How a Shodashamsha D16 Chart Is Calculated

The rule in the classical text

Bṛhat Parāśara Horā Śāstra, chapter 6, verse 16 names Aries as the start for movable signs, Leo for fixed signs, and Sagittarius for dual signs. It also names four presiding deities whose sequence runs forward in odd signs and in reverse in even signs. This is the Parāśari assignment used here; a program set to another varga convention need not match it.

The movable D1 signs are Aries, Cancer, Libra, and Capricorn. Their first D16 part maps to Aries. The fixed signs Taurus, Leo, Scorpio, and Aquarius begin from Leo. The dual signs Gemini, Virgo, Sagittarius, and Pisces begin from Sagittarius. These start signs are properties of the D1 sign class, not of its ruling planet or its parity. A Taurus point and an Aquarius point therefore both begin their D16 count in Leo.

The verse's deity order is separate from the sign mapping. An odd D1 sign assigns Brahma, Vishnu, Shiva, and Surya to its first four parts, then repeats the quartet four times. An even D1 sign assigns them in reverse order, Surya, Shiva, Vishnu, Brahma, and repeats. Reversing deities does not reverse the zodiac sign count; all D16 sign sequences advance forward.

All sixteen exact intervals

Every D1 sign uses the same arc boundaries. The start of an interval is included and its end is excluded. At exactly 1°52′30″, for example, the second part begins. At exactly 30° the point belongs to the next D1 sign and its first D16 part. The table lists the destination sign for each possible D1 sign class. The 13th through 16th parts continue beyond one zodiac circuit, so they repeat Aries–Cancer, Leo–Scorpio, or Sagittarius–Pisces respectively.

Calculate a placement by hand

Normalize sidereal D1 longitude into 0° through just under 360°. Let s be the zero-based D1 sign index, with Aries equal to zero, and d the degree inside that sign. The zero-based portion is floor(d ÷ 1.875), between zero and fifteen. The sign class is s modulo three: zero means movable, one fixed, and two dual. Select a start sign index of zero, four, or eight, then add the portion index and take modulo twelve. The derived D16 degree is 16 × (d − portion × 1.875).

At 10° Taurus, d ÷ 1.875 = 5⅓, so the point is in portion six (index five). Taurus is fixed and begins from Leo. Five steps after Leo lands in Capricorn. The within-part offset is 10° − 5 × 1.875° = 0.625°; multiplied by sixteen it becomes 10° Capricorn in the derived D16 coordinate. In an even D1 sign such as Taurus, index five has deity Shiva because the reversed four-name cycle is Surya, Shiva, Vishnu, Brahma.

For a boundary check, exactly 1°52′30″ Aries is part two and maps to Taurus; one second before remains in part one and maps to Aries. Exactly 30° Aries is 0° Taurus, a fixed sign: its first D16 part maps to Leo. These examples check that the sign class is recalculated when the D1 sign changes.

Use and limits of a D16 chart

Bṛhat Parāśara Horā Śāstra 7.4 associates Shodashamsha with the comfort and discomfort of conveyances. Modern readers sometimes broaden the topic to vehicles, travel comfort, and material ease. Those are interpretive uses, not measurable outcomes implied by the arithmetic. A derived position cannot establish whether a journey is safe or whether a person will own a vehicle.

Sixteen portions make the result sensitive to exact birth data. D16 Lagna depends on the D1 ascendant, so a birth time, coordinates, and historical UTC offset are required. If a point is within 0.05° of a portion boundary, the output flags it; differences in birth time, ayanamsha, or ephemeris can change that D16 sign. The approximate Lahiri ayanamsha and Astronomy Engine 2.1.19 are stated openly so a reader can compare settings. Mean Rahu and Ketu may be omitted if conversion to UTC crosses outside their supported 1800–2100 range. The date form covers local dates 1800–2100, and the calculator never infers a historical offset from a city name.

A D16 chart is a transformation of the sidereal D1 longitudes, not an additional sky map or proof of a prediction. To inspect the source values, first open the D1 calculator; to understand another divisional method, compare the separately documented Dashamsha D10 guide. The chart can be used as a study reference while keeping the D1 and D16 conventions distinct.