Chaturthamsa D4 Calculation: Four Parts, Twelve Signs and Boundary Checks

How is a Chaturthamsa D4 sign calculated?

This is the Parashari D4 mapping described in the cited sources and implemented in Astrogyana's Vargas service. Chaturthamsa is also called Turyamsa. The number four describes the division; it does not mean that every planet goes into the fourth house.

The four intervals and the counting trap

Here d is the degree inside the natal sign. The two final columns express the same rule with different counting conventions. “Fourth from Leo” counts Leo as one, Virgo as two, Libra as three and Scorpio as four. It therefore requires three steps forward, not four.

The interval widths are exact: 7.5 decimal degrees equals 7°30′ because half a degree is thirty arcminutes. Written as 7.30 decimal degrees, the value would instead be 7°18′. Keep decimal degrees and degrees-plus-minutes distinct.

At exactly 7°30′, choose part two; at 15°, part three; at 22°30′, part four. A value of 30° belongs at the start of the next natal sign and must be normalized before classification.

A lookup table for all twelve signs

Use the row for the natal sign and the column for the degree interval. Unlike D7, this D4 rule does not change its starting rule according to whether a sign is odd or even. Every row begins from its own sign and advances in steps of three signs.

For example, the Aquarius row is Aquarius, Taurus, Leo and Scorpio. The count wraps past Pisces into Aries without stopping at the end of the zodiac. A diagram's page orientation does not change that sign sequence.

Work from a full longitude in four steps

1. Normalize the full sidereal longitude into the interval from 0° up to, but excluding, 360°.
2. Find its natal sign and subtract that sign's starting longitude.
3. Locate the remaining degree in one of the four intervals.
4. Read the corresponding first, fourth, seventh or tenth sign from that natal sign.

Take the invented longitude 195°. Libra starts at 180°, leaving d = 15°. The lower boundary belongs to part three. The seventh sign from Libra is Aries, so the D4 destination is Aries.

For a compact calculation, let k be the natal sign index with Aries = 0, and q the part index from zero to three. The destination index is (k + 3q) mod 12. Add one only when returning to sign numbers Aries = 1 through Pisces = 12.

Eight coordinates that test the boundaries

Each adjacent pair differs by one arcsecond. The first three pairs cross the three internal quarter boundaries; the final pair crosses from Pisces to Aries at the end of the circle. These are constructed arithmetic examples, not a person's birth record.

The last input normalizes from 360° to 0°. Keeping it as a fictitious “thirteenth sign” would corrupt both the natal and divisional results. Similarly, feeding the full 195° into a within-sign interval test would miss the required subtraction of 180°.

A useful error check: the modality stays the same

Read down the table in three groups. The movable signs Aries, Cancer, Libra and Capricorn map only among themselves. The fixed signs Taurus, Leo, Scorpio and Aquarius form a second group. Gemini, Virgo, Sagittarius and Pisces form the dual group.

This follows arithmetically because every D4 offset is a multiple of three. It is an invariant of this assignment, not a prediction about someone's character. If a program maps Leo to Virgo under this rule, the output fails the group check before you even inspect the degree.

Passing the group check is necessary but insufficient. Leo 8° must map to Scorpio. Aquarius belongs to the same group but would still be wrong for that input. Use the invariant to catch a class of errors, then verify the exact interval and destination.

Why multiplying the full longitude by four is different

Leo 8° has full longitude 128°. Multiplying by four gives 512°, or 152° after subtracting 360°. That lies in Virgo. The stated D4 rule gives Scorpio because Leo 8° lies in its second quarter, assigned to the fourth sign from Leo.

Thus a fourth-harmonic sign cannot simply replace this Chaturthamsa rule. Some divisional mappings do have a harmonic equivalence, as the D7 guide demonstrates. Check the assignment rather than assuming the chart number supplies the entire algorithm.

Read a report without mixing signs and houses

Map the natal ascendant's longitude through the same rule to obtain the D4 ascendant. A house position then needs that ascendant and a house convention. The “fourth from the natal sign” instruction in the table selects a zodiac sign; it is not already a D4 house label.

When comparing Kundli reports, match the birth inputs, time zone, sidereal reference and retained coordinates. A rounded display can hide a value close to a boundary. More decimal places cannot fix uncertain birth information.

These checks establish whether a declared calculation was followed. They do not establish a guaranteed event, a property outcome or the validity of an interpretation. The D12 interval guide offers another way to practise keeping arithmetic and interpretation separate.

Frequently asked questions