How a Vimsamsa D20 Chart Is Calculated

The rule in the classical text

Bṛhat Parāśara Horā Śāstra, chapter 6, verse 17 gives Aries for movable signs, Sagittarius for fixed signs, and Leo for dual signs as the three starts. A rāśi of 30° divided by twenty yields 1°30′ per portion. The verse supplies the start rule used by this calculator; the advance by one zodiac sign for each consecutive portion follows the standard forward Parāśari assignment. The rule is named because other varga implementations may differ.

The movable D1 signs are Aries, Cancer, Libra, and Capricorn. Their first D20 part maps to Aries. The fixed signs Taurus, Leo, Scorpio, and Aquarius begin from Sagittarius. The dual signs Gemini, Virgo, Sagittarius, and Pisces begin from Leo. These starts depend on D1 sign modality, not on the planet's ruler. In particular, the D20 starts for fixed and dual signs are the reverse of this website's D16 Shodashamsha starts.

The text also lists presiding deities in neighboring verses. Their spellings and editions vary, and this calculator does not assign a deity column: its documented contract is the sign and degree transformation. The deity lists therefore belong to their chosen editions rather than one universal spelling or interpretive result.

All twenty exact intervals

Every D1 sign uses the same boundaries. An interval includes its start and excludes its end. At exactly 1°30′, the second part begins. At 30° the point belongs to the next D1 sign and starts its first D20 part under the new sign class. The table gives the destination sign for each possible D1 class; after twelve portions, the zodiac sequence wraps and continues for parts thirteen through twenty.

Calculate a placement by hand

Normalize the sidereal D1 longitude to 0° through just under 360°. Let s be the zero-based D1 sign index, Aries equal to zero, and d the degree within that sign. The zero-based portion is floor(d ÷ 1.5), from zero through nineteen. The sign class is s modulo three: zero for movable, one for fixed, two for dual. Pick the start sign index zero, eight, or four, add the portion index, then take modulo twelve. The derived D20 degree is 20 × (d − 1.5 × portion index).

At 10° Taurus, d ÷ 1.5 = 6⅔, so the point is in portion seven (index six). Taurus is fixed and begins from Sagittarius. Six signs after Sagittarius lands in Gemini. The remainder inside the portion is 10° − 6 × 1.5° = 1°; multiplied by twenty, that gives 20° Gemini in the derived D20 coordinate. At 10° Gemini, a dual sign starts from Leo: index six instead lands in Aquarius, also at 20°.

At exactly 1°30′ Aries, part two begins and maps to Taurus; one arcsecond before remains in part one and maps to Aries. At exactly 30° Aries, the position becomes 0° Taurus. Taurus is fixed, so its first D20 part begins in Sagittarius. These cases check both exact boundaries and the new sign-class start after a D1 sign change.

Traditional use and calculation limits

Bṛhat Parāśara Horā Śāstra 7.4 associates Viṃśāṃśa with worship or religious practice. Some modern interpretations discuss spiritual inclination or practice. Those are interpretive traditions; the numerical transform cannot measure faith, attainment, or a person's character. A D20 position is a way to study a historical chart convention beside the D1 chart.

Twenty portions make the result sensitive to exact birth data. The D20 Lagna transforms the D1 ascendant, so a recorded time, place, and historical UTC offset are necessary. A point within 0.05° of a boundary is flagged. A different birth time, ayanamsha, ephemeris, or mean versus true lunar node may shift derived placements. This tool states its approximate Lahiri ayanamsha and Astronomy Engine 2.1.19 rather than claiming exact agreement with all Jyotish software.

The local date form covers 1800–2100. Historical offsets are entered explicitly; a city name alone does not reconstruct them. Mean Rahu and Ketu may be omitted if conversion to UTC crosses outside the source calculator's supported range. When comparing D20 charts, align the D1 positions, ayanamsha, node choice, birth details, and varga method first. See the D1 calculation and the separately documented D16 guide for context.