Whole Sign vs Equal vs Placidus Houses, Compared

The same birth can put the same planet in two different houses, and nothing in the sky has to change for that to happen. Only the rule for drawing the twelve house boundaries changes. This page states four of those rules as arithmetic, applies all four to one imaginary birth, and then counts, over a full turn of the sky at six Indian cities, how often a point of the zodiac lands in a different house under one rule than under another. At Delhi the whole-sign house and the Placidus house disagree for 52% of the points sampled.

Four Rules for Drawing Twelve Houses

Every system starts from the ascendant, the degree of the zodiac rising on the eastern horizon at the birthplace. Two of them also use the midheaven (MC), the degree crossing the meridian overhead, and its opposite, the IC. Beyond that they part ways:

• Whole sign. The sign holding the ascendant, all of it from its 0° to its 30°, is the 1st house; the next sign is the 2nd, and so on. The ascendant’s degree decides nothing except which sign that is. This is the count used for every chart on the site’s houses pages.
• Equal house. The 1st house begins at the ascendant degree itself, and every later house begins 30° further on. Each house is a full sign wide but straddles two signs.
• Porphyry. The ecliptic arc from the MC forward to the ascendant is cut into three equal pieces, and so is the arc from the ascendant on to the IC; the opposite houses mirror them. The MC is the 10th cusp and the IC the 4th.
• Placidus. Here the division is made in time, not in longitude. Each degree of the zodiac takes a certain time to travel from the eastern horizon up to the meridian (its diurnal semi-arc). The 12th cusp is the degree that has covered one third of that journey, the 11th the one that has covered two thirds; below the horizon the 2nd and 3rd cusps are found the same way on the night half of the arc. Like Porphyry, it puts the MC on the 10th cusp.

These are conventions, not measurements. The site’s kundli pages count by whole sign; Western astrologers work with all four, and with others such as Koch and Campanus that this page does not compute. The equal house here is not quite the equal bhava of the bhava chalit chart: that scheme makes the lagna degree the middle of the 1st bhava, where the Western equal house makes it the start.

The site’s code finds the Placidus cusps by repeated approximation, then finds them again a second, independent way, by bisecting along the ecliptic for the degree whose hour angle is exactly the right fraction of its semi-arc. Over 8,480 cusps at latitudes from the equator to 60° N the two answers agree to better than a millionth of a degree. At the equator every semi-arc is a quarter-turn, so the Placidus cusps fall at steps of exactly 30° of right ascension from the meridian, and the code checks that too. At 67° N, beyond the polar circle, part of the zodiac never rises or never sets, and Placidus has no answer at all for part of the day; every city in the census below is far south of that.

One Birth, Four Sets of Cusps

The birth is the imaginary one used in how to calculate lagna manually: 09:20 IST on 8 July 1992, Delhi. That page derives its sidereal lagna, 10°51′ Leo, and the midheaven page derives its MC, 9°20′ Taurus. Every position below is sidereal, with the Lahiri ayanamsa of 23.8° subtracted; in the tropical zodiac the same ascendant reads 4°37′ Virgo and the MC 3°06′ Gemini, and every other cusp shifts by the same amount.

Three things stand out. The 1st, 4th, 7th and 10th cusps of Porphyry and Placidus are identical, because both systems take the four angles as given and differ only in how they fill the quarters between them. The equal 10th cusp is not the MC: it misses it by 1.5°. And the house sizes differ. Porphyry’s houses here come in only two widths, 29.5° and 30.5°, three of each per half of the chart; Placidus’s run from 26.4° (the 1st and 7th) to 32.1°. The largest gap between a Porphyry cusp and the matching Placidus cusp is 3.1°.

Now the Sun and the Moon of that birth, from the site’s own position code. The Sun is at 22°29′ Gemini and the Moon at 5°39′ Libra.

The Sun sits in the 11th house whichever rule is used. The Moon does not. By whole sign it is in the 3rd, because Libra is the 3rd sign from Leo. In the other three systems the 3rd house only begins part of the way into Libra (10°51′ Libra equal, 9°51′ Libra Porphyry, 7°15′ Libra Placidus), and a Moon at 5°39′ of the sign has not reached any of those cusps, so each of them counts it in the 2nd.

How Often the Systems Disagree, City by City

One chart shows that the rules can disagree; a census shows how often. For each latitude the code steps the local sidereal time through a full turn in 720 equal steps and, at each step, places 360 evenly spaced points of the zodiac in their houses under all four rules, with the obliquity and ayanamsa of 1 January 2026. The six cities are from the site’s city list, from its southernmost, Thiruvananthapuram, to its northernmost, Jammu. The equator and 50° N are added for reference; no listed city lies at either. The shares are shares of this grid of sky positions and zodiac points, not of people or births.

The first three columns all sit close to one half, and that is mostly the whole-sign rule’s doing, not latitude’s. Against the equal house the arithmetic is exact: when the ascendant is d degrees into its sign, a share d ÷ 30 of every sign falls in the house before its whole-sign house, and the census checks this at every step. The ascendant’s degree runs through the whole sign over the day, so the average is a half at every latitude. Placidus and Porphyry add their unequal widths on top, which pushes the disagreement only a little higher: across the six cities the whole-sign against Placidus share moves within 1.6 percentage points, and it is only by 50° N, at 57.3%, that it stands clearly above every city.

What does grow steadily with latitude is the unevenness of Placidus. At Thiruvananthapuram its houses range from 26.4° to 34.4°; at Delhi, 22.6° to 41.0°; at Jammu, 21.7° to 43.0°. Even on the equator they are not all 30° (27.6° to 32.6°), because equal steps of right ascension are not equal steps of longitude. With the unevenness comes a rare case: a point two houses apart between whole sign and Placidus, 1.6% of the grid at Delhi and 2.1% at Jammu.

Placidus vs Porphyry

The two quadrant systems share all four angles, so they can only disagree inside a quadrant, near the intermediate cusps. That disagreement rises with latitude at every row of the table: from 3.0% of points at the equator to 6.8% at Delhi and 8.0% at Jammu, under one in ten at every listed city, and 14.7% at 50° N. The widest gap between matching cusps over the day grows the same way, from 3.5° at Thiruvananthapuram to 8.0° at Delhi and 20.5° at 50° N. Porphyry’s house widths stay inside Placidus’s range at every city: at Delhi, 24.4° to 35.6° against 22.6° to 41.0°.

Tropical or Sidereal: Which Houses Change

Equal, Porphyry and Placidus cusps are fixed by the horizon and the meridian. Switching from the tropical zodiac to the Lahiri sidereal one relabels every cusp and every planet by the same 24.2°, so no point changes house; the census confirms that for Placidus at every step. Whole-sign houses are different, because their boundaries are the sign boundaries themselves, and those move against the horizon when the zodiac changes. A point changes whole-sign house when exactly one of it and the ascendant crosses a sign line in the switch. Over the census that happens for 32% of points at Delhi, and within two percentage points of 31.1% at every latitude, which is the share expected for a 24.2° shift if the two degrees within their signs were independent and evenly spread. The worked Moon shows it: by tropical whole sign it is in the 2nd house, by sidereal whole sign in the 3rd.

Is One System More Accurate?

Not in any sense arithmetic can check. Each rule is a definition, and each puts its cusps exactly where it says it will; the code above confirms that and nothing more. A claim that one system describes lives better than another is a claim about readings, which a geometry census cannot test. The choice follows the tradition a practitioner works in. The guide to the 12 houses sets out the whole-sign count the site’s kundli pages use, and the vertex page works another horizon-based point with the same city set.

What This Page Does Not Give

Nothing here says what a planet means in a house, under any of the four rules, or what it means when a planet changes house between them. The worked chart belongs to no one. No Koch, Campanus or Regiomontanus cusps are printed, because none was computed.

In Brief

• Whole sign: houses are signs, counted from the ascendant’s sign
• Equal: 30° houses starting at the ascendant degree
• Porphyry: each quadrant between the angles cut into three equal arcs of longitude
• Placidus: each quadrant cut into thirds of time on every degree’s semi-arc; MC on the 10th cusp
• Worked birth: the Sun in the 11th in all four; the Moon 3rd by whole sign, 2nd in the other three
• Census at Delhi: whole sign and Placidus disagree for 52% of points; Placidus houses run 22.6° to 41.0°
• Zodiac: only whole-sign houses change between tropical and sidereal, for about 32% of points