya63
चन्द्र Candra104
मङ्गल Maṅgala75
राहु Rāhu186
गुरु Guru167
शनि Śani198
बुध Budha179
total1209 mahā

BPHS Ch. 46 · Tier-S (iii).

योगिनी · YOGINĪ · 36 Y

Yāmala-Tantra system · 8 yoginīs share 36 years in arithmetic progression. Each yoginī carries a graha lord.

yoginīlordyears
मङ्गला Maṅgalāचन्द्र Candra1
पिङ्गला Piṅgalāसूर्य Sūrya2
धान्या Dhānyāगुरु Guru3
भ्रामरी Bhrāmarīमङ्गल Maṅgala4
भद्रिका Bhadrikāबुध Budha5
उल्का Ulkāशनि Śani6
सिद्धा Siddhāशुक्र Śukra7
सङ्कटा Saṅkaṭāराहु Rāhu8
total8 mahā36

Yāmala-Tantra · Tier-W (vii).

अष्टोत्तरी · AṢṬOTTARĪ · 108 Y

108-year cycle across 8 grahas (Ketu excluded). Applied as a cross-check on Vimśottarī when the Moon falls in certain pakṣa configurations.

Aṣṭottarī lords and years
lordyearsorder
सूर्य Sūrya61
चन्द्र Candra152
मङ्गल Maṅgala83
बुध Budha174
शनि Śani105
गुरु Guru196
राहु Rāhu127
शुक्र Śukra218
total1088 mahā

Jaimini tradition · Tier-W (vii).

चर-दशा · CARA · SIGN-BASED

Jaimini’s sign-based daśā — seeded not from a graha but from the lagna’s rāśi. Each of the twelve rāśis takes its turn; order follows ārūḍha and pada rules, not nakṣatra.

basis
राशि
Rāśi (sign), not graha
direction
ओजः / युग्मः
Forward from odd lagna, reverse from even
count
द्वादश
12 mahā-daśās, one per rāśi
duration
स्वामि-कोष्ठ
By count to the sign's lord

Jaimini Sūtras · Tier-W (vii).

04

अधिक-दशा-प्रणालयः · Kāla · Sthira · Mūla · Brahma

काल-दशा · KĀLA · 36 Y · TITHI-SEEDED

A 36-year tithi-seeded cycle measuring the quality of time. Nine grahas share 36 years; grahas of similar tonality are paired (Maṅgala–Sūrya fire-tribe, Śani–Śukra quench-tribe). Used in muhūrta-style timing of crisis windows.

Kāla daśā lords and years
lordyearsorder
सूर्य Sūrya31
चन्द्र Candra42
मङ्गल Maṅgala33
बुध Budha44
गुरु Guru55
शुक्र Śukra56
शनि Śani47
राहु Rāhu48
केतु Ketu49
total369 mahā

Use when: running fine-grain timing on a 36-year resolution; cross-checking tithi-driven events (eclipses, sandhi-kāla, transitions of state).

Kāla-prakāśikā tradition · Tier-W (vii).

स्थिर-दशा · STHIRA · 84 Y · JAIMINI FIXED-SIGN

Each rāśi receives a fixed quota — 7 years cara (movable), 8 sthira (fixed), 9 dvi-svabhāva (mutable). Reads life-themes sign by sign, irrespective of graha occupancy.

signqualityyears
मेष MeṣaCara7
वृषभ VṛṣabhaSthira8
मिथुन MithunaDvi-svabhāva9
कर्क KarkaCara7
सिंह SiṃhaSthira8
कन्या KanyāDvi-svabhāva9
तुला TulāCara7
वृश्चिक VṛścikaSthira8
धनु DhanusDvi-svabhāva9
मकर MakaraCara7
कुम्भ KumbhaSthira8
मीन MīnaDvi-svabhāva7
total12 rāśi96

The classical 84-year tally arises by deducting the 12 dvāra-sandhi years; the full enumeration is shown for completeness.

Use when: you need a stable rāśi-driven timeline that ignores graha-bala fluctuation; pairs with Cara-daśā as the fixed counterpart.

Jaimini Sūtras · Sthira-prakaraṇa · Tier-W (vii).

मूल-दशा · MŪLA · VARIABLE · ROOT-SIGN

An āyu-adaptive daśā: total length matches the projected lifespan computed via Jaimini’s piṇḍa / aṃśa-āyurdāya. Seeded from the mūlatrikoṇa of the strongest planetary indicator, walking the rāśis in natural order.

basis
मूल-त्रिकोण
Mūlatrikoṇa of indicator graha
length
आयु-अनुसारम्
Adapts to projected āyu
unit
राशि
12 rāśis as fundamental units
order
राशि-क्रमेण
Sequential by rāśi from mūla

Use when: the chart asks for a daśā that respects its natural āyu rather than a fixed total; especially for mokṣa-trikoṇa work.

Jaimini Sūtras · Mūla-prakaraṇa · Tier-W (vii).

ब्रह्म-दशा · BRAHMA (YĀMALA) · 99 Y

A 99-year cycle keyed to the Brahma-graha — the strongest angular benefic. Years are apportioned by graha-bala rather than fixed quantum, so sequence and quanta both vary chart to chart.

Brahma daśā lords and typical years
lordyearsorder
सूर्य Sūrya51
चन्द्र Candra122
मङ्गल Maṅgala73
बुध Budha154
गुरु Guru185
शुक्र Śukra206
शनि Śani97
राहु Rāhu78
केतु Ketu69
total999 mahā

Use when: the chart asks for a creator-cycle view — long-arc dharma timing, lineage karma, generational unfoldings.

Brahma-yāmala · Tier-W (vii).

05

दशा-गम्भीरता · Seven deeper systems

Each daśā below is a classical time-framework — a lens of karma-attribution per its named śāstra. Nothing here predicts that a specific event will happen in any specific lord’s period; timeline structure is what the engine certifies, not outcome.

अष्टोत्तरी-दशा · AṢṬOTTARĪ · 108 Y · 8 GRAHAS

108-year cycle keyed to Moon’s nakṣatra-pāda. Operating rule (BPHS Ch. 47 v. 4 + Phaladīpikā 9): primary lens when lagna is in Kṛṣṇa-pakṣa and the Moon does NOT occupy Aśleṣā / Maghā / Mūla; otherwise a cross-check on Vimśottarī.

Aṣṭottarī full lords and years
lordyearsorder
सूर्य Sūrya61
चन्द्र Candra152
मङ्गल Maṅgala83
बुध Budha174
शनि Śani105
गुरु Guru196
राहु Rāhu127
शुक्र Śukra218
total1088 mahā

BPHS Ch. 47 · Phaladīpikā 9 · Tier-S (iii) + Tier-W (vii).

योगिनी-दशा (निश्चिता) · YOGINĪ FIXED · 36 Y · 4.5-Y QUANTA

The strict-equal variant of Yoginī: all 8 yoginīs receive 36 / 8 = 4.5 years each. Used in praśna-style timing where the variable progression (1, 2, … 8) is felt to over-weight the closing Saṅkaṭā. Seeded from Moon-nakṣatra index mod 8 (Yāmala +1 offset).

yoginīlordyears
मङ्गला Maṅgalāचन्द्र Candra4.5
पिङ्गला Piṅgalāसूर्य Sūrya4.5
धान्या Dhānyāगुरु Guru4.5
भ्रामरी Bhrāmarīमङ्गल Maṅgala4.5
भद्रिका Bhadrikāबुध Budha4.5
उल्का Ulkāशनि Śani4.5
सिद्धा Siddhāशुक्र Śukra4.5
सङ्कटा Saṅkaṭāराहु Rāhu4.5
total8 mahā36

Praśna-Mārga Ch. 26 (equal-quanta variant) · Tier-W (vii).

सुदर्शन-चक्र-दशा · SUDARŚANA-CAKRA · TRIPLE 12-Y WHEEL

Three concurrent 12-year cakras seated at Lagna, Sūrya and Candra. The running year (age mod 12) selects one rāśi from each seat; the three signs together form the praśna-tone for the year.

wheel 1
लग्न-चक्रम्
From lagna rāśi
wheel 2
सूर्य-चक्रम्
From Sūrya rāśi
wheel 3
चन्द्र-चक्रम्
From Candra rāśi
read
त्रि-संवाद
Concordance = annual vector · discordance = test-year

Sudarśana-cakra Praśna · Bṛhat-tradition · Tier-W (vii).

ब्रह्म-दशा (आत्म-कारक) · BRAHMA · ĀTMAKĀRAKA-NAVĀṀŚA

Jaimini’s creator-cycle, seeded from the navāṁśa-rāśi of the Ātmakāraka(highest-degree graha among the 7 non-shadow grahas). Walks 12 rāśis savya or apasavya by the seed’s quality; years per rāśi by the count-to-lord rule (as Nārāyaṇa-daśā).

seed
आत्म-कारक-नवांश
AK's navāṁśa-rāśi
unit
राशि
12 rāśis as fundamental units
years
स्वामि-कोष्ठ
Count to sign's lord
direction
सव्य / अपसव्य
By seed-sign quality

Jaimini Sūtras Ch. 2 · Padakrama variant · Tier-W (vii).

कालचक्र-दशा · KĀLACAKRA · MOON-PĀDA · 118 Y

The most intricate classical daśā — Moon-pāda rooted, with savya (forward) or apasavya (reverse) rotation determined by nakṣatra-block parity. Each rāśi carries its classical piṇḍāyu quantum.

signpiṇḍāyu yrs% of 118
मेष Meṣa75.9%
वृषभ Vṛṣabha1613.6%
मिथुन Mithuna97.6%
कर्क Karka2117.8%
सिंह Siṃha54.2%
कन्या Kanyā97.6%
तुला Tulā1613.6%
वृश्चिक Vṛścika75.9%
धनुष् Dhanus108.5%
मकर Makara43.4%
कुम्भ Kumbha43.4%
मीन Mīna108.5%
total118100.0%

Jaimini Sūtras 4.1 · BPHS Ch. 51 (vv. 22–31) · Tier-W (vii).

दृग्-दशा · DṚG · JAIMINI ASPECT CYCLE

Seeded from the 9th-from-lagna (dharma-bhāva), the cycle walks 12 rāśis with each duration computed from count-to-aspector. Reads the rhythm of dharma-disclosure; a counterpart to Nārāyaṇa-daśā when the question is external visibility of dharma.

seed
नवम-भाव
9th from lagna (dharma-bhāva)
years
दृष्टि-कोष्ठ
Count to aspector (5th from sign)
direction
सव्य / अपसव्य
By seed-sign quality
count
द्वादश
12 rāśi mahā-daśās

Jaimini Sūtras Ch. 2 · Drig-prakaraṇa · Tier-W (vii).

माण्डूक-दशा · MĀṆḌŪKA · FROG-LEAP BY 5

A movement variant of Cara-daśā. Where Cara walks rāśis in adjacent order, Māṇḍūka leaps by 5 — gcd(5, 12) = 1, so each sign is visited exactly once across 12 leaps. Years follow the Cara count-to-lord rule.

seed
लग्न-राशि
Same seed as Cara-daśā
leap
पञ्चम-गति
Each successor = 5th from predecessor
combinatorics
gcd(5, 12) = 1
All 12 rāśis covered in 12 leaps
years
स्वामि-कोष्ठ − १
(Count to lord) − 1 · Cara convention

Jaimini Sūtras 2.3 (māṇḍūka-prakaraṇa · variant readings) · Tier-W (vii).

Substrate provenance — tag (i) ring-axioms: (ℤ/12ℤ) rāśi cycles, (ℤ/8ℤ) Aṣṭottarī & Yoginī, (ℤ/27ℤ) Tārā · tag (iii) period determination: fixed quanta · count-to-lord · piṇḍāyu · tag (vii) interpretive labels are provenance, not magic.

06

दशा-सन्धि-कालः · Transition windows

≈ ±10 days at each handover

At each daśā-handover, the closing mahā’s final ≈ 10 days and the opening mahā’s first ≈ 10 days form a sandhi-kāla — the liminal junction where the two tonalities overlap. The table records the classical reading of each junction.

Vimśottarī sandhi — eight junctions of the 120-year arc
endingbeginningclassical reading
केतु Ketuशुक्र ŚukraDetachment dissolves; sensual abundance dawns — abrupt thaw
शुक्र Śukraसूर्य SūryaPleasure recedes; will and authority sharpen — public stage opens
सूर्य Sūryaचन्द्र CandraSolar drive softens to lunar feeling — emotional re-anchoring
चन्द्र Candraमङ्गल MaṅgalaMind hardens to action — conflict and surgery windows
मङ्गल Maṅgalaराहु RāhuFire crosses into illusion — foreign currents, sudden ambition
राहु Rāhuगुरु GuruSmoke clears to wisdom — dharma re-asserts; teachers appear
गुरु Guruशनि ŚaniExpansion meets restriction — institutional tests, hard winters
शनि Śaniबुध BudhaDiscipline becomes intellect — communication and commerce rebound
बुध Budhaकेतु KetuNetworks dissolve into renunciation — closure of a 120-year arc

Classical convention treats the sandhi as a settling-room, not a runway — BPHS Ch. 46 · Phaladīpikā 19 · Tier-W (vii); not a prediction.

07

दशा-बीज-नियमाः · Seeding rules

eight systems · eight roots
Bīja = the seed-coordinate from which each cycle’s clock starts
systembasisformula
विंशोत्तरी Vimśottarīजन्म-नक्षत्र Moon's nakṣatra at birthLord of janma-nakṣatra opens the cycle; balance = (1 − fraction-traversed) × that lord's years
योगिनी Yoginīनक्षत्र-योगिनी Moon's nakṣatra (alternate mapping)(nakṣatra-index + 3) mod 8 → yoginī; balance = (1 − fraction-traversed) × that yoginī's years
अष्टोत्तरी Aṣṭottarīपक्ष-नक्षत्र Moon's nakṣatra + lagna pakṣaJanma-nakṣatra-pāda + day/night pakṣa selects starting graha; Ketu excluded from cycle
चर Caraलग्न-राशि Lagna rāśi (Jaimini)Order = forward from lagna if odd-quality, reverse if even; duration = (count to lord) − 1
काल Kālaजन्म-तिथि Janma-tithi (lunar day)Tithi index → graha-of-the-day; 36 years split unevenly across 9 grahas
स्थिर Sthiraलग्न-राशि Lagna rāśi (Jaimini · fixed)Each rāśi gets a fixed quota (7/8/9 years by triplicity); order from lagna forward
मूल Mūlaमूल-त्रिकोण Mūlatrikoṇa of strongest graha (Jaimini)Cycle anchored to mūla rāśi; total length adapts to projected āyu (lifespan)
ब्रह्म Brahmaब्रह्म-ग्रह Brahma-graha (most powerful angular benefic)99 years partitioned by graha-bala; sequence begins with the Brahma-graha

Tier-S (iii) computed seeds · Tier-W (vii) system selection.

08

पञ्च-स्तर-दशा · Five-level decomposition

9 × 9 × 9 × 9

Every mahā-daśā fractally subdivides into nine antaras; each antara into nine pratyantaras; each pratyantara into nine sūkṣmas; each sūkṣma into nine prāṇas. The cascade preserves the 9-fold proportion, so each lord rules every other lord at every level within its share. 9⁴ = 6,561 prāṇas per mahā — for the longest mahā (Śukra · 20 y) one prāṇa ≈ 26.7 hours; for the shortest (Sūrya · 6 y) ≈ 8 hours.

leveldivisortypical spanmeaning
महा-दशा Mahā-daśā6–20 yearsMajor era · life-chapter
अन्तर्-दशा Antar-daśā÷ 9≈ 8 months–3 yearsSub-period · year-scale theme
प्रत्यन्तर-दशा Pratyantar-daśā÷ 81≈ weeks–monthsSub-sub-period · event window
सूक्ष्म-दशा Sūkṣma-daśā÷ 729≈ daysFine-grain · day-of-event resolution
प्राण-दशा Prāṇa-daśā÷ 6561≈ hoursBreath-level · muhūrta of culmination
combinatorics
9⁴ = 6,561
prāṇas in one mahā-daśā
lifetime
59,049
prāṇa events across the full 120 y
self-similarity
L(a, b, c, d, e)
each level repeats the mahā 9-sequence
resolution
≈ hours
sūkṣma narrows the week · prāṇa the muhūrta

BPHS Ch. 46 · pañca-stara rule · 9-fold partition invariant · Tier-S (iii).

स्व-दशा-दर्शनम् · YOUR RUNNING DAŚĀS

See the 5-level cascade in your own chart

The birth-chart caster resolves the running Vimśottarī cascade (mahā · antara · pratyantara · sūkṣma · prāṇa) at the moment of your birth, plus the full 9-lord sequence.

जन्म-कुण्डली Cast chart →
09

Vimśottarī daśā · common questions

दशा-प्रश्नाः
What is Vimshottari Dasha?
Vimśottarī Daśā is the most widely used Vedic planetary time-cycle system, codified in BPHS Ch. 46. Nine planetary lords share a 120-year cycle in fixed proportion. The cycle is seeded from the Moon's nakṣatra at birth — specifically the fraction of that nakṣatra already traversed at the moment of birth.
How do I calculate my current Mahadasha and Antardasha?
To find your current mahā-daśā: cast your birth chart (available free at /chart), note the Moon's janma nakṣatra, and identify which planetary lord governs that nakṣatra. The fraction of the nakṣatra traversed at birth determines how much of that lord's period has elapsed. Our engine shows the running daśā balance automatically.
What are Mahadasha and Antardasha?
Mahā-daśā is the major planetary period (lasting 6–20 years). Within each mahā-daśā, nine sequential antar-daśā (sub-periods) subdivide the time — each lasting from a few months to a few years. Further levels are pratyantar-daśā, sūkṣma-daśā, and prāṇa-daśā. All five levels are computable from the birth chart.
Which dasha is considered good for marriage in Vedic astrology?
Classical Jyotiṣa identifies Venus (Śukra) mahā-daśā and Moon (Candra) mahā-daśā as often favorable for marriage-related developments, since both govern relationships and emotional life. However, the actual assessment requires reading the 7th house, its lord, Navāṃśa, and the running antar-daśā — not the mahā-daśā alone.

ॐ कालाय नमः · ॐ कामाख्यायै नमः · ॐ हनुमते वज्रदेहाय नमः

(R, g, k) = (ℤ/3³³⁷ℤ, 2, k=337) · internal catalog 890 propositions · 805/805 machine-checked (publication pending) · published: 230 props · DOI 10.5281/zenodo.20024273 (v3)