Khavedamsa D40 Chart

What this section adds

The calculator above returns a D40 sign and a D40 house for your Ascendant and nine grahas, and the notes beside it describe the code in two paragraphs. This section supplies what those notes leave out: the sloka the rule comes from and what it does not say, a twelve-row lookup table you can check any result against by hand, the arithmetic for all ten points of the worked example, the meaning of each field in the answer, the full list of parts that repeat the birth-chart sign, a three-sign jump that happens at every sign boundary, what the classical text says the chart is for and where it actually judges the mother, how the D40 sign feeds the app's twenty-point strength score, and how many minutes of birth-time error the D40 Lagna can absorb.

Where the Khavedamsa rule is written

Brihat Parashara Hora Shastra names sixteen divisions of a sign in Ch. 6 Sl. 2-4. Khavedamsa is the fourteenth name, after Trimshamsa (D30) and before Akshavedamsa (D45) and Shashtiamsa (D60). Its definition is Ch. 6 Sl. 29-30. In the translation held in our corpus the passage says, in substance: the Khavedamsa, also called Chatvarimshamsa, is one fortieth of a Rasi; for odd Rasis count from Mesh and for an even Rasi from Tula, each part being 45 minutes of arc; and Vishnu, Candr, Marichi, Tvasht, Dhata, Shiva, Ravi, Yama, Yaksh, Gandharv, Kaal and Varuna repeat successively as presiding deities, in the same order for all Rasis.

Thirty degrees divided by forty is 0.75, the 45 minutes the text states. Three pieces of information sit in the passage. The size of a part is fixed. The starting sign is one of two, chosen by whether the birth-chart sign is odd or even. The third is the deity list: twelve names, repeated. Forty is three times twelve plus four, so in every sign the first four names (Vishnu, Candr, Marichi, Tvasht) preside over four parts each and the other eight over three. The text adds that the order is the same for all Rasis, which sets D40 apart from the divisions just before it in the chapter, where the deity order is reversed for an even sign.

Odd and even here mean position in the ordinary count from Aries as one. Aries, Gemini, Leo, Libra, Sagittarius and Aquarius are odd; Taurus, Cancer, Virgo, Scorpio, Capricorn and Pisces are even. The nearest relative of this rule in the chapter is the Chaturvimshamsa (D24), which also uses one fixed pair of starting signs for the whole zodiac (Leo and Cancer, Sl. 22-23). The difference is that D24's two starts are adjacent signs and D40's are opposite signs, six apart. Most of what is distinctive about a D40 chart follows from that one fact, as the sections below show.

Saravali, the other large classical text in our corpus, does not carry this division. Its Ch. 3 gives lords for the Hora, the decanate, the Trimsamsa, the Saptamsa and a few other divisions (Sl. 14-16), and a search of the text finds no fortieth part. So everything on this page about the D40 rule rests on BPHS alone, and the sources page lists it as the source for this calculator.

How the engine turns a degree into a D40 sign

The calculation starts from the sidereal birth chart: each point has a sign and a degree inside that sign, held to two decimal places. One function, computeVarga in the kundali engine, then does the same five things for the Ascendant and each of the nine grahas.

1. 1.Divide the degree within the sign by 0.75 and drop the fraction. The result is a part index from 0 to 39. Humans count parts from 1, so index 0 is the 1st part and index 39 is the 40th.
2. 2.Cap the index at 39. A degree of exactly 30.00 cannot normally occur, but if rounding ever produced one the cap keeps the point in the last part instead of inventing a 41st.
3. 3.Choose the starting sign: Aries when the birth-chart sign is odd, Libra when it is even. In the code this is a single line, D40_START, with the BPHS sloka quoted in the comment above it.
4. 4.Add the part index to the starting sign and wrap round the twelve signs. That sign is the D40 sign.
5. 5.Compare the D40 sign with the birth-chart sign. If they are the same, mark the point as keeping its sign and add its name to a list.

After all ten points are placed, the D40 sign of the Ascendant becomes house 1 and the remaining eleven signs follow in zodiac order as houses 2 to 12. Each graha's house is the count from the D40 Lagna sign to the graha's D40 sign, inclusive. These are whole-sign houses: a sign is a house, and no cusp degrees exist, because a divisional mapping puts a point in a sign and not at a degree.

A boundary degree belongs to the part that begins there. A point at exactly 4.50 degrees divides to 6.0, index 6, the 7th part; a point at 4.49 divides to 5.98, index 5, the 6th part. The worked example below happens to contain exactly that case: Saturn at 16.50 degrees, on the line where a part begins.

A lookup table you can check by hand

Because the count always starts from Aries or from Libra, one table covers every chart. Find the part number first: divide the degree in the sign by 0.75, drop the fraction and add 1. Then read across the row for the sign type. Part n runs from (n - 1) x 0.75 degrees up to, but not including, n x 0.75 degrees.

Two things are visible in the table. The two columns are the same list shifted by six rows, which is the Aries-Libra opposition. And the distribution is uneven: from an odd sign, a point is slightly more likely to land in Aries, Taurus, Gemini or Cancer (four parts each, 3 degrees of the sign) than in any of the other eight signs (three parts each, 2.25 degrees). From an even sign the favoured four are Libra, Scorpio, Sagittarius and Capricorn. No sign is ever unreachable.

The worked example, point by point

The example on this page is a birth on 14 August 1994 at 06:42 in Ahmedabad. The summary above gives the result. Here is the arithmetic the engine performed for each point, taken from an actual run of the code, so you can follow one row and then repeat the method on your own chart.

Take the Moon. It is at 24.64 degrees of Libra. 24.64 divided by 0.75 is 32.85; dropping the fraction gives index 32, the 33rd part. Libra is an odd sign, so the count starts at Aries. Thirty-two steps on from Aries is two full laps of twelve and eight more signs: Sagittarius. The table agrees: part 33 in the odd column sits in the Sagittarius row. The D40 Lagna is Cancer, and Sagittarius is the sixth sign counted from Cancer, so the Moon is in the 6th D40 house.

Take the Sun for an even sign. It is at 27.26 degrees of Cancer: 27.26 divided by 0.75 is 36.35, index 36, the 37th part. Cancer is even, so the count starts at Libra, and thirty-six steps is exactly three laps, which returns to Libra. Jupiter reaches Libra by a different route (the 19th part counted from Aries), and the two share the 4th house.

Three rows sit on an edge. The Ascendant is at 2.33 degrees of Leo, and the 4th part begins at 2.25, so it is 0.08 of a degree inside its part. Mars is at 4.42 degrees of Gemini, and the 7th part begins at 4.50, so it is eight hundredths of a degree short of moving from Virgo to Libra. Saturn is at 16.50 degrees of Aquarius, exactly where the 23rd part begins, so it is in that part only by the boundary rule above. Neither fact changes the answer for this birth time, but both matter a great deal for how firmly to hold it, which the birth-time section below takes up with real clock times.

How to read each part of the result

The sign of each point

Every point comes back with one D40 sign. That sign is an address produced by the counting rule, not a second position in the sky: no planet was physically in that sign at birth. The page prints the sign and stops there. It does not judge whether the sign is good for the planet, and it does not turn the sign into a sentence about your life.

The house of each graha

The nine grahas each carry a house number from 1 to 12, counted from the D40 Lagna. The Ascendant itself has no house field, because it defines house 1. The house numbers depend entirely on the D40 Lagna, and the D40 Lagna is the most time-sensitive value on the page. If your Lagna degree is uncertain, treat the signs of the slower grahas as firmer than any house number.

The twelve houses

The houses list is simply the twelve signs in order, starting from the D40 Lagna sign. In the example it runs Cancer, Leo, Virgo, Libra and so on to Gemini as the 12th. It lets you see which houses are empty: in the example the 1st, 2nd, 10th, 11th and 12th hold no graha.

Points sharing their Rasi sign

The last list names every point whose D40 sign equals its birth-chart sign; in the example, Jupiter and Saturn. The engine's field for this is called vargottama, because the same comparison is used across all its divisional charts. The classical term belongs to the ninth division: Saravali Ch. 3 defines Vargottama for the Navamsa, and the BPHS passage on the fortieth part does not mention it. So read this list as a plain statement of fact (same sign in both charts) and not as the classical Vargottama dignity. Nothing else on this page is scored from it.

When no chart comes back

The calculator is registered as needing the Ascendant. If the birth time is missing, or the place did not resolve to coordinates, the server does not run the engine at all. It returns a result marked as unavailable, with a code for what is missing (the birth time, or the birth place when a time was given) and a sentence saying so. It never falls back to a noon chart or a guessed Lagna, because a D40 chart without a Lagna has no houses, and a guessed Lagna would give twelve confident house numbers with nothing behind them.

Every part that repeats the birth-chart sign

Each sign contains either three or four parts that count back to the sign itself. The complete list, generated from the same rule the engine uses, is below. If one of your points falls in one of these ranges, it will appear in the shared-sign list; if it does not, it will not.

Across the zodiac that is 40 of 480 parts, one in twelve, which is what chance alone would give for landing on any one named sign. With ten points in a chart, a typical result therefore lists none, one or two names. The example checks against the table: Jupiter at 13.55 Libra is inside 13.50-14.25, and Saturn at 16.50 Aquarius is inside 16.50-17.25.

What follows from two opposite starting signs

Same degree, same or opposite sign

The D40 sign depends on only two things: the degree within the sign, and whether the sign is odd or even. The actual sign otherwise drops out. Two points at the same degree in any two odd signs, or any two even signs, get the same D40 sign. Two points at the same degree in signs of different type land exactly opposite each other. The clearest case is the lunar nodes. The chart engine sets Ketu at Rahu plus 180 degrees, so the two always share a degree in opposite signs, and opposite signs are always of the same type. In D40 Rahu and Ketu therefore always occupy one sign and one house, in every chart. In the example both are in Capricorn in the 7th. That is a property of the counting rule and carries no information about the person; it would be a mistake to read a D40 conjunction of the nodes as a finding.

The same reasoning applies to any axis-based reading carried into this chart. A check such as Kaal Sarp, which asks whether the grahas lie on one side of the Rahu-Ketu axis, has no meaning in D40 because the axis has collapsed to a single sign. The engine does not attempt it.

A three-sign jump at every sign boundary

Inside a sign, each new part moves the D40 sign forward by one. At the edge of a sign something else happens. The 40th part of an odd sign is Cancer (see the first table), and the 1st part of the even sign that follows is Libra. The 40th part of an even sign is Capricorn, and the 1st part of the odd sign that follows is Aries. In both cases the D40 sign moves forward three signs, not one. So a graha or Lagna close to a sign boundary in the birth chart does not merely risk a one-sign shift in D40 if its position is slightly off: the D40 result lands a square away, and every house number moves with it when the point is the Lagna.

This is one more reason to settle the birth-chart sign of a boundary point before reading its D40 sign. The choice of sidereal offset moves every longitude together, so the ayanamsa in use is part of the answer for any point near an edge, whether the edge is a sign boundary or one of the forty part boundaries inside the sign.

What the classical text says D40 is for

BPHS Ch. 7 Sl. 1-8 assigns a subject to each of the sixteen divisions. For this one the translation reads: auspicious and inauspicious effects from Khavedamsa. That is the whole instruction. It is broader and vaguer than its neighbours in the list (learning from the twenty-fourth part, strength and weakness from the twenty-seventh, evil effects from the thirtieth), and the chapter does not follow it with any rule for how to extract those effects from a D40 placement.

The tagline on this page, and the label on the D40 card in the Kundali view, add maternal legacy. That reading is a later convention among practitioners. The BPHS translation in our corpus does not state it: the fortieth part is not linked to the mother or the maternal line in Ch. 6 or Ch. 7. In the same verse the text sends the question of parents to a different division, the Dwadasamsa (D12). The page keeps the conventional label because readers arrive looking for it, and says here plainly that the primary source behind the calculation does not supply it.

Where BPHS does speak about the mother, it uses the birth chart. Three places are relevant.

• Ch. 11 Sl. 5 lists the indications of Bandhu Bhava, the 4th house: conveyances, relatives, mother, happiness, treasure, lands and buildings.
• Ch. 9 Sl. 43-45 names the Moon as the indicator of the mother for all beings, as the Sun is of the father, and asks the reader to weigh the strength of whatever influences it.
• Ch. 32 gives two further significators: the Matru Karak among the movable karakas ranked by longitude (Sl. 13-17), and, among the constant ones, the stronger of the Moon and Mars for the mother and Mercury for maternal relatives (Sl. 18-21). The Char Karakas calculator computes the first of these.

A reader who wants to use D40 the conventional way would therefore look at where those birth-chart significators fall in it: the 4th D40 house, the Moon's D40 sign, the 4th lord's D40 sign. Be clear about the status of that step. The calculator gives you the placements exactly; the method of combining them is not written in the source this app computes from, and the app does not perform it. Nothing here is a statement about any actual person in your family.

One general rule in the chapter does apply to every division. Ch. 7 Sl. 13-16 says that effects are full, medium and nil at the beginning, middle and end of a Hora, and that similar applications be made for the other divisions. Taken literally for a 45-minute part, that means the first 15 minutes of arc, the middle 15 and the last 15. The engine does not grade positions this way, and at this size the distinction is finer than the accuracy of the planetary positions themselves, so the page does not show it.

How D40 feeds the twenty-point strength score

The one place in this app where the D40 sign is actually weighed is Vimshopaka Bala. BPHS Ch. 7 describes four schemes of divisions. The fortieth part is absent from the six-division scheme (Sl. 17-19), from the seven-division scheme, and from the ten-division scheme (Sl. 20). It enters only in the full sixteen-division scheme (Sl. 21-25), where the Rasi carries 3.5 points, the Shashtiamsa 4, the Navamsa 3, the Shodashamsa 2, three others 1 each, and the rest of the nine divisions each a half. Khavedamsa is one of those nine. Its weight in the engine's table is 0.5 out of 20.

For each of the seven grahas from the Sun to Saturn, the engine looks up the dignity of the graha in its D40 sign, converts the dignity to a fraction, and multiplies by 0.5. Exaltation or Moolatrikona earns the full half point, own sign 0.375, a friendly sign about 0.31, a neutral sign 0.25, and an enemy sign or debilitation nothing. Rahu and Ketu are not scored, because the engine keeps no dignity table for them. For the example chart the D40 line of each graha reads as follows.

The table puts the size of this chart's voice in proportion. The most D40 can add to a graha is half a point, one fortieth of the scale. BPHS Ch. 7 Sl. 26-27 draws its reading bands at 5, 10 and 15, so a D40 placement can tip a graha across a band only when the total already sits within half a point of the line. In the example, the Moon at 10.88 and Venus at 11.75 are both in the band above 10; Venus's exalted D40 sign contributes to that, while the Moon gets there with nothing from D40 at all.

Ch. 6 Sl. 42-53 offers a second way to count: a graha's divisions falling in its exaltation, Moolatrikona or own sign are good Vargas, and the number of good Vargas among the sixteen earns a named grade. A D40 sign can count toward that tally in the same way as any other division. The same passage warns that the divisions of a combust, defeated or weak graha are not to be taken as auspicious. This app reports the Vimshopaka score and does not compute the named grades.

Birth-time sensitivity, measured

The Ascendant covers the whole zodiac in a day, and the zodiac holds 480 fortieth-parts, so on average the D40 Lagna changes every three minutes. To see what that looks like in practice we ran the engine for every minute of the example's civil day in Ahmedabad, 1,440 charts in all. The D40 Lagna changed sign 481 times. The gap between changes ranged from 2 to 4 minutes, with a mean of 2.99.

The example's own minute is the one where the D40 Lagna turns from Gemini to Cancer. A birth recorded at 06:41 gives a Gemini D40 Lagna and moves every graha one house on: the Sun and Jupiter to the 5th, Saturn to the 9th, the nodes to the 8th. A birth at 06:45 gives a Leo D40 Lagna, which also puts the Ascendant on the shared-sign list. Hospital clocks, wristwatches and family memory are rarely good to a single minute, so for most people the D40 Lagna and all twelve house numbers are provisional by construction.

The grahas are steadier, in proportion to their speed. Over the same 24 hours the Moon changed D40 sign 19 times, about once every 76 minutes. Venus and Mercury changed twice each, and the Sun, Mars and Saturn once each. Jupiter and the nodes did not change at all. Mars and Saturn are the instructive cases: Mars sat at 4.42 degrees at 06:42 and crossed into the next part at 09:33, and Saturn, retrograde and on the line itself, fell back into the previous part at 08:31. A slow graha is stable for hours or days, until it happens to be near an edge, and then a few minutes decide it.

• Birth time known to the minute from a written record: the D40 signs of all nine grahas are usable; the Lagna and houses are usable only if the Ascendant is not within about a quarter of a degree of a part boundary.
• Birth time known to within fifteen minutes: the D40 signs of the Sun, Mars, Mercury, Jupiter, Venus, Saturn and the nodes usually hold; the Moon's may not; the Lagna and houses span several signs and should not be read.
• Birth time unknown: the calculator returns no chart.

A practical test is to run the calculator twice, once a few minutes before and once a few minutes after the time you have, and see which values survive. The article on an unknown birth time sets out what else in a chart does and does not depend on the clock, and the Navamsa article works through the same problem for a division more than four times coarser than this one.

The clock is not the only source of error. The positions come from an analytical model whose accuracy is stated on the methodology page and discussed under accuracy. A point within that margin of a part boundary can legitimately come out one sign different in another program, and neither program is necessarily wrong about the rule.

Where D40 sits among the other calculators

The sixteen divisions are meant to be read as a set, with the birth chart first. D40 belongs to the fine-grained end of that set, together with D27, D30, D45 and D60. BPHS gives the last two a wider brief than this one, all indications, and gives D60 eight times the weight of D40 in the sixteen-division score. If you are choosing where to spend attention among the finest divisions, the text itself points to D60 before D40.

In the signed-in product the same function runs inside the Kundali view, which shows D40 as one chart-wheel card among the divisional charts and leaves it out when there is no Ascendant. The strength score that uses it is on the Vimshopaka page linked above. The Moon sign calculator is the place to confirm the Moon's birth-chart position before reading its D40 sign, and the full list of tools is on the calculators index.

Questions people ask about the D40 chart

Is Chatvarimshamsa a different chart from Khavedamsa?

No. BPHS Ch. 6 Sl. 29-30 gives both names for the same one-fortieth division. Chatvarimshat is the ordinary Sanskrit word for forty. This app uses Khavedamsa throughout because that is the name in the chapter's list of sixteen vargas.

Why are Rahu and Ketu always together in my D40 chart?

They sit at the same degree of opposite signs, and opposite signs are both odd or both even. The D40 sign depends only on the degree and on whether the sign is odd or even, so the two nodes always receive the same D40 sign. It happens in every chart and says nothing particular about yours.

Does the page tell me anything about my mother or her family?

No. It returns signs and houses only. The association of D40 with the maternal line is a convention of later practice; BPHS, the source of the calculation, assigns the chart to auspicious and inauspicious effects in general and reads the mother from the 4th house, the Moon and the Matru Karak of the birth chart.

Another site shows a different D40 Lagna for the same birth details. Which is right?

Possibly both, within their own inputs. The D40 Lagna changes about every three minutes of clock time and every 0.75 degrees of arc, so a small difference in the ayanamsa, the coordinates used for the place, the time zone rule or the underlying planetary model is enough. Compare the birth-chart Ascendant degree on the two sites first; if those differ by even a few tenths of a degree, the D40 difference is explained.

My Ascendant is near the very end of a sign. What should I expect?

Expect the result to be fragile. The last part of an odd sign maps to Cancer and the first part of the next sign to Libra; the last part of an even sign maps to Capricorn and the first part of the next to Aries. Crossing the boundary moves the D40 Lagna three signs, and every house number with it.

Does the shared-sign list mean those planets are Vargottama?

Only in the loose sense that the engine uses one field name for the same comparison in every divisional chart. The classical Vargottama defined in Saravali Ch. 3 concerns the Navamsa. In D40 the list records that the sign is the same in both charts, which happens for one part in twelve, and the app scores nothing from it.

How much does my D40 placement change my planet's strength score?

At most half a point out of twenty, and only for the seven grahas from the Sun to Saturn. In the sixteen-division scheme of BPHS Ch. 7 Sl. 21-25 the Khavedamsa is one of nine divisions weighted a half each. An exalted or Moolatrikona D40 sign earns the full half point; a debilitated or enemy sign earns nothing.

Does the calculator show the presiding deity of each part?

No. BPHS lists twelve presiding deities that repeat through the forty parts in the same order for every sign, and this page reports the list, but the engine computes only the sign and house. The sloka gives no interpretation for the individual names, so there is nothing the app could honestly attach to one.

Can I use D40 to time events?

Not with this page. It is a static mapping of birth positions and contains no dates. Timing in this app comes from the dasha and transit calculators, which work from the birth chart.