Shodashamsa D16 Chart

What this section adds

The calculator above gives a D16 sign and a D16 house for your Ascendant and nine grahas, and the notes beside it describe the code in two paragraphs. This section fills in the rest: the single sloka the rule comes from and what that sloka leaves unsaid, a lookup table that lets you check any result with a pencil, the meaning of each field in the answer, the geometry that decides which parts repeat the birth-chart sign, what the classical text says the chart is for, where else in this app the same ten signs are reused, and how many minutes of birth-time error it takes to change the answer. Every figure was produced by the engine for the same sample birth the page already uses.

Where the Shodashamsa rule is written

Brihat Parashara Hora Shastra lists sixteen divisions of a sign in Ch. 6 Sl. 2-4. Shodashamsa is the ninth name on that list, after Dwadasamsa (D12) and before Vimshamsa (D20). Its whole definition is Ch. 6 Sl. 16. In the translation held in our corpus the sloka says, in substance: starting from Mesh for a Movable Rasi, from Simh for a Fixed Rasi and from Dhanu for a Dual Rasi, the sixteen Shodashamsas, each a sixteenth of a sign or 1 degree 52 minutes 30 seconds, are regularly distributed; their presiding deities repeat in the order Brahma, Vishnu, Shiva and Surya four times for an odd Rasi, and in the reverse order for an even Rasi.

The same sloka gives the division a second name, Kalamsa. Both names mean the same thing arithmetically: shodasha is sixteen, and the part is one sixteenth of thirty degrees. Thirty divided by sixteen is 1.875 degrees, which is the 1 degree 52 minutes 30 seconds the text states.

Three separate pieces of information sit in that one sloka, and it helps to keep them apart. The size of a part is fixed at 1.875 degrees. The starting sign depends only on whether the birth-chart sign is movable, fixed or dual. BPHS defines those three classes in Ch. 4 Sl. 5, where Movable, Fixed and Dual are assigned to the twelve signs in order, so Aries, Cancer, Libra and Capricorn are movable, Taurus, Leo, Scorpio and Aquarius are fixed, and Gemini, Virgo, Sagittarius and Pisces are dual. The third piece is the deity sequence, and it is the only place where the sloka distinguishes odd signs from even ones.

That last point matters for how the count is coded. In the same chapter, when an even sign is meant to change the resulting sign, the text says so by naming a different starting sign: the Saptamsa starts from the seventh sign for an even Rasi (Sl. 10-11) and the Dashamsa from the ninth (Sl. 13-14). Sl. 16 names no such alternative for Shodashamsa. The word 'reverse' in it is attached to the deities. The engine therefore counts forward for every sign and applies no odd/even branch to the D16 sign.

The phrase 'regularly distributed' is all the sloka says about the order of the count after the starting sign. The engine reads it as one sign per part, moving forward through the zodiac, the same consecutive step it uses for Navamsa. That reading is a convention carried over from the neighbouring slokas, and the code comment says so. Nothing in Sl. 16 contradicts it, and nothing else in the sloka could produce sixteen parts from one starting sign.

The full lookup table

Because the starting sign depends on modality alone, the whole division fits in one table of sixteen rows and three columns. Find the row for the part your point falls in, then read across to the column for its birth-chart sign's modality.

Two features of the table are worth noticing before you use it. The three starting signs, Aries, Leo and Sagittarius, are the three fire signs, four signs apart from each other, so the three columns are the same sequence shifted by four rows. And because sixteen parts are more than twelve signs, rows 13 to 16 repeat rows 1 to 4. The first four signs of each count therefore receive two parts of every sign, and the remaining eight receive one. For a movable sign the doubled signs are Aries, Taurus, Gemini and Cancer; for a fixed sign they are Leo, Virgo, Libra and Scorpio; for a dual sign they are Sagittarius, Capricorn, Aquarius and Pisces.

Taken over the whole zodiac the doubling evens out. Each modality has four signs, each contributes two parts to its four doubled signs and one part to the other eight, and the three modalities double three different sets of four signs. Every sign of the D16 wheel ends up with exactly sixteen parts out of the 192 in the zodiac. No D16 sign is more likely than another for a point at a random longitude.

How the engine computes it, step by step

The calculator's handler is a thin wrapper. It builds the sidereal birth chart, the same one the birth chart calculator shows, and passes it to computeShodashamsa, which calls the shared divisional routine computeVarga with three arguments: sixteen divisions, the modality-based start function, and a step of one sign per part. For each of the ten points the routine does the following.

1. 1.Take the point's degree within its birth-chart sign, a number from 0 up to but not including 30. The engine works from the value rounded to two decimals.
2. 2.Divide by 1.875 and drop the fraction. This gives a part index from 0 to 15; the table above shows it as part 1 to 16.
3. 3.Cap the index at 15. A degree can never reach 30, so the cap only protects against a rounded 30.00 producing a seventeenth part.
4. 4.Look up the sign's modality in a twelve-entry table and pick the starting sign: Aries for movable, Leo for fixed, Sagittarius for dual.
5. 5.Add the part index to the starting sign and wrap past Pisces back to Aries. The result is the D16 sign.
6. 6.Compare the D16 sign with the birth-chart sign. If they match, mark the point vargottama and add its name to the list.

Once all ten signs are known, the routine builds houses. House 1 is the sign holding the D16 Ascendant, house 2 the next sign, and so on for twelve whole signs. Each graha's house is the count from the D16 Lagna's sign to its own. There are no cusps and no degrees inside the D16 chart; a varga puts a point in a sign and nothing finer. The longitudes that feed step 1 are sidereal, using the Lahiri value described on the ayanamsa calculator page.

Saravali offers an independent way to check step 2. Ch. 3 Sl. 17-18 states that each sign has 1800 kalas, minutes of arc, and that for any varga you convert the longitude within the sign to minutes, multiply by the varga figure and divide by 1800. For a point at 24.64 degrees that is 1478.4 minutes, times 16, divided by 1800, which gives 13.14. Thirteen parts are complete and the point is in the fourteenth. Dividing 24.64 by 1.875 gives the same 13.14, so the engine's arithmetic and Kalyana Varma's general rule agree.

The worked example, with the parts shown

The page's sample is a birth on 14 August 1994 at 06:42 IST in Ahmedabad. The note above the fold reports the resulting signs and houses. The table below adds what the note leaves out: the birth-chart degree each result was computed from, the part it falls in, and the modality that picked the column. These are the engine's own numbers.

Follow one row through the lookup table. The Ascendant is at 2.33 degrees of Leo. Dividing 2.33 by 1.875 gives 1.24, so one part is complete and the point is in part 2. Leo is fixed; the fixed column at row 2 reads Virgo. Virgo becomes house 1 of the D16 chart and every other house is numbered from it.

Now Saturn, at 16.50 degrees of Aquarius. Dividing by 1.875 gives 8.80, so Saturn is in part 9. Aquarius is fixed; row 9 of the fixed column is Aries. Aries is the eighth sign counted from Virgo, so Saturn sits in D16 house 8.

Mercury shows the wrap. It is at 28.35 degrees of Cancer, in the last part, part 16. Cancer is movable, and row 16 of the movable column is Cancer again, because the count from Aries has gone round the zodiac once and is on its fourth sign for the second time. Mercury's D16 sign equals its birth-chart sign, so it is the one point flagged in the vargottama list.

It is also worth reading how close each point sits to an edge. Venus at 12.92 degrees is 0.205 of a degree, about twelve minutes of arc, short of the boundary at 13.125 where part 8 begins. The Moon at 24.64 is about sixteen minutes of arc past the boundary at 24.375. The Ascendant is 0.455 of a degree past the edge at 1.875. These margins are what the limits section above the fold means by borderline, and the section on birth time below converts them into minutes on the clock.

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 D16 Lagna. The Ascendant entry carries no house number because it defines house 1. The vargottama value is true or false per point and simply reports whether the D16 sign equals the birth-chart sign. The engine applies that test to all ten points, the Ascendant and the nodes included, in the same way.

vargottama: the list

This is the same information gathered into one array of names, so a reader can see at a glance which points repeat. It can be empty; most charts have between none and two entries. The word comes from Navamsa practice. Saravali Ch. 3 describes the Navamsa that matches its own sign as Vargottama and adds that a Lagna in such a Navamsa makes a person important in their circle. That statement is about the Navamsa (D9). Neither Saravali nor BPHS Ch. 6 attaches a result to a matching sixteenth part, so on this page the flag is a description of the arithmetic and carries no reading.

houses: the twelve-sign layout

The houses array lists house 1 to house 12 with the sign each one holds. It exists so the chart can be drawn as a wheel and so you can read an empty house: in the sample, houses 1, 2, 4, 5, 7 and 12 hold no graha. An empty D16 house is the ordinary case. Nine grahas go into twelve signs, and in D16 Rahu and Ketu always share a sign, so at least four houses are empty in every chart.

available: false

The calculator is registered as needing an Ascendant. If the request has no birth time, the server returns available: false with missing set to birthTime and a message saying the chart rests on the Ascendant, which needs a time as well as a place. If a time is given but the place does not resolve to real coordinates, missing is birthPlace. In both cases 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 quickly the rising sign itself moves.

Which parts repeat the birth-chart sign

The FAQ above the fold says that every sign has at least one part that counts back to itself and that some have two. The lookup table makes it possible to list them all. A part is vargottama when the sign in its row and column is the sign the point already occupies.

The grouping is by element, and the reason is mechanical. The three starting signs are the fire signs, so a fire sign is always the first sign of its own count and returns at part 13. A water sign is always the fourth sign of its count and returns at part 16. Air signs are seventh and earth signs tenth, and neither comes round again within sixteen parts. Fire and water signs therefore repeat across 3.75 degrees of their thirty, air and earth signs across 1.875 degrees. Over the whole zodiac that is 33.75 degrees out of 360, a little under one in ten, which is why a list of ten points usually shows none, one or two names.

Patterns the rule forces on every chart

Some features of a D16 result are properties of the division and appear in every chart. Knowing them stops you from reading a pattern as personal when it is structural.

• Rahu and Ketu always share a D16 sign. They stand at the same degree of opposite signs, opposite signs have the same modality, and so they fall in the same row and the same column. The sample shows both in Taurus. A reading of Rahu and Ketu as an axis, which is how they behave in the birth chart, has nothing to work with in D16.
• Any two points at the same degree in signs of the same modality share a D16 sign. Signs of one modality are three signs apart, so planets in square or opposition by degree end up conjunct in D16. In the sample the Moon at 24.64 degrees of Libra is in the same part as the nodes at 25.40 degrees of Libra and Aries, and all three are in Taurus.

What BPHS says the chart is for

BPHS Ch. 7 Sl. 1-8 assigns a subject to each of the sixteen divisions in one long sentence: the physique from the Lagna, wealth from Hora, happiness through co-born from Dreshkan, fortunes from Chaturthamsa, and so on. The clause for this chart reads 'benefits and adversities through conveyances from Shodashamsa'. That clause is the entire classical statement of purpose in our corpus. This app's Kundali screen labels the D16 card 'Vehicles & general comforts'; the first word comes from that clause, and the second follows the usual modern gloss.

The translation says conveyances, and the translator's own aside elsewhere shows how he understood the word: in the dasha chapters (Ch. 52 Sl. 34-36) he writes 'comforts of conveyance, like palanquin (motor car in the present times)'. In the birth chart the same subject belongs to the fourth house. BPHS Ch. 11 Sl. 5 lists conveyances, relatives, mother, happiness, treasure, lands and buildings as the matters of Bandhu Bhava, and the article on the 4th house, Sukha Bhava covers that list in full.

Ch. 15 then gives the working rules, and they are all birth-chart rules. Sl. 3 ties comforts of lands, conveyances and houses to the fifth lord in its own house, own Navamsa or exaltation. Sl. 10-14 treat conveyances directly: they name Venus as the significator, read the fourth lord's placement and its link to the tenth and eleventh lords, and close with a general statement that a benefic in the fourth house, aspecting it, or joined with or aspecting its lord goes with happiness from conveyances, while a malefic in the same position goes with losses concerning vehicles. Those slokas mention the Navamsa once. They do not mention the Shodashamsa at all.

So the classical position, as far as our sources carry it, is narrow. The topic of conveyances is judged from the fourth house, its lord and Venus in the birth chart. D16 is named as the division that speaks to the same topic. BPHS does not give a house-by-house method for reading the D16 wheel. Later practice commonly carries the fourth-house logic into the D16 chart, looking at the D16 fourth house and the D16 position of the birth chart's fourth lord and of Venus; that is a reasonable extension, and it is an extension. In the sample the D16 fourth house is Sagittarius and is empty, and Venus is in Gemini in D16 house 10. The calculator reports those facts and stops there.

Ch. 7 Sl. 1-8 ends with a second remark that uses the word. After saying that a house whose lord is in a malefic Shashtiamsa diminishes, the translation continues: 'The Bhava, whose Lord is in a benefic Shodashamsa, flourish.' The sentence does not define what makes a sixteenth part benefic. It may refer to this division or to the sixteen-varga scheme as a whole, which carries nearly the same name, and the translation does not settle it. This app does not compute a benefic or malefic label for D16 parts.

D16 inside the Vimshopaka score

The place where BPHS gives D16 real weight is the twenty-point strength called Vimshopaka Bala, set out in Ch. 7 Sl. 17-27. The text describes four schemes. The six-varga and seven-varga schemes (Sl. 17-19) leave Shodashamsa out. Sl. 20 adds it, along with Dashamsa and Shashtiamsa, to make the ten-varga scheme, where it carries 1.5 points. In the full sixteen-varga scheme of Sl. 21-25 it carries 2 points, more than any division except Shashtiamsa at 4, the Rasi at 3.5 and Navamsa at 3. Nine of the sixteen charts carry only half a point each. On BPHS's own weighting, then, a graha's D16 sign counts four times as much as its Dashamsa sign. The Vimshopaka Bala calculator uses the sixteen-varga scheme, and its weight table gives D16 exactly those 2 points.

How the 2 points are earned is this app's own stated choice, and the code comment says so. For each of the seven grahas from the Sun to Saturn, the engine takes the D16 sign, grades the graha's dignity in that sign, 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. This is the same dignity scale the app's Shad Bala runs on. Friendship includes the temporary relationship read from the birth chart, so the same D16 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 D16 sign doing real work. The sample's Moon is the second strongest graha on the twenty-point scale at 10.88, behind Venus at 11.75, and its exalted D16 sign contributes 2 of those points. Take them away and it would stand at 8.88, below Venus. 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; the engine's bands use the same three thresholds. The Moon's exalted sixteenth part is therefore what lifts it across the line at 10 in this chart.

This also explains the vargottama Mercury more soberly than the flag alone would. Mercury keeps Cancer in D16, and Cancer grades as neutral for it in this chart, so it earns 1 point of 2. Repeating a sign is not the same as being strong in it. One further boundary: the older six-fold strength, Shad Bala, does not use D16. BPHS Ch. 27 counts seven divisions for its Sapt Vargaj Bal, the Rasi, Hora, Dreshkan, Saptamsa, Navamsa, Dwadasamsa and Trimsamsa, and the sixteenth part is not among them.

Birth time: what the sweep shows

The notes above the fold say the page cannot put one number on the precision needed. A sweep of the sample day puts numbers on that particular day and place. The engine was run for every minute of 14 August 1994 at Ahmedabad, 1,440 charts, and the D16 Ascendant recorded each time.

• The D16 Lagna changed sign 192 times in the day. That is the expected count: twelve rising signs times sixteen parts each.
• The average stay in one D16 sign was 7.5 minutes. The shortest stay found was 5 minutes and the longest 9, because signs take different lengths of time to rise at that latitude.
• Around the sample's birth the changes fell at 06:32 (Leo), 06:40 (Virgo), 06:49 (Libra) and 06:57 (Scorpio). The 06:42 birth is two minutes inside the Virgo window.

Read the last line carefully. A birth recorded at 06:42 that actually happened at 06:39 would have a Leo D16 Lagna, and every graha would move one house forward: Saturn from the eighth to the ninth, the Sun and Venus from the tenth to the eleventh. A birth at 06:50 would have Libra rising in D16 and every graha would move one house back. The ten D16 signs of the grahas would be unchanged in both cases; only the numbering would shift. Hospital records rounded to the nearest five minutes cannot separate these cases.

The grahas are far more stable than the Lagna, with one exception. Over the same day the Moon changed D16 sign seven times, roughly once every three hours and eleven minutes: it was in Aries from 03:04, in Taurus from 06:15 and in Gemini from 09:26. Mercury and Venus each changed once in the day, and the Sun and Mars did not change. So an uncertainty of an hour leaves nine of the ten D16 signs alone in most charts, puts the Moon at risk only 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 disagree on a fine division while agreeing on the birth chart. 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. 16 assigns Brahma, Vishnu, Shiva and Surya to the parts in repeating order, reversed 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 sixteenth part; it reports the part.
• The named designations. Ch. 6 Sl. 42-53 gives a graha a title according to how many of the sixteen vargas are 'good' for it, from Bhedak for two up to Sri Vallabh for all sixteen, where good means its exaltation, Moolatrikona or own sign and certain signs tied to the Arudha Lagna. This app does not compute those titles; its cross-varga summary is the Vimshopaka score.
• A verdict on vehicles or comfort. The classical rules for conveyances are fourth-house rules in the birth chart, as shown above. The calculator returns placements only.

How D16 connects to the rest of the app

The same computeShodashamsa 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 shows no D16 card when there is none. The Vimshopaka score reads its seven graha signs. All three therefore always agree with one another.

Among the divisional charts, D16 sits between two neighbours with related subjects. The Chaturthamsa (D4), which BPHS reads for fortunes, divides a sign into four parts of 7.5 degrees; each D4 part contains exactly four D16 parts, so the two charts cut the sign at the same edges at 7.5, 15 and 22.5 degrees. Next in BPHS's list after D16 comes Vimshamsa (D20), which also starts by modality with Aries for a movable sign but swaps the other two, taking Sagittarius for a fixed sign and Leo for a dual one (Ch. 6 Sl. 17-21). Navamsa (Sl. 12) is the third modality-based division. The finest chart, Shashtiamsa (D60), has parts of half a degree and is correspondingly more sensitive to birth time than D16.

For the subject itself, begin with the birth chart's fourth house, its lord and Venus, which is where BPHS Ch. 15 places the judgement of conveyances. For when a period connected with those factors runs, use the Vimshottari Dasha calculator; BPHS's dasha chapters mention the acquisition of conveyances repeatedly among the results of well-placed dasha lords. 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 D16?

Not in this engine, and the sloka does not ask for it. The reversal in Sl. 16 is stated for the order of the four presiding deities. Where BPHS wants an even sign to change the resulting sign, as in Saptamsa and Dashamsa, it names a different starting sign. For Shodashamsa the starting sign depends on modality only, and the count runs forward.

My D16 shows a planet conjunct both Rahu and Ketu. Is that significant?

It is structural. Rahu and Ketu always share a D16 sign, so any graha that joins one joins both. It happens whenever the graha is in the same degree band as the nodes in a sign of the same modality. The sample chart shows it: the Moon and both nodes fall in part 14 of movable signs, and all three are in Taurus.

Is a vargottama point in D16 strong?

The flag reports only that the D16 sign equals the birth-chart sign. Our sources attach a result to a matching Navamsa and say nothing about a matching sixteenth part. In the Vimshopaka score, what earns points is the graha's dignity in its D16 sign. The sample's Mercury repeats Cancer, a neutral sign for it in that chart, and earns 1 point of the available 2.

How much does D16 count in the Vimshopaka score?

Two points of twenty in the sixteen-varga scheme this app uses, per BPHS Ch. 7 Sl. 21-25. Only Shashtiamsa (4), the Rasi (3.5) and Navamsa (3) weigh more. In the ten-varga scheme of Sl. 20 it carries 1.5 points, and it is absent from the six-varga and seven-varga schemes.

Can the calculator tell me whether or when I will own a vehicle?

No. It returns ten signs, nine house numbers and a list of repeated signs. BPHS names conveyances as the subject of this division and then judges the matter from the fourth house, its lord and Venus in the birth chart (Ch. 15 Sl. 10-14). The app gives no verdict or date from D16.

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 D16 Lagna and that Lagna changes about every seven and a half minutes. Without a time the server returns available: false with missing: birthTime and no chart, so that nothing is estimated. The graha signs do not depend on the Ascendant, though the Moon's D16 sign changes about every three hours, so it too needs a time.

Two apps give me different D16 charts. Which is right?

Check three things in order. First the ayanamsa, since a shift of a fraction of a degree moves points across part edges. Second the birth time and timezone, since a few minutes can change the D16 Lagna. Third the rule itself: an implementation that counts backward for even signs will differ for every point in an even sign. This engine uses Lahiri, a forward count for all signs, and the modality starts of BPHS Ch. 6 Sl. 16.