Part of Fortune: How to Calculate It, Day and Night

The Part of Fortune, or Lot of Fortune, is not a body in the sky. It is a point of the zodiac worked out from three that are: the ascendant, the Moon and the Sun. You need nothing beyond those three longitudes, all in the same zodiac, and one decision that calculators do not all make the same way: whether the birth was by day or by night. This page sets out the arithmetic, works one birth through it four ways, and measures, over a year of sky at Delhi, how often the different choices give different signs.

The Two Formulas

For a day birth the lot is the ascendant plus the Moon minus the Sun. For a night birth, in the practice that the English Wikipedia article “Arabic parts” traces to Hellenistic and Arab astrologers, the Sun and Moon swap places: the ascendant plus the Sun minus the Moon. The same article notes that William Lilly, the seventeenth-century English astrologer, used the day formula for every chart. Both conventions are in use, and this site does not rule between them; a calculator should say which one it applies.

Add or subtract in degrees counted from 0° Aries, then take away 360° as many times as needed (or add it, if the sum went negative) to bring the result between 0° and 360°. Every 30° is one sign, counted from Aries.

Tajik annual-chart (varshaphal) practice computes a whole family of such points, the sahams, and its Punya Saham is the one rendered in English as the saham of fortune. That is as far as this page goes with it: the saham rules belong to a different system and none of them is computed here.

What the Formula Measures

Rearranged, the day formula says: lot − ascendant = Moon − Sun. The right-hand side is the Moon’s elongation from the Sun, the very angle that defines the lunar phase (see what moon phase was I born under). So the day lot sits exactly as far ahead of the ascendant, through the zodiac, as the Moon is ahead of the Sun. At a new moon the angle is 0° and the day lot falls on the ascendant itself; at a full moon it is 180° and the lot falls on the descendant.

The night formula measures the same angle the other way, backwards from the ascendant. The two lots are therefore mirror images across the line from ascendant to descendant: the code behind this page checks that at all 52,560 sample moments described below. They coincide only when the Moon and Sun are together or opposite, which is why the choice of formula changes the sign so often.

A Night Birth Worked Through

Take an imaginary birth at 23:10 IST on 3 September 1998 in Delhi (28.6139° N, 77.209° E). The Sun was 50° below the horizon, so by any test this is a night birth. The ascendant comes from the site’s lagna code and the Moon and Sun from its ephemeris; the sidereal column takes off the Lahiri ayanamsa, 23.84° for this date, as the site’s kundli does. The tropical column is the zodiac Western astrology uses.

In the tropical column the day formula reads 69.17 + 304.73 − 161.02 = 212.88°, which is Scorpio 2°52′. The night formula reads 69.17 + 161.02 − 304.73 = −74.54°; adding 360° gives 285.46°, Capricorn 15°27′. The Moon was 143.7° ahead of the Sun, a waxing gibbous moon, and both lots stand that far from the ascendant, one on each side.

The sidereal column needs no new arithmetic. Two of the three inputs carry the ayanamsa with a plus sign and one with a minus, so the sidereal lot is simply the tropical lot less one ayanamsa, like any planet. That is enough to move it a sign here, as it moved the ascendant from Gemini to Taurus. One birth, one minute, four answers: Scorpio, Libra, Capricorn and Sagittarius, depending on the formula and the zodiac. For this night birth, a calculator that reverses the formula by night prints the night-formula row; a calculator using the day formula for everyone prints the other row. The Lahiri ayanamsa page explains the size of that offset and why it grows each year.

Day or Night: Two Tests That Disagree

The article cited above defines a day chart as one with the Sun above the horizon. Calculators test that in two ways. One computes the Sun’s altitude. The other looks at the Sun’s house: houses 7 to 12 are the half of the chart above the horizon, so a Sun in those houses is called a day birth. With whole-sign houses, the scheme the site’s kundli uses, the two tests do not always agree.

The reason is that the horizon cuts the zodiac at the ascendant degree, not at the start of the ascendant’s sign. A Sun in the rising sign but at a lower degree than the ascendant has already risen; whole-sign houses still put it in the 1st house, below the horizon. Likewise, a Sun in the descendant’s sign but at a lower degree than the descendant has already set, yet the house count puts it in the 7th, above the horizon. Sampling Delhi every 10 minutes through 2027, 52,560 moments in all:

• the Sun was above the horizon at 50.2% of moments
• the altitude test and the whole-sign house test disagreed at 8.4% of moments, about one in twelve
• every disagreement had the Sun in the 1st or 7th house: 50% of the 1st-house moments and 50% of the 7th-house moments; a Sun in any of the other ten houses never produced one
• in the 1st house the Sun was up while the houses said night; in the 7th it was down while the houses said day

Because the house test then picks the other formula, the lot’s sidereal sign itself changed at 7.7% of moments between the altitude test and the house test. A third, smaller source of difference is where the horizon is drawn. The figures here use the Sun’s centre on the geometric horizon; the conventional visible sunrise and sunset put the Sun’s centre a little under a degree lower, because of refraction and the Sun’s disc. Those two definitions differed at 0.5% of moments, about 8 minutes a day split between dawn and dusk.

How Often the Choices Change the Sign

The same 52,560 Delhi moments of 2027, taken one every 10 minutes, are a share of time, not of people. Each row compares the sign the lot falls in under two choices:

The two formulas agree on the sign at only 8.3% of moments; the two mirror-image points meet only at new and full moon. The zodiac choice moves the sign about four times in five, because the ayanamsa is most of a sign. The “day formula for all” row is a little under half: by day the two methods are identical, so the whole difference comes from the night moments. So before comparing your result with a friend’s calculator, check three settings: zodiac, formula and the day-night test.

Birth Time Decides It

Over a few minutes the Moon and Sun hardly move, so the lot moves almost entirely with the ascendant: across the 2027 sample the day-formula lot ran only about 3% faster than the ascendant itself, and the night-formula lot runs about as much slower, since it subtracts the same gain of the Moon on the Sun that the day formula adds. At Delhi the ascendant takes on average about 4.0 minutes of clock time to move one degree and about 120 minutes to move a sign. The rate is not even: at its quickest it covered a degree in 2.8 minutes, at its slowest in 4.7. A birth time rounded to the nearest quarter hour can be up to seven and a half minutes out, enough to shift the lot by as much as 2.8°, and when the lot lands near a sign edge, only an accurate birth time settles which sign it is in. The method for the ascendant itself, step by step, is on how to calculate lagna manually.

Finding Your Own Inputs

The ascendant calculator gives the rising sign and degree, tropical and sidereal, for a birth in one of its listed places. The free kundli, which needs you to sign in, prints the sidereal longitudes of the lagna, the Moon and the Sun, which are the three numbers the formula needs. Neither tool prints the lot itself, so the addition is yours to do. The annual-chart counterpart of a birth chart, and the instant it is cast for, is on varshphal and the varsh pravesh time.

What This Page Does Not Give

No meaning for the lot in any sign or house, nothing about wealth, luck or well-being, and no other lot or saham. The calculation can say where the point is; what anyone says the point signifies is a claim no longitude can check, so this page stops at the position.

In Brief

• Day formula: ascendant + Moon − Sun, reduced to 0°–360°
• Night formula: ascendant + Sun − Moon, the Hellenistic reversal; some authors never reverse
• Geometry: the lot stands the Moon’s phase angle from the ascendant, ahead by day, behind by night
• Day or night: Sun’s altitude above zero; a whole-sign house count can misjudge a Sun in the 1st or 7th
• Zodiac: sidereal lot = tropical lot − ayanamsa
• Precision: the lot moves with the ascendant, about a degree every four minutes of birth time