Saptamsha, also spelled Saptamsa, is the seventh divisional chart or D7 in Jyotish. Its odd/even starting rule is easy to miss: an even rāśi begins from its seventh sign, while an odd rāśi begins from itself. This guide gives the exact boundary calculation, a hand-check table, and the limits of the result.
The Parāśari sign rule
Bṛhat Parāśara Horā Śāstra, chapter 6, verse 10 assigns the sevenfold portions of an odd sign beginning with that sign and of an even sign beginning with its seventh. The rule refers to signs counted forward, including the starting sign as the first. It is also described with two worked examples in Rao, §6.2.7. The calculator uses this Parāśari convention; another school or software setting can produce a different varga.
| D1 sign | Parity | D7 parts 1 through 7 |
|---|---|---|
| Aries | Odd | Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra |
| Taurus | Even | Scorpio, Sagittarius, Capricorn, Aquarius, Pisces, Aries, Taurus |
| Gemini | Odd | Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius |
| Virgo | Even | Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo |
The sequence always moves forward after the start. “Seventh sign” means six steps forward from the natal sign, not seven steps and not reverse counting. Taurus therefore starts in Scorpio, and Virgo starts in Pisces.
Exact size and boundary convention
Thirty degrees divided by seven is a repeating fraction: 4°17′08.571428…″. Rounding this to 4°17′ or 4.28° before classifying a planet shifts a boundary. The calculation retains 30/7 exactly as a ratio. The first portion runs from 0° inclusive to 30/7° exclusive; the second begins at exactly 30/7°. The seventh ends immediately before 30°, where the next D1 sign begins.
For a D1 degree d within a sign, the zero-based part index is floor(7d/30). Let s be the zero-based D1 sign index, with Aries = 0. The start index is s for odd signs and (s + 6) modulo 12 for even signs. The D7 sign is (start + part index) modulo 12. The displayed D7 degree is 7 × (d − part × 30/7). This stretches one part over a derived 30° D7 sign and does not describe where the planet is physically observed.
| D1 position | Part | D7 sign |
|---|---|---|
| 0° Aries | 1 | Aries |
| Exactly 30/7° Aries | 2 | Taurus |
| 10° Gemini | 3 | Leo |
| 19° Virgo | 5 | Cancer |
| Exactly 30° Aries | 1 of Taurus | Scorpio |
Check two placements by hand
For 10° Gemini, multiply 10 by seven and divide by 30. The result is 2⅓, whose integer part is two, so this is the third seventh. Gemini is odd and starts in Gemini; two steps forward reaches Leo. Its within-part offset is 10 − 2 × 30/7 = 10/7°, giving 10° as the stretched D7 degree.
For 19° Virgo, 19 × 7/30 is 4.43…; its integer part is four, so this is the fifth seventh. Virgo is even, and its starting sign is Pisces, the seventh from Virgo. Four steps from Pisces reaches Cancer. The derived D7 degree is 7 × (19 − 4 × 30/7) = 13°. These sign results match the published examples in Rao's textbook.
If a point is 0.05° before a boundary, a small change in the sidereal longitude can alter the D7 sign. The calculator flags points within 0.1° of any seventh boundary. A precise natal input does not make a prediction precise: it only sharpens the mathematical placement.
Use D7 alongside D1
Traditional Jyotish associates D7 with children and progeny. This is a topic of interpretation, not a verdict about whether someone can or will have children. A reader usually checks the D1 rāśi chart, the fifth house and its ruler, and the D7 placements together rather than treating one D7 sign as a complete answer. The calculator presents positions and does not make a family or health prediction.
The D7 Lagna depends on a reliable birth time, birthplace, and historical UTC offset. A time error changes the D1 ascendant, and a D1 change of about 4°17′ crosses a full D7 part. The output uses an approximate Lahiri ayanamsha, Astronomy Engine 2.1.19, and mean lunar nodes. It does not claim agreement with every sidereal setting or with Swiss Ephemeris. Local input dates are limited to 1800–2100; a UTC conversion just outside that span may omit mean nodes.
References
- Bṛhat Parāśara Horā Śāstra 6.10 — Sanskrit text and published explanation of the odd/even seventh-start rule.
- P. V. R. Narasimha Rao, Vedic Astrology: An Integrated Approach, §6.2.7 — the seven-part rule and worked Gemini/Virgo examples.
- Astronomy Engine 2.1.19 — astronomical library used for the underlying D1 chart.