Akshavedamsa D45 Chart

What this section adds

The calculator above gives the D45 sign of your Ascendant and nine grahas, the twelve houses from the D45 Lagna, and a short account of the method and its limits. This section goes further into the same ground: the exact verses that define the chart, the three presiding deities the page does not display, how little the classical text actually says about what to read from it, the arithmetic slice by slice on the sample birth, how each line of the result should be read, what D45 contributes to the sixteen-chart strength score, and a measured test of how fast the chart changes with birth time.

The classical rule, and where it is written

Akshavedamsa is one of the sixteen divisions of a sign listed in Brihat Parashara Hora Shastra (BPHS). Ch. 6 Sl. 2-4 names them in order: Rasi, Hora, Dreshkan, Chaturthamsa, Saptamsa, Navamsa, Dashamsa, Dvadashamsa, Shodashamsa, Vimshamsa, Chaturvimshamsa, Saptavimshamsa, Trimshamsa, Khavedamsa, Akshavedamsa and Shashtiamsa. It is the fifteenth of the sixteen, sitting between Khavedamsa (D40) and Shashtiamsa (D60). The list of texts this site draws on is on the sources page.

The rule itself is two verses long. BPHS Ch. 6 Sl. 31-32 calls Akshavedamsa the 1/45th part of a sign and says that Mesh, Simh and Dhanu (Aries, Leo and Sagittarius) are the signs from which the distribution starts for Movable, Immovable and Common signs respectively. Thirty degrees divided by forty-five is two-thirds of a degree, which is 40 minutes of arc. The verse then names the presiding deities, covered in the next section. That is the whole definition: a part size, three starting signs, and three deities.

Which signs are Movable, Fixed and Common comes from an earlier chapter. BPHS Ch. 4 Sl. 5 says that Movable, Fixed and Dual are the names given to the twelve signs in order, so the pattern repeats every three signs from Aries. The engine holds the same sequence in a twelve-entry list and looks the Rasi sign up in it.

Two things about this rule are worth noticing. First, it is word for word the starting rule BPHS Ch. 6 Sl. 16 gives for Shodashamsa (D16), which is why the engine uses one identical function for both. The charts still differ, because a D16 part is 1 degree 52.5 minutes wide and a D45 part is 40 minutes wide, so the same degree lands a different number of steps from the same starting sign. Second, the neighbouring chart on the list works differently: Khavedamsa in Sl. 29-30 starts from Aries for an odd sign and Libra for an even sign. Each of the higher vargas has its own starting rule, and none can be guessed from another.

The three presiding deities

BPHS Ch. 6 Sl. 31-32 assigns each of the forty-five parts a presiding deity from a set of three, and the order depends on the modality of the Rasi sign. In Movable signs the order is Brahma, Shiva, Vishnu. In Immovable signs it is Shiva, Vishnu, Brahma. In Common signs it is Vishnu, Brahma, Shiva. In each case the three repeat fifteen times, which fills the forty-five parts exactly.

The calculator does not compute or display these deities. The engine function returns a sign, a house and a same-sign flag for each point, and nothing else. They are described here because they are half of what the verse says, and because a short piece of counting shows how they relate to the chart you do see.

Take a Movable Rasi sign. Its count starts at Aries, and the first, fourth, seventh and tenth parts fall in Aries, Cancer, Libra and Capricorn - the four Movable signs - and so does every third part after them. Those are exactly the parts the verse gives to Brahma. The parts given to Shiva fall in Taurus, Leo, Scorpio and Aquarius, and those given to Vishnu fall in the four Common signs. Run the same count for a Fixed sign starting at Leo, or a Common sign starting at Sagittarius, and the result is the same. So the three triads in the verse reduce to one statement: a part that lands in a Movable D45 sign is presided over by Brahma, one that lands in a Fixed D45 sign by Shiva, and one that lands in a Common D45 sign by Vishnu. This is hand arithmetic from the verse, not a line in the text and not engine output, but it means the deity can be read straight off the D45 sign on the page.

What BPHS reads from this chart, and how little it says

BPHS Ch. 7 Sl. 1-8 gives one use to each division: physique from the Lagna, wealth from Hora, happiness through co-born from Dreshkan, fortunes from Chaturthamsa, sons and grandsons from Saptamsa, spouse from Navamsa, power and position from Dashamsa, parents from Dvadashamsa, conveyances from Shodashamsa, worship from Vimshamsa, learning from Chaturvimshamsa, strength and weakness from Saptavimshamsa, evil effects from Trimshamsa, auspicious and inauspicious effects from Khavedamsa. The list ends with "all indications from both Akshavedamsa and Shashtiamsa".

That phrase is the entire classical statement of what D45 is for. It gives the chart no topic of its own. Fourteen of the sixteen divisions are tied to a subject; the last two are tied to everything, jointly. The same passage then says two specific things about its neighbours - a house whose lord is in a malefic Shashtiamsa diminishes, and one whose lord is in a benefic Shodashamsa flourishes - and says nothing comparable about Akshavedamsa. There is no verse in these chapters that tells a reader what a graha in a given D45 sign or D45 house means.

The tagline on this page mentions paternal legacy, and the Kundali sheet labels the chart "general indications, paternal legacy". The first half of that label is BPHS. The second half is a reading in common use that the BPHS translation in this site's corpus does not state, and the other texts searched - Saravali, Bhrigu Sutras and the modern case-study book - do not mention Akshavedamsa at all. Where BPHS itself speaks of the father, it points elsewhere: Ch. 7 Sl. 39-43 says the 9th house (Dharma Bhava) and the 9th counted from the Sun deal with the father, and Ch. 7 Sl. 1-8 gives parents to Dvadashamsa (D12). This is why the calculator reports placements and attaches no paternal reading to them.

Two more general statements in BPHS apply to every division, D45 included. Ch. 7 Sl. 13-16, after describing Hora, says effects are full, medium and nil at the beginning, middle and end of a division and that similar application should be made for the other divisions. In a part only 40 minutes wide that gradient runs over a few minutes of arc, well inside the precision limits listed further down, so the engine does not attempt it. And Ch. 6 Sl. 42-53 defines a good varga as a division falling in the graha's exaltation, Moolatrikona or own sign, or in a sign owned by the lord of a Kendra from the Arudha Lagna, while the divisions of a combust, defeated or weak graha are to be set aside. Counting good vargas across all sixteen is where D45 does its classical work, and the strength section below shows the form of that count this site computes.

How the engine computes it, step by step

The calculator runs the same chart computation as the birth chart and Lagna calculators, then passes the result to a shared equal-part routine with the number 45 and the modality rule. The page already describes the division and the wrap round the zodiac. The full sequence, as written in the code, is this.

1. 1.Compute the sidereal longitude of the Ascendant and the nine grahas for the birth moment and place. The zodiac is sidereal; the offset applied is shown by the ayanamsa calculator. Each point is stored as a sign and a degree within that sign, rounded to two decimals.
2. 2.Take the part width as 30 divided by 45, which is 0.6667 of a degree.
3. 3.For each point, divide its degree within the sign by that width and drop the fraction. The result is a part index from 0 to 44. A guard caps it at 44 so a value of exactly 30.00 cannot spill into a forty-sixth part.
4. 4.Look up the modality of the Rasi sign and take the starting sign: Aries for Movable, Leo for Fixed, Sagittarius for Common.
5. 5.Add the part index to the starting sign and take the remainder on division by twelve. That sign is the point's D45 sign.
6. 6.Flag the point if its D45 sign is the same as its Rasi sign, and add its name to the list of matches.
7. 7.Make the D45 sign of the Ascendant the 1st house and number the rest in zodiacal order, one whole sign per house. Each graha's house is its D45 sign counted from there.

Because forty-five is three laps of twelve plus nine, the first nine signs counted from the start receive four parts of each Rasi sign and the last three receive three. The page says this in general terms. Spelled out by modality, it looks like this.

One consequence is not obvious until it is counted. Inside a sign, each 40-minute step moves the D45 sign forward by one. At the boundary between two Rasi signs it does not. The last part of a Movable sign falls in Sagittarius and the first part of the Fixed sign that follows falls in Leo; the last part of a Fixed sign falls in Aries and the next sign opens in Sagittarius; the last part of a Common sign falls in Leo and the next opens in Aries. In every case the D45 sign jumps forward eight signs at the boundary instead of one. The engine output confirms it on the sample day: an Ascendant at Cancer 29.64 has a D45 sign of Sagittarius, and three minutes of clock time later, at Leo 0.31, it is Leo.

The sample chart, slice by slice

The worked example on the page is a birth on 14 August 1994 at 06:42 in Ahmedabad. The page lists the resulting signs and houses. The table below shows how each one was reached, with the Rasi position the engine computed, the part it falls in, and the count from the starting sign. Parts are numbered here from 1 to 45, so part 4 is the engine's index 3.

Follow one row through. The Ascendant is at Leo 2.33. Dividing 2.33 by 0.6667 gives 3.49, so the index is 3 and the Ascendant is in the fourth part. Leo is a Fixed sign, so the count starts from Leo itself: Leo, Virgo, Libra, Scorpio. The D45 Lagna is Scorpio. Now the Sun, at Cancer 27.26: the index is 40, Cancer is Movable so the count starts from Aries, forty steps on from Aries is three full laps and four more signs, which is Leo. Leo is the tenth sign from Scorpio, so the Sun is in the 10th D45 house.

Mars is the row the page singles out. At Gemini 4.42 it is in the seventh part. Gemini is Common, the count starts from Sagittarius, and six steps on from Sagittarius is Gemini again. Its D45 sign equals its Rasi sign, so the engine lists it. Rahu and Ketu sit at 25.40 of Libra and Aries, opposite signs that are both Movable, so both start from Aries, both are in the thirty-ninth part, and both land in Gemini with Mars.

For completeness, the presiding deities of these ten parts by the verse, worked by hand: the Ascendant's part, the fourth of a Fixed sign, is Shiva; the Sun's and Saturn's are Shiva; the Moon's, Mercury's and Venus's are Brahma; Mars's, Jupiter's, Rahu's and Ketu's are Vishnu. Each agrees with the shortcut above: Scorpio and Leo are Fixed D45 signs, Aries, Libra and Cancer are Movable, Gemini and Sagittarius are Common.

How to read each kind of result

The D45 Lagna

The Ascendant row is the frame for everything else. Its D45 sign becomes the 1st house, and every house number on the page is counted from it. It is also the most fragile figure on the page, because the Ascendant is the fastest-moving point in a chart. If your birth time is rounded or remembered, treat the D45 Lagna, and therefore every house number, as provisional. The sensitivity section below puts a number on that.

A graha's D45 sign

The sign is the firmer half of each row. It depends only on the graha's own degree, not on the Ascendant, so for the slow grahas it survives any plausible error in the clock. What can be done with it classically is limited to dignity: whether the graha is in its exaltation, own, friendly, neutral, enemy or debilitation sign there, which is the test of a good varga in BPHS Ch. 6 Sl. 42-53. This page does not print the dignity; the Vimshopaka Bala calculator does, in its row for D45.

A graha's D45 house

The house is the D45 sign counted from the D45 Lagna, whole sign by whole sign. BPHS Ch. 7 Sl. 33-36 classifies houses in general: the 1st, 4th, 7th and 10th are Kendras, the 5th and 9th are Kons, and the 6th, 8th and 12th are Dusthanas. In the sample that puts the Sun and Saturn in a Kendra, Venus in a Kon, and the Moon, Mars, Mercury, Rahu and Ketu in Dusthanas. That is a classification, and it is as far as the text goes; BPHS gives no house-by-house reading for this chart. A house number here is also only as reliable as the birth time, since a three-minute shift in the sample moves every graha one house.

The same-sign list

The list at the foot of the result names every point whose D45 sign equals its Rasi sign. The field in the code is called vargottama, but the classical term is narrower. The note to BPHS Ch. 36 Sl. 38-39 defines Vargottama as a graha occupying the same Rasi and the same Navamsa, so the classical test belongs to the Navamsa (D9) chart. A match in D45 is a fact about arithmetic: the point sits in one of the three or four parts of its sign that count back to that sign. Which parts those are depends on the element of the sign.

One in twelve is what chance alone would give, since a point has to land in one of twelve signs. With ten points in a chart, most charts will show one match or none, and the sample shows one: Mars, in the 4°00'-4°40' span of Gemini. The engine attaches no score to it.

Rahu and Ketu together

Rahu and Ketu will always share a D45 sign and house on this page. The engine places Ketu exactly 180 degrees from Rahu, so they are at the same degree of opposite signs, opposite signs have the same modality, and the same degree counted from the same starting sign gives the same result. It is a property of the rule and carries no extra meaning for a particular chart. The same happens in D16, for the same reason.

When no chart is shown

The handler for this calculator requires an Ascendant, which needs a birth time and a resolved birth place. Without either, it returns no chart at all. The underlying routine could still place the nine grahas by sign without houses, but at this resolution a noon-cast Moon and Sun would often be wrong, so the page declines. The same applies inside the Kundali feature, where the D45 chart is not computed when there is no Ascendant. If you do not know your time, the article on unknown birth times explains what still holds.

D45 inside the sixteen-chart strength score

BPHS Ch. 7 builds a twenty-point strength, Vimshopaka Bala, from four different sets of divisions. D45 is absent from three of them. The Shad Varga and Sapta Varga of Sl. 17-19 do not include it, and neither does the Dasha Varga of Sl. 20. It enters only when all sixteen are taken together in Sl. 21-25, where Hora, Trimshamsa and Dreshkan carry 1 each, Shodashamsa 2, Navamsa 3, Rasi 3.5, Shashtiamsa 4, and "the rest of the nine divisions each a half". D45 is one of those nine. Half a point in twenty is 2.5 per cent of the score.

The engine implements exactly that sixteen-chart scheme and checks at load that the weights total twenty. For each of the seven grahas from the Sun to Saturn it takes the D45 sign, grades it on the dignity scale shared with Shad Bala - 10 for exaltation or Moolatrikona, 7.5 for own sign, 6.25 for a friendly sign, 5 for neutral, 0 for an enemy or debilitation sign - and multiplies the weight by that grade over ten. So D45 can add 0.5, 0.375, 0.3125, 0.25 or nothing to a graha's total. Rahu and Ketu are left out, because the engine keeps no dignity table for them. On the sample chart the D45 row comes out as follows.

Two things stand out. Jupiter earns the full half-point in D45 and still has the lowest total of the seven, while the Moon earns nothing in D45 and has the second highest, behind Venus. A weight of 0.5 cannot move a twenty-point score far; the bands BPHS sets in Ch. 7 Sl. 26-27 are five points wide. And Mars, the one same-sign match on the D45 page, grades only as neutral here, because being in the same sign as in the Rasi chart says nothing about dignity when that sign is not one the graha is strong in. The match and the grade are separate facts.

Birth-time sensitivity, measured

The page warns that a birth time a few minutes out can move the D45 Lagna. To see how few, the engine was run on the sample birth with the clock shifted and everything else held fixed. Around 06:42 on that morning in Ahmedabad the Ascendant was moving about 0.22 of a degree per minute, so it crossed a 40-minute part roughly every three minutes.

The Scorpio Lagna on the page holds for a window of about three minutes, from 06:41 to 06:43. Two minutes earlier it is Libra; two minutes later it is Sagittarius. Across the twenty-one minutes from 06:33 to 06:54 the D45 Lagna passes through eight different signs, and the Sun, whose own D45 sign stays Leo throughout, is counted in eight different houses. The row for 06:33 also shows the Ascendant itself appearing on the same-sign list, because the first part of Leo counts from Leo.

The Moon column shows a second kind of fragility that has nothing to do with the Ascendant. The Moon was moving about 0.58 of a degree an hour, so on its own it would cross a part in a little over an hour. But in the sample it sits at Libra 24.64, and the edge of its part is at 24°40', which is 24.67. Three minutes later the engine has it in the next part and its D45 sign is Taurus. The page states that the Moon is modelled to about 0.1 of a degree, which is larger than the gap to that edge. For this particular birth, then, the Moon's D45 sign of Aries is within the model's own margin of Taurus, and another tool could reasonably show either.

A birth time rounded to the nearest five minutes is already wider than a whole D45 Lagna window in this sample. This is the plain reason to hold the house numbers lightly and to rely on the sign column for the slower grahas. The accuracy page and the methodology page describe the precision of the underlying positions.

Limits of this calculation

• The classical text gives this chart no topic of its own and no placement-by-placement readings, so the page offers none. Anything more specific would have to come from outside the sources this site uses.
• Degrees are rounded to two decimals before the division. A hundredth of a degree is 36 seconds of arc against a part of 2,400 seconds, so the rounding matters only for a point sitting almost exactly on an edge, as the sample Moon nearly does.
• Rahu and Ketu are taken from the mean lunar node. A tool using the true node can differ by more than a degree, which is more than one D45 part, so the node rows may not match another program.
• The presiding deities of BPHS Ch. 6 Sl. 31-32 are not computed, and neither is the beginning, middle and end gradient of Ch. 7 Sl. 13-16.
• The same-sign list is a comparison of two sign names. It is not the classical Vargottama, which BPHS defines against the Navamsa.
• BPHS Ch. 6 Sl. 42-53 sets aside the divisions of a combust, defeated or weak graha when counting good vargas. Neither this page nor the Vimshopaka score applies that exclusion; every graha is graded on its sign alone.

Where D45 sits among the other charts

D45 belongs with the finest divisions. BPHS pairs it with D60 for "all indications", it shares a starting rule with D16, and it sits beside D40 in the list. Running the four on the sample birth shows how differently they scatter the same ten points, even where the rules overlap. All of them are linked from the calculators index.

No point has the same sign in D16 and D45, although both counts start from the same sign for every point: the part widths differ, so the step counts differ. Each chart has its own same-sign matches - Mercury in D16, Jupiter and Saturn in D40, Mars in D45 - which is what one-in-twelve odds per chart would lead you to expect. Rahu and Ketu are together in D16, D40 and D45 and opposite in D60. If you want one divisional chart to study closely, the classical weight is on the Navamsa; the Navamsa article explains why. For the other modality-based chart, where the Fixed and Common starting signs are swapped, see Vimshamsa (D20).

More questions

Where exactly does the Akshavedamsa rule come from?

BPHS Ch. 6 Sl. 31-32. The verse gives the part as 1/45th of a sign, the starting signs as Aries, Leo and Sagittarius for Movable, Immovable and Common signs, and the presiding deities as Brahma, Shiva and Vishnu in an order that depends on the modality. The engine implements the first two and cites the verse in its source.

Does BPHS say D45 shows the father?

Not in the translation this site works from. Ch. 7 Sl. 1-8 says "all indications from both Akshavedamsa and Shashtiamsa" and gives parents to Dvadashamsa. Ch. 7 Sl. 39-43 places the father in the 9th house and the 9th from the Sun. The paternal-legacy label is a reading in common use that the page repeats as a label and does not compute.

Can I find the presiding deity of a part from this page?

Indirectly. Counting through the verse shows that a part landing in a Movable D45 sign is Brahma's, in a Fixed D45 sign Shiva's, and in a Common D45 sign Vishnu's, whatever the Rasi sign. The page does not print this and attaches no reading to it.

How precise does my birth time need to be for the D45 houses?

In the measured sample the D45 Lagna changed about every three minutes, and a three-minute shift moved every graha by one house. A time known only to the nearest five or ten minutes cannot fix the D45 Lagna. The D45 signs of the slower grahas do not depend on the clock to that degree and are the steadier part of the result.

Why does the D45 sign jump when a planet crosses into a new sign?

Inside a sign each 40-minute part moves the D45 sign forward by one. The next Rasi sign has a different modality and so a different starting sign, and the arithmetic works out to a jump of eight signs at every boundary: Sagittarius to Leo, Aries to Sagittarius, or Leo to Aries.

Is a planet on the same-sign list Vargottama?

Not in the classical sense. The note to BPHS Ch. 36 Sl. 38-39 defines Vargottama as the same Rasi and the same Navamsa. The list here only records that the D45 sign equals the Rasi sign, which happens for one part in twelve across the zodiac.

Why might another program show a different D45 sign for my Moon or nodes?

A D45 part is two-thirds of a degree. The Moon is modelled here to about 0.1 of a degree, and Rahu and Ketu come from the mean node, which can differ from the true node by more than a full part. Differences in ayanamsa between programs shift every point as well. A point near a part edge can fall either side.

How much does D45 change my Vimshopaka score?

At most half a point out of twenty per graha, and nothing for Rahu and Ketu, which are not scored. In the sample it ranged from 0 for the Moon and Saturn to the full 0.5 for Jupiter. The bands are five points wide, so D45 alone rarely decides one.

Does the calculator read the D45 houses for me?

No. It numbers them and stops. BPHS classifies houses in general as Kendras, Kons and Dusthanas in Ch. 7 Sl. 33-36 and gives no house readings specific to this chart, so the page reports the placement and leaves it there.