Chaturvimshamsa D24 Chart

What this section adds

The calculator above returns a D24 sign and a D24 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 meaning of each field in the answer, a full list of the parts that repeat the birth-chart sign, a quirk at sign boundaries that follows from having two adjacent starting signs, what the classical text says about learning and where it actually judges it, how the D24 sign feeds the app's twenty-point strength score, and how many minutes of birth-time error change the result. Every figure was produced by the engine for the same sample birth the page already uses.

Where the Chaturvimshamsa rule is written

Brihat Parashara Hora Shastra names sixteen divisions of a sign in Ch. 6 Sl. 2-4. Chaturvimshamsa is the eleventh name, after Vimshamsa (D20) and before Saptavimshamsa (D27). Its definition is Ch. 6 Sl. 22-23. In the translation held in our corpus the passage says, in substance: the Chaturvimshamsa is one twenty-fourth of a Rasi, 1 degree 15 minutes each, and its distribution commences from Simh and Kark, respectively, for an odd and an even Rasi. For an odd Rasi the ruling deities repeat twice in the order Skand, Parusdhar, Anal, Vishwakarma, Bhag, Mitr, Maya, Antaka, Vrisha-Dwaja, Govinda, Madan and Bhima; for an even Rasi they are reversed, starting from Bhima, again twice.

Chatur-vimshati is twenty-four, and thirty degrees divided by twenty-four is 1.25, the 1 degree 15 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 deity sequence is the third, and it is a list of twelve names used twice, which matches the arithmetic: twenty-four parts stepping one sign at a time go round the twelve signs exactly twice.

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. Several divisions in the chapter use that split, and they use it differently. The Saptamsa starts from the sign itself when it is odd and from the seventh sign when it is even (Sl. 10-11); the Dashamsa does the same with the ninth sign (Sl. 13-14). In both, the starting sign is worked out from the sign the point occupies, so there are twelve different starts. D24 names two signs outright, Leo and Cancer, and every sign of the zodiac uses one or the other. The only other division this engine builds from a named pair is the Khavedamsa (D40), whose pair, Aries and Libra, sits six signs apart. Leo and Cancer are next to each other, and that adjacency produces the boundary effect described further down.

The word reverse in Sl. 22-23 is attached to the deities. The sloka already tells you what an even sign changes about the count: it starts from Cancer. It does not ask for a backward count as well, and the engine does not apply one. The count runs forward through the zodiac from Leo or from Cancer, one sign per part. The step of one sign per part is the same consecutive step the engine uses for Navamsa, Saptamsa and Dashamsa; the sloka says only that the distribution commences from the named sign, and twenty-four parts covering twelve deities twice leaves no other regular reading.

The full lookup table

Because the second lap repeats the first, the whole division fits in twelve rows. Find the row holding the part your point falls in, then read the column for an odd or an even birth-chart sign.

Three things are visible in the table. The even column is the odd column moved down one row, which is the statement above the fold that an odd-sign point lands one D24 sign ahead of an even-sign point at the same degree. The second lap begins at exactly 15 degrees, so the first half of every sign and the second half each contain all twelve D24 signs once. And the last row of the odd column reads Cancer, the same sign as the first row of the even column.

How the engine computes it, step by step

The calculator's handler is a thin wrapper. It builds the sidereal birth chart, the one the birth chart calculator shows, and passes it to computeChaturvimshamsa, which calls the shared divisional routine computeVarga with twenty-four divisions and the two-way start function. For each of the ten points the routine does the following.

1. 1.Take the point's degree within its birth-chart sign, from 0 up to but not including 30, as held by the chart to two decimals.
2. 2.Divide by 1.25 and drop the fraction. This is a part index from 0 to 23; the table shows it as part 1 to 24.
3. 3.Cap the index at 23. A degree never reaches 30, so the cap only stops a rounded 30.00 from producing a twenty-fifth part.
4. 4.Test whether the sign is odd or even. The code numbers Aries as 0, so an odd sign in the classical count is an even index there; the comment beside the function records that so the two conventions are not confused.
5. 5.Pick the starting sign: Leo for an odd sign, Cancer for an even one.
6. 6.Add the part index to the starting sign and wrap past Pisces to Aries. The result is the D24 sign.
7. 7.Compare the D24 sign with the birth-chart sign. If they are equal, set the point's vargottama flag and add its name to the list.

With all ten signs known, the routine numbers the houses. House 1 is the sign holding the D24 Ascendant and the other eleven follow in zodiac order, each a whole sign. A graha's house is the count from the Lagna's D24 sign to its own. There are no degrees inside a divisional chart, so there are no cusps and no orbs to consider. The longitudes that feed step 1 are sidereal, on the Lahiri value shown by the ayanamsa calculator.

The worked example, with the parts shown

The sample is a birth on 14 August 1994 at 06:42 IST in Ahmedabad. The note above the fold reports the Lagna, Saturn and the nodes. The table below gives all ten points with the working: the birth-chart degree, whether the sign is odd or even, the part, and the result. These are the engine's own numbers.

Follow the Ascendant through the lookup table. It is at 2.33 degrees of Leo. Dividing by 1.25 gives 1.86, so one part is complete and the point is in part 2. Leo is the fifth sign, odd; the odd column at the row for parts 2 and 14 reads Virgo. Virgo becomes house 1.

Saturn reaches the same sign by the second lap. At 16.50 degrees of Aquarius it is in part 14, which shares a row with part 2. Aquarius is the eleventh sign, odd, so the answer is again Virgo and Saturn stands in D24 house 1. Two points fourteen degrees apart in different signs have landed together because they sit in the same row of the same column.

The Sun shows the one-row shift between columns. It is at 27.26 degrees of Cancer, part 22, and Cancer is even; the even column at the row for parts 10 and 22 reads Aries. Rahu and Ketu are in part 21 of odd signs, one row higher, and the odd column there also reads Aries. So the Sun shares its D24 sign with both nodes although it is a part further on. Ketu is in Aries in the birth chart too, which is why it is the single name in the vargottama list.

It is worth reading how near each point sits to an edge, because that is where another tool may differ. Jupiter at 13.55 degrees is 0.20 of a degree, about twelve minutes of arc, short of the edge at 13.75 where part 12 begins. The Ascendant is 0.17 of a degree short of the edge at 2.5. The Sun is 0.24 short of 27.5. Saturn is 0.25 past 16.25, and the nodes 0.40 past 25. The limits above the fold put the planetary model at a few arcminutes, so Jupiter is the one graha in this chart whose D24 sign is genuinely close to that margin.

Reading each field of the result

positions: sign, house and the vargottama flag

Every point has a sign. Each of the nine grahas also has a house counted from the D24 Lagna; the Ascendant entry has none because it defines house 1. The vargottama value is true or false and reports only whether the D24 sign equals the birth-chart sign. The engine applies that comparison to all ten points alike, the Ascendant and the nodes included.

vargottama: the list

The same flags gathered into one array of names. It is often empty and rarely has more than two entries. The term belongs to Navamsa practice: Saravali Ch. 3 calls the Navamsa that matches its own sign Vargottama and attaches a result to a Lagna placed there. That statement concerns the Navamsa (D9). Neither Saravali nor BPHS Ch. 6 gives a result for a matching twenty-fourth part, so here the list describes the arithmetic and carries no reading.

houses: the twelve-sign layout

The houses array lists house 1 to house 12 with the sign each holds, so the chart can be drawn as a wheel and so you can see which houses are empty. In the sample, houses 2, 4, 5, 6, 11 and 12 hold no graha. That is ordinary. Nine grahas go into twelve signs, and Rahu and Ketu always share one in D24, so at least four houses are empty in every chart.

available: false

The calculator is registered as needing an Ascendant. When the birth details cannot supply one, the server answers with a successful response that says available: false and names what is missing, and no chart object is returned. The engine does not estimate a Lagna from sunrise or noon to fill the gap. The article on what can still be read without a birth time explains which parts of a chart survive, and the Lagna calculator shows how fast the rising sign itself moves.

Which parts repeat the birth-chart sign

The FAQ above the fold says that exactly two of the twenty-four parts of every sign count back to the sign itself. The lookup table makes it possible to name them. A part is vargottama when the sign in its row and column is the sign the point already occupies.

The signs pair up as an even sign with the odd sign after it, and the reason is the one-row shift. Cancer is the first sign of the even count and Leo the first of the odd count, so both return to themselves in part 1 and again twelve parts later. Each following pair is two rows further down. The repeating part is always an odd-numbered one. In every sign the two bands add up to 2.5 degrees of the thirty, one twelfth, so across ten points a chart shows on average a little under one match. Ketu at 25.40 degrees of Aries falls in the second Aries band, and that is the whole explanation of the sample's single entry.

Patterns the rule forces on every chart

Some features of a D24 result belong to the division and appear in every chart. Recognising them stops you from reading a structural pattern as a personal one.

• Rahu and Ketu always share a D24 sign. They stand at the same degree of opposite signs, and opposite signs are both odd or both even. A reading of Rahu and Ketu as an axis across the chart, which is how they behave in the birth chart, has nothing to work with here.
• Any two points in the same part of two odd signs, or of two even signs, are conjunct in D24, whatever their distance in the birth chart. Any odd-sign point and an even-sign point one part later are conjunct as well. The sample's eighth house, holding the Sun with both nodes, is that second case.
• The D24 sign does not change at the boundary from an odd sign into the even sign after it. The last part of Aries, Gemini, Leo, Libra, Sagittarius or Aquarius is Cancer, and the first part of the sign that follows is Cancer too. A point crossing from 29.9 degrees of Leo to 0.1 of Virgo changes its birth-chart sign and keeps its D24 sign.
• At the other six boundaries the D24 sign jumps two signs. The last part of an even sign is Gemini and the first part of the next odd sign is Leo, so Cancer is skipped. A slow-moving point can be seen to go from Gemini to Leo in D24 with no Cancer stay between.

The last two items cancel out over the zodiac. Each D24 sign still receives two parts from each of the twelve birth-chart signs, twenty-four of the 288 parts in all, so no D24 sign is more likely than another for a point at a random longitude.

What BPHS says the chart is for

BPHS Ch. 7 Sl. 1-8 gives each of the sixteen divisions a subject in one long sentence: the physique from the Lagna, wealth from Hora, fortunes from Chaturthamsa, sons and grandsons from Saptamsa, spouse from Navamsa, and so on down the list. The clause for this chart is three words in translation: learning from Chaturvimshamsa. That clause is the entire classical statement of purpose in our corpus. The app's Kundali screen labels the D24 card Education & learning, which is that clause with its common modern gloss beside it.

BPHS then judges learning from the birth chart, and it does so mostly through the fifth house. Ch. 11 Sl. 6 lists learning and knowledge among the indications of Putr Bhava, next to sons and authority; the article on the 5th house, Putra Bhava covers that list. The chapter on bhava lords returns to the theme several times. Ch. 24 Sl. 59 says that with the fifth lord in the eleventh house the native will be learned and an author of treatises. Sl. 113 says that with the tenth lord in the fifth the native will be endowed with all kinds of learning. Sl. 43 connects a high degree of education with the fourth lord in the seventh. These are statements about lords in houses of the birth chart, and the translation's wording, 'will be', is the classical idiom for an indication; none of them is a promise about a particular person.

Two grahas carry the subject by nature. Ch. 3 Sl. 12-13 calls Budh the speech-giver and says Guru confers knowledge, and the physical descriptions that follow (Sl. 26-27) give Mercury the capacity to use words with many meanings and call Jupiter intelligent and learned in Shastras.

The nearest BPHS comes to joining learning with divisional charts is Ch. 41 Sl. 20-22. It reads the fifth lord by how many of the standard vargas place it in a good division: in Parijatamsa the native takes to the branch of learning befitting the family, in Uttamamsa there is excellent learning, and higher designations bring honours and Vedic knowledge. Those designations are counts across a set of vargas, defined in Ch. 6 Sl. 42-53. They are not a reading of the D24 wheel, and this app does not compute them.

So the classical position, as far as our sources carry it, is narrow. Learning is judged from the fifth house, its lord, Mercury and Jupiter in the birth chart, with the fifth lord's standing across the vargas as a refinement. D24 is named as the division that speaks to the same subject. BPHS gives no house-by-house method for the D24 chart. Later practice commonly carries the birth-chart logic across, looking at the D24 fourth, fifth and ninth houses and at where Mercury, Jupiter and the birth chart's fifth lord fall; that is a reasonable extension, and it is an extension. In the sample the D24 fifth house is Capricorn and empty, Mercury is in Taurus in house 9 and Jupiter in Gemini in house 10. The calculator reports those placements and stops.

D24 inside the Vimshopaka score

The one place the D24 sign is used for arithmetic in this app is the twenty-point strength called Vimshopaka Bala, set out in BPHS Ch. 7 Sl. 17-27. The text describes four schemes. The six-varga and seven-varga schemes (Sl. 17-19) leave Chaturvimshamsa out, and so does the ten-varga scheme of Sl. 20, which adds only Dashamsa, Shodashamsa and Shashtiamsa. It enters in the sixteen-varga scheme of Sl. 21-25, where Hora, Trimsamsa and Drekkana carry 1 point each, Shodashamsa 2, Navamsa 3, the Rasi 3.5, Shashtiamsa 4, and 'the rest of the nine divisions each a half'. D24 is one of those nine. The Vimshopaka Bala calculator uses that scheme, and its weight table gives D24 half a point of the twenty.

How the half point is earned is this app's stated choice. For each of the seven grahas from the Sun to Saturn, the engine takes the D24 sign, grades the graha's dignity there, and awards a fraction of the weight: all of it for exaltation, three quarters for its own sign, five eighths for a friendly sign, half for a neutral one and nothing for an enemy sign or debilitation. The friendship test includes the temporary relationship read from the birth chart, so the same D24 sign can grade differently in two charts. Rahu and Ketu are not scored, because the engine keeps no dignity table for them.

The table shows the scale of the thing. The Sun is exalted in its D24 sign and collects the full half point; the Moon is in an enemy sign and collects nothing; and the Moon still stands at 10.88, second of the seven behind Venus (11.75), while the Sun stands at 8.69. Half a point is one fortieth of the total. BPHS Ch. 7 Sl. 26-27 reads a total under 5 as unable to give good results, 5 to 10 as giving some, 10 to 15 as middling and above 15 as wholly favourable, and a half-point swing moves a graha across one of those lines only when it was already sitting on it.

The table also puts a number on the Jupiter margin noted earlier. Jupiter is seven minutes of arc short of part 12, and part 12 of an odd sign is Cancer, where Jupiter is exalted. A longitude that small amount higher would grade Jupiter's D24 sign as Exalted and earn 0.5 where it now earns 0.25. The effect on the total is a quarter of a point. This is the honest size of a part-edge disagreement between two tools for D24: a different sign on the wheel, and a change in the strength score too small to alter its band. One further boundary: the older six-fold strength, Shad Bala, does not use D24 at all.

Birth time: what the sweep shows

The limits above the fold say a birth time a few minutes out can move the D24 Lagna. A sweep of the sample day puts figures on that for one date and place. The engine was run for every minute of 14 August 1994 at Ahmedabad, 1,440 charts, and each point's D24 sign recorded.

• The D24 Lagna changed sign 282 times in the day. Twelve rising signs times twenty-four parts is 288; the six missing changes are the six odd-to-even boundaries, where the sign on either side is Cancer.
• A part of the Lagna lasts five minutes on average. Ordinary stays in one D24 sign ran from 3 to 7 minutes, nearly all of them 4, 5 or 6, because signs take different lengths of time to rise at that latitude.
• The four longest stays, 10 to 12 minutes, were all Cancer, each straddling a boundary between an odd rising sign and the even one after it.
• Around the sample's birth the changes fell at 06:26 (Gemini), 06:32 (Leo), 06:38 (Virgo), 06:43 (Libra) and 06:49 (Scorpio). The step from Gemini straight to Leo at 06:32 is the rising sign passing from Cancer into Leo, with Cancer skipped in D24.

Read the last line against the birth time. The 06:42 birth is in the final minute of a five-minute Virgo window. A birth that actually happened at 06:43 has a Libra D24 Lagna: Saturn moves from house 1 to house 12 and the Sun and the nodes from house 8 to house 7. A birth at 06:37 has Leo rising in D24, with Saturn in house 2 and the Sun in house 9. In both cases the D24 signs of the nine grahas are unchanged and only the numbering moves. A time rounded to the nearest five minutes cannot separate these three charts.

The grahas are far steadier, with one exception. Over the same day the Moon changed D24 sign ten times, about once every two hours and eight minutes: it entered Pisces at 05:11 and Aries at 07:19. Its one long stay, in Cancer from 13:41 to 17:57, was the Moon crossing from Libra into Scorpio, the same boundary effect seen in the Lagna. The Sun and Mercury each changed once in the day, at 12:28 and 11:23, and Mars, Jupiter, Venus, Saturn and the nodes did not change. An uncertainty of an hour therefore leaves most D24 signs alone, puts the Moon at risk when the birth is near one of its changes, and makes the house numbers unreliable.

The same reasoning applies to anything that shifts longitudes by a fraction of a degree. A different ayanamsa moves every point by the same amount and can carry several across a part edge at once, which is one reason two apps can agree on a birth chart and disagree on a fine division. The page on accuracy and the methodology page state what this engine's positions are built from and how precise they are.

What the calculator leaves out, and why

• The presiding deities. Sl. 22-23 assigns twelve names from Skand to Bhima to the parts, twice over, and reverses them for an even sign. The engine does not return them. BPHS names the deities and gives no rule for using them, so the calculator would have a label to show with no reading behind it.
• Strength by position inside a part. BPHS Ch. 7 Sl. 13-16 says the effects of a Hora are full at its beginning, medium in its middle and nil at its end, and that similar applications be made for other divisions. The engine does not grade a point by where it sits inside its twenty-fourth part; it reports the part.
• The named designations. Ch. 6 Sl. 42-53 gives a graha a title according to how many vargas are good for it, and Ch. 41 Sl. 20-22 reads the fifth lord's title for learning. This app does not compute those titles; its cross-varga summary is the Vimshopaka score.
• A verdict on study, exams or a field of education. The classical rules for learning are fifth-house and significator rules in the birth chart, as shown above. The calculator returns placements only.

How D24 connects to the rest of the app

The same computeChaturvimshamsa call runs in three places. This calculator returns it directly. The Kundali screen draws it as one of its divisional wheel cards when a birth time is on file and leaves the card out when there is none. The Vimshopaka score reads the seven graha signs from it. The three therefore always agree with one another.

For the subject itself, begin with the birth chart's fifth house, its lord, Mercury and Jupiter, which is where BPHS places the judgement of learning. For when a period connected with those factors runs, use the Vimshottari Dasha calculator; the dasha chapters of BPHS list education among the results of several sub-periods, for example 'gain of intelligence, education' under Mercury within Mercury at the third level (Ch. 61 Sl. 56). The texts behind every statement here are listed on the sources page, and the full set of tools is on the calculators index.

Further questions

Does an even sign count backward in D24?

Not in this engine, and the sloka does not ask for it. Sl. 22-23 states what changes for an even sign: the count commences from Cancer in place of Leo. The reversal it mentions is the order of the twelve presiding deities. The sign count runs forward from the starting sign in both cases.

My planet moved into the next birth-chart sign but its D24 sign stayed the same. Is that an error?

No. The last part of every odd sign and the first part of the even sign after it are both Cancer, so a point crossing from Aries to Taurus, Gemini to Cancer, Leo to Virgo, Libra to Scorpio, Sagittarius to Capricorn or Aquarius to Pisces keeps Cancer in D24 for two parts running. In the sample day's sweep the Moon did this between 13:41 and 17:57.

Why did the D24 sign jump from Gemini to Leo with no Cancer between?

That is the other kind of boundary. The last part of an even sign is Gemini and the first part of the next odd sign is Leo. Cancer is skipped there, which balances the double Cancer stay at the odd-to-even boundaries. The sample's D24 Lagna did this at 06:32, as the rising sign passed from Cancer into Leo.

Can the calculator tell me how my studies or exams will go?

No. It returns ten signs, nine house numbers and a list of repeated signs. BPHS names learning as the subject of this division in one clause and then judges learning from the fifth house, its lord, Mercury and Jupiter in the birth chart. The app gives no verdict, field of study or date from D24.

Why does the calculator refuse to run without a birth time?

The handler is registered as needing an Ascendant, because the house numbers are counted from the D24 Lagna and that Lagna changes about every five minutes. Without one the server returns available: false and no chart, so that nothing is estimated. The graha signs do not depend on the Ascendant, though the Moon's D24 sign changes roughly every two hours, so it too needs a time.

Two apps give me different D24 charts. Which is right?

Check three things in order. First the ayanamsa, since a shift of a fraction of a degree moves points across edges only 1.25 degrees apart. Second the birth time and timezone, since a few minutes change the D24 Lagna. Third the rule: an implementation that counts backward for even signs will differ for every point in an even sign. This engine uses Lahiri, a forward count, and the Leo and Cancer starts of BPHS Ch. 6 Sl. 22-23.