One of the greatest misconceptions spread in astrology today is the concept of Divisional Charts and Houses. It is probably one of the strongest misconceptions which is so rampant today that it is the first thing a beginner in astrology is introduced to.

Through all my experience as a professional astrology, almost every beginner in astrology who comes for a consultation wants to know an answer to what would Jupiter do in the 8th house of Navamsha (D-9) or what does Sun in the 10th house of Dwadashamsha (D-12) mean.

This is a question that cannot be answer accurately by anyone. Simply because the question is absolutely, completely wrong and has no basis in astrology. There is no mathematical concept that supports it and no astrological texts that mentions it. Not one, in the entire literature of astrology that spans several thousand years!

The idea that a planet in a particular division is also in some “house” in that division, is a modern construct by astrologers who never bothered learning the true mathematical and astronomical principles behind astrology. With the advent of computers and even before that with printed and published Almanacs being available in the market, astrologers simply stopped learning the mathematical principles. Today, we may have a lot of advanced software to calculate horoscopes within a second, but we’ve left the mathematical skills needed by an astrologer to actually interpret the horoscopes far far behind.

So, this blog post is an attempt to bring to light those very mathematical concepts that form the backbone of astrology. And the irony of the situation is, these fundamental and basic mathematical principles will be introduced to the readers (probably for the first time) who otherwise have an understanding of the more advanced astrological concepts.

**Definition of houses:**

So the first question that comes up is, what exactly are houses? Are they signs? Are they different form signs? Where do they begin, where do they end? Now there are multiple house systems. So just to clarify, I am using Sripati Paddhati in my answer. Others can try using the same rules for other house system as well, mathematical calculation varies for these, the concept is the same.

Sripati Paddhati for reference is the Indian system of houses used through Vedic astrology. The rules were compiled by Acharya Sripati in its current form who is attributed to be a descendant of Maharishi Kashyapa.

Now, moving forward:

A house or a bhava is defined as an arc that rules a specific area of life. Just as there are 12 signs, there are 12 houses divided across the 360 degree of signs. Each of these arc, called as a house, rules an area of life. As is commonly known, the first house is self, second is wealth, third is courage, fourth is home and so on.

However, the houses are not equal. Unlike signs, these are not 30 degrees each. To understand, see the image below:

The zodiac (the 12 signs) are star clusters in the sky. They are defined by the constellations that make them and they are fixed.

Houses are the sky as visible from the earth. And depending on where you stand on the Earth, you’ll be able to see more than one sign in a single house or two or more houses in one sign.

If you see at the image above, the colored belt is the zodiac. And the diagram shows the division of houses. If you see the 4th house, (the triangle with 4 written), it covers approximately 2.5 signs. If you see the 2nd house, it covers half a sign. This skewness is a result of distance from the equator. Why it happens, I’ll explain below. But first, we need to know the mathematics of it.

**There is absolutely no text in astrology that says each sign can be taken as a house. Every single text has its own method of calculating houses and any time any astrologer tries to say that for a person born in Gemini Ascendant, Cancer sign is the 2nd house, Leo sign is the 3rd house and so on, is making a grave error that directly violates all written works on Vedic Astrology. **

**Calculation of Houses:**

The lagna which is found out through Poorvanata on Lankodaya by means of traversed degrees etc. through the Paschimanat on Lankodaya by means of the traversed degrees that is the 10th house. 6 signs added to the 10th house gives the 4th house.

The Ascendant is deducted from the 4th house, and the 4th house deducted from the 7th house. Both the resultants are divided by 3 separately. The first figure arrived at is multiplied by one and two and is added to the 4th house. In this way, there will be 6 houses.Brihat Parashara Hora Shastra, Chapter 5, Verse 21-24

The half of the summation of the former and latter is called Bhava Sandhi. In this way, by adding 6 signs in the 6 houses and 6 Sandhis, all the other houses and sandhis will be known.

All calculations by mathematics require a few given quantities. Like, to calculate speed, you need the distance traveled and the time taken. To calculate force, you need mass and acceleration.

Simiarly, to calculate the houses, you need two points:

- Ascedant (the eastern horizon, the point from where sun rises)
- Zenith (Cusp of 10th house, the point exactly above our head in the sky; also known as Mid-heaven)

Based on these two, you derive two more quantities:

- The descendant (the western horizon, the point from where the sun sets): Mathematically it is taken as Ascendant + 180 degrees. If Ascendant is 1 degree Aries, descendant become 1 degree Libra.
- Nadir or Patala (the point exactly below us, the opposite of Mid-Heaven): Again, mathematically it is the opposite of Zenith or Zenith + 180 degrees.

Now, when we have these four points, we use these as the way of calculating the houses by division. To explain:

- Ascendant becomes the cusp of first house (cusp means a point, a house is an arc or a span of several degrees, whenever we refer to one specific point, it is called a cusp)
- Zenith is the cusp of 10th house
- Descendant is the cusp of 7th house
- Nadir is the cusp of 4th house

Now, to explain it astrologically in a chart:

Lets take an ascendant to be 15 degrees Aries, descendant will become 15 deg Aries + 180 degrees, or 15 deg Libra. Lets take Zenith as 15 degrees Capricorn, so Nadir will become 15 degrees Cancer.

Now, the difference between the ascendant and Zenith, (15deg Capricorn to 15 deg Aries) is 90 degrees. Hence, the 90 degrees need to be divided into 3 equal halves to give the cusps of 11th and 12th houses respectively.

So,

90/3 = 30

Hence, beginning from 15 deg Capricorn, the cusp of the next house (11th house), becomes 15deg Capricorn + 30 degrees. This gives us 15 degrees Aquarius.

Adding 30 degrees to it again we get 15 degree Pisces as the cusp of 12th house.

Adding 30 degrees again we come back to the cusp of first house at 15 degrees Aries.

Similarly, you can calculate for all the houses. Take the difference between Ascendant and first house, divide by three, add that value to the degree of Ascedant to get the cusps of 2nd and 3rd houses. And so on.

Ultimately, you will get the below house configuration.

Now, there are two ways forward:

**Cusp as middle of the house:**Sripati Paddhati says that cusps are the middle of the house. We arrived that the house span is of 30 degrees (the value of Ascendant minus zenith divided by three that we calculated is the bhava length). So if we find out the houses by Sripati paddhati, the houses will span from plus 15 degrees of the cusp to minus 15 degrees of the cusp. For example:- If Ascendant is 15 deg Aries: The first house becomes 0 deg Aries to 30 degree Aries
- If 2nd house Cusp is 15 degree Taurus: The 2nd house becomes from 0 deg Taurus to 30 degree Taurus

**Cusp as start of the house:**The Placidus system of houses (calculations differ for the system) and the KP system based on it say that cusps are the beginning of the house and the house spans from the cusp to the next cusp. For example:- If Ascendant is 15 deg Aries: The first house starts from 15 deg Aries itself and goes to 15 deg Taurus (plus 30 degrees)
- If 2nd house Cusp is 15 degrees Taurus: The 2nd house starts from 15 deg Taurus and goes to 15 deg Gemini

In this way, the houses are calculated. However, there is a difference. The shape of the earth is not how I showed in the above diagrams. It is this:

The Sun does not rise from the exact East, travels linearly to the point above and then sets in the exact west. The path of the sun is this:

Now, taking the above case:

The distance between the Ascendant (eastern horizon) and the Zenith (the mid-heaven) is not always the same. Hence, the houses are not always 30 degrees.

It is possible that the difference between Ascendant and Zenith can be as low as 60 degrees for some places during some time of the year. So then, the 10th house, 11th house and 12th house would be of 20 degrees each. While the 8th house, 9th house etc. could be of 40 degrees each.

Now, we come to the divisional charts:

For the sake of clarification I’ll use the Western Circular chart, and South indian chart. It is easy to represent navamshas in them:

So, in a horoscope, the situation is like this:

This is a chart of today. Lagna is 15 degrees Gemini. 7th cusp thus becomes 15 degrees Sagittarius.

The North Indian chart for this is:

And considering one divisional chart, (the D10), the chart is this:

Now, in order to calculate houses for divisional charts, we need the following:

- Ascendant Cusp (D10 lagna)
- 7th House Cusp
- 10th House Cusp
- 4th House Cusp

But there is a problem with that. Do you see it? I’ll explain:

- We need the degree of the lagna. Because the horizon of the Earth is at the 15th degree of Gemini, we say that 15 degrees Ascendant is the Lagna or the Ascendant. For D10 however, the rule says that 15th to 18th degree makes up one dashamsha (d10). For Gemini ascendant, th 6th dashamsha (15–18 degrees) falls in Scorpio. But then, in the dashamsha chart, how do we define the exact degree of lagna?
- 7th house cusp is where the Sun sets in the sky. 7th house is the house diametrically opposite the ascendant and complements the ascendant/lagna (spouse, business partners, etc.) However, in the D10, the lagna is Libra and the 7th sign from it has no definition. For a divisional chart, the 7th sign is not 180 degrees apart. And remember, Libra dashamsha falls in Cancer as well. Leo as well and many other signs. How do we define the 7th house cusp?
- Similarly, where is the mid-heaven? In the sky, mid-heaven falls at 2 degrees Pisces. But Pisces here becomes the 8th sign. The 10th sign of Dashamsha, which is the cancer, does not have mid-heaven cusp. What to use to calculate the house?
- One solution is to use the cusp of the 10th house and 7th house just as we place the lagna. If lagna is at 15 degrees Gemini, we place it in the Libra Dashamsha. Likewise, we can place the respective cusps in the division.

This way, the distribution of the various cusps becomes:

- 1st house cusp in D10: Scorpio
- 2nd house: Sagittarius
- 3rd house: Libra
- 4th house: Taurus
- 5th house: Sagittarius
- 6th house: Aries
- 7th house: Taurus
- 8th house: Gemini
- 9th house: Aries
- 10th house: Scorpio
- 11th house: Gemini
- 12th house: Libra

The chart will become like this:

All divisional charts will end up with two or more house cusps falling in a particular house and others being blank.

Alternatively, we can do another thing. We can take the cusp of 1st house and 10th house and calculate the three houses between them. We can take:

3 degrees of Rashi chart = 30 degrees of D10 chart (because 3 degrees make up one dashamsha)

Thus: 1 degree = 10 degrees of D10

0.1 degree = 1 degree of D10

So if Ascendant falls at 15:00 degrees Gemini, in D10 it will be 00:01 Scorpio

If 10th house cusp falls at 14:18 degree Leo, in D10 it will be 20:25 Scorpio or (360 – 20.4) degrees Scorpio (Since D-10 is ahead of D1, we subtract 360).

So, we have the difference between the three houses as 339.6 degrees. Now, dividing it by three:

Span of a house = 339.6/3=113.2 degrees

So, the 10th house ranges from 20:25 deg Scorpio of D-10 to the entire Sagittarius sign, Capricorn Sign until the Aquarius Sign, until the 3rd degree of Pisces. The 11th house starts from 3.2 degree Pisces and goes up to 16.4 degrees of Gemini. And finally, the 12th house ranges from 16.4 Gemini to 0 degrees Scorpio in the D10 chart.

Which basically means, houses will overlap and expand several signs. Which is absurd.

Now, as of now we conclude two things:

- Houses cannot be calculated in divisional charts on their own.
- House cusps can be projected from their original Rashi chart position to the divisional chart; but in that case several houses will fall in the same sign and many signs will remain empty.

Now, coming to the next part:

**What do the textbooks say about divisional charts and houses?**

- Brihat Parashara Hora Shastra – Nothing
- Brihat Jataka – Nothing
- Jaimini Sutra – Nothing
- Most other textbook – Nothing

**But does some text ever mention divisional charts and houses?**

Yes! Jataka Parijata mentions houses in divisional chart. However, what it mentions is:

- The cusps of the houses in the rashi chart can be projected in the divisional charts
- Multiple cusps will fall in same houses but only those houses are relevant that are relevant to the divisional chart
- The plants conjunct the house cusps in divisional charts and the signs can be used to make assessment about the house.
- Houses do not exist in divisional chart itself. If someone has lagna in Aries navamsha, Taurus does not become the 2nd house, Gemini does not become the 3rd house and so on. As shown, it is mathematically impossible.

**Do Nadi texts mention divisional charts with houses?**

Yes! Dhruva Nadi does but only for navamsha. The principle is attributed to Maharishi Satyacharya. What it says is:

If for someone, Mercury falls in the navamsha in the sign of Taurus, and Taurus happens to be the 1st house in the Rashi chart; for such a person Mercury is said to be *lagnabhavayuktam *(conjunct the 1st house).

If likewise, any other planet falls in another sign and that sign happens to be 5th house; the planet is said to be *putrabhavayuktam *(conjunct the 5th house) and so on.

Such a planet will give the results of that house and will impact the results of that house based on its strength.

**What do authors of astrological softwares, who know the mathematics of astrology say?**

- Jagannatha Hora: You cannot create a Bhava Chart for a division
- Parashara Light: You cannot create a Bhava Chart for a division. Try selecting both together, it will not allow you. (Parashara light was created through consultations with K. N. Rao ji. He was the advising astrologer for the first version of Parashara Light. Yet, to this day the computers have not been able to calculate Bhavas for divisional charts. Several astrologers use the signs with bhavas but that further complicates the problem.
- Kala: Kala gives an option of using the house cusp and projecting them in divisions. It is as shown:

Lastly, **why exactly is it wrong to treat each sign as a house? Why do we need to go into the mathematics of it?**

It is so because either we say that astrology is 100% intuition and theories don’t exist. We discard all the rules and just say that astrology is divine knowledge of pure intuition, meditation and does not require studying. In which case there is no need to cast the horoscope even.

Or else, we say that theory and learning is needed for astrology. Even if intuition and understanding helps give the prediction, the horoscope must be cast by astronomical rules.

If we say that each sign is a house in divisional charts; we are making a statement that houses and signs are the same thing. Any sign rising in the eastern horizon will become the 1st house and subsequent signs will become the subsequent houses.

And when we say this, we make a great error. Because if signs and houses are equal, the theory must apply to the rashi chart as well.

If we are using houses and bhavas in both D1 and D9; it needs to mean the same thing. In D1 it cannot mean house cusps and in D9 it cannot magically change its meaning and say that houses mean signs. If we say that in divisional charts, houses are equal to signs, then we need to uphold the concept in rashi chart (D1) too.

And if we uphold the concept in rashi chart:

- If someone is born at 29:59 degree Aries, and Sun is at 0 degree Taurus, we need to say that Sun falls in the second and Lagna falls in the first house. We then need to say that Sun cannot affect the physical appearance of a person because it is the 1st house that affects the appearance and if signs are houses, 1st house ends at 30:00 Aries despite sun being just 0.001 degrees away.
- If someone is born with Moon at 29:59 Taurus and Venus at 00:01 Gemini, we need to say that the two planets are not in conjunction. Because Moon is in 2nd house and Venus is in 3rd house.
- If someone is born with ascendant at 0.01 degree Cancer, Mars is at 29:59 Gemini (just 0.01 degree apart) and Sun is at 29:59 degrees Cancer (almost 30 degrees apart), we need to say that Sun will have the strongest impact on his appearance and Mars will absolutely not impact the person. Because Sun is in the 1st house and Mars is in the 12th house.

Basically, accepting that signs are equal to Rashi, means we discredit all the rules of astrology ever written.

We cannot pick and choose concepts depending on what we like and what we hate. We cannot say that it is Sunny outside and the whether is clear but I got wet in Rain. If someone gets wet in rain, they need to accept that the sky was not clear but clouds were raining. If they say the weather was Sunny and clear, they cannot say they got wet in rain.

Likewise, if we say houses are equal to sign, we discard the importance of degrees entirely. If we say that degrees are important and houses need to be calculated; we need to accept that it is mathematically impossible for houses to exist in divisional charts.

So basically, there are two or three ways about it:

- Do not use the concept of houses in divisional charts. Stick to what 99% textbooks of astrology teach.
- Use the concept of either Dhruva Nadi or Jataka Parijata. Both are mathematically consistent, possible, valid and exist.
- Assume that houses are equal to signs and discredit that two planet who are 1 degree apart but in different signs are conjunct and that astrological textbooks are wrong.
- Say that in the rashi chart, houses exist as per the principles of Vedic astrology but in divisional charts it magically changes and houses become equal to signs which is mathematically impossible, unproven, never mentioned in textbooks and has no supporting logic for it other than the fact that someone chooses to believe in it.

Hope it helps all the learners.

## 2 Comments

Excellent article Arsh ji! Kudos to you for writing this wonderful mathematical explanation. None of my gurus nor his guru ever give importance to divisional charts. Modern-day astrologers heavily use divisional charts, probably due to the fact that software will provide all divisional charts with a click of a button. As you said, they should check the mathematical viability of houses in the divisional chart.

Dear Arsh Sir. As you said Jagannath Hore doesn’t create Bhava Chalit for Divisional Charts but I have myself seen that it creates. Infact, PVR N. Rao himself in a video showed to make Bhava chalit for Divisions. Can you please check this and elaborate?