Khavedamsa D40 Calculation: Forty Exact Parts and the Odd–Even Rule

How is the Khavedamsa or D40 sign assigned?

This guide explains the Khavedamsa, also called Chatvarimsamsa, sign rule. It shows how to audit a result from a stated sidereal longitude. The calculation alone does not establish claims about a person's family, inherited merit or future.

Choose the starting sign before counting portions

Odd and even refer to the natal sign's conventional number, not the planet's name, the house number or the day of birth. Aries is sign 1 and therefore odd. A program may internally call Aries index 0; that indexing choice must not reverse the traditional parity.

For the same within-sign degree, the two columns differ by six signs. Thus a coordinate in Aries and the same coordinate in Taurus produce opposite destination signs. Two odd signs, such as Aries and Gemini, produce the same D40 destination when their within-sign degrees agree.

The full forty-portion table

Read d as the degree within the natal sign, not the full 0°–360° longitude. Each interval includes its lower boundary. An exact upper boundary starts the next row. An exact 30° belongs to the next natal sign, so you must select the parity again.

Forty portions make three complete twelve-sign cycles plus four further portions. Rows 13–24 and 25–36 repeat rows 1–12; rows 37–40 repeat the first four. Four destinations appear four times and eight appear three times in each column. The repeated labels do not collapse forty input intervals into twelve.

Five steps with a worked Cancer example

1. Normalize the full sidereal longitude to 0° ≤ L < 360°.
2. Find the natal sign and its within-sign degree. Use the conventional 1–12 sign number for parity.
3. Convert the within-sign value to arcseconds and divide by 2,700.
4. Take the floor and add one to obtain the one-based portion number.
5. Start at Aries or Libra and advance portion minus one places through the zodiac.

Take an invented full longitude of 101°15′00″. This is Cancer 11°15′00″. Cancer is sign 4, so its start is Libra. The within-sign 40,500″ contains fifteen complete portions and begins portion 16. Advancing fifteen places from Libra gives Capricorn.

One arcsecond earlier, at 101°14′59″, the within-sign value is 40,499″. It belongs to portion 15, which gives Sagittarius. The two positions look identical if a display rounds both to 101°15′. Use the original coordinate when deciding a boundary.

Nineteen coordinates to test a spreadsheet or report

The 29°59′59″ to 30°00′00″ pair demonstrates a natal-sign transition: the last Aries portion is Cancer, while the first Taurus portion is Libra. A continuous zodiac longitude does not require this particular divisional sign mapping to change continuously at the boundary.

The final pair checks the end of the full zodiac. Pisces ends in D40 Capricorn; 360° normalizes to Aries 0° and gives D40 Aries. Do not create a forty-first portion or a thirteenth natal sign to hold an excluded endpoint.

A compact formula, with the indexing stated

Let p be the zero-based portion index, from 0 to 39. Let b = 0 for an odd natal sign and b = 6 for an even one. If destination signs are also numbered from Aries = 0 through Pisces = 11, then destination = (b + p) mod 12.

In the Cancer example, p = 15 and b = 6. The remainder of 21 divided by 12 is 9, the zero-based index of Capricorn. If your worksheet uses Aries = 1 instead, add one only after taking the remainder. Mixing zero-based and one-based labels is a common source of an otherwise consistent one-sign error.

The formula operates on sign assignment. It does not automatically identify a house or prescribe a method for displaying a degree within the destination sign. Compare like fields when two reports appear different.

Why multiplying the full longitude by forty is not enough

The harmonic check in the D27 guide works for its particular element-based construction. It should not be transferred to D40 merely by changing the multiplier. The following original counterexamples use exact natal-sign boundaries, so no rounding issue is involved.

At Taurus 0°, the stated D40 rule begins at Libra. Multiplying its full longitude, 30°, by forty gives a 120° remainder, which is Leo. Both calculations are internally consistent, but they implement different mappings.

Even 40 times the within-sign degree would always start from Aries unless the parity-dependent starting offset were added. A chart's number states how many input portions it uses; it does not fully specify where those portions are assigned.

Do not confuse angular minutes with clock minutes

The 45′ width means forty-five arcminutes, or 0.75 degrees. It is not forty-five minutes of time. Written as 0°45′00″, its exact angular value is 2,700 arcseconds; it is not 0.45 decimal degrees.

Here is a deliberately invented sensitivity model: if a coordinate changed at a fixed 15° per hour, it would traverse 0.75° in three minutes. This arithmetic does not say that the real ascendant always moves at that speed. Its rate depends on the circumstances, and the planets have different motions.

For a real report, use the actual calculation to compare the earliest and latest plausible birth times, keeping location and reference settings fixed. Record which placements remain the same and which cross a boundary. A finer division does not create more certainty than the birth information supports.

Keep the source rule and interpretation distinct

BPHS 6.29 states the odd-sign Aries and even-sign Libra starts; the following verse lists presiding deities. Narasimha Rao's section 6.2.18 gives forty equal 45′ portions and the same sign starts. These are the construction statements used for the table.

A deity sequence, destination sign and house label are separate layers. This article does not infer an ancestor's conduct or assign blame to a family from a D40 placement. Such a claim would require more than reproducing the arithmetic of a traditional chart.

The D24 guide uses a different odd/even start, while D30 uses unequal intervals. Keep the named rule visible rather than assuming all fine divisions behave alike.

A six-point check before using a D40 interpretation

1. Confirm the same unrounded sidereal longitude and reference setting.
2. Separate the full longitude from its within-sign remainder.
3. Use natal-sign parity with Aries numbered 1.
4. Check the 2,700″ interval with its lower boundary included.
5. Compare the assigned sign before comparing houses or deity labels.
6. Retain any birth-time uncertainty in the conclusion.

You can use Kundli to examine the placements available in your report. When asking about a discrepancy, provide the longitude, the sign rule and the field being compared. A reproducible calculation is a clearer starting point than arguing from two chart names alone.

Frequently asked questions