A Kerala astrologer sweeps three small heaps of cowrie shells into one on a wooden board while a boy holding a palm-leaf bundle watches.

Sphuṭas and bindus

Sphuṭas and bindus derive new zodiac points by arithmetic on existing positions. Mạghā calculates fifteen in the planetary ledger, drawing on Praśna Mārga, Phaladīpikā and later sources. Each formula needs its own interpretive basis beyond the resulting degree.

Ascendant Libra 0°45′38″

Moon Capricorn 24°15′13″

Gulika Libra 17°51′17″

Sum 672°52′08″ − 360°

Tri Sphuṭa Aquarius 12°52′08″

+ Sun Virgo 26°40′23″ → Catuḥ Sphuṭa Leo 9°32′31″

+ Rāhu Libra 22°09′41″ → Pañca Sphuṭa Pisces 1°42′12″

Nila Raman’s birth chart

Each step from Tri to Pañca Sphuṭa adds one more planet

Praśna Mārga (chapter 5) builds a chain. Tri Sphuṭa, the triple point, adds the longitudes of the ascendant, the Moon and Gulika. Add the Sun and you have Catuḥ Sphuṭa, the fourfold point; add Rāhu and you have Pañca Sphuṭa, the fivefold point. Whenever a total passes 360°, one full circle comes off.

Nila's ascendant, Moon and Gulika add up to 672°52′. Less 360°, that leaves 312°52′, so her Tri Sphuṭa sits at Aquarius 12°52′ in Śatabhiṣā. Adding the Sun carries it to Leo 9°32′, and adding Rāhu to Pisces 1°42′.

The text then judges a question partly by the sign, navāṁśa and nakṣatra that hold Tri Sphuṭa, and times events by the Sun's and Moon's transits through its sign.

A young woman offers betel leaves to an astrologer on a veranda while an old man sits up on a cot in the room behind.

Prāṇa Sphuṭa counts the ascendant five times

The same chapter of Praśna Mārga gives three weighted sums. Prāṇa Sphuṭa (breath) is the ascendant times five plus Gulika. Deha Sphuṭa (body) is the Moon times eight plus Gulika. Mṛtyu Sphuṭa (death) is Gulika times seven plus the Sun. Chapter 6 adds all three together to make Sūkṣma Tri Sphuṭa, the subtle triple point.

These are horary tools. Praśna Mārga computes them for the moment someone asks about an illness, then compares them to judge the chance of recovery. Mạghā applies the same formulas to any chart, including a birth chart, and its Praśna charts have their own Sphuṭas tab. Nila's Prāṇa Sphuṭa falls at Aries 21°39′ and her Mṛtyu Sphuṭa at Leo 1°39′.

At dawn a young couple sow a ploughed field, the husband scattering seed from a pouch and the wife pressing soil into a furrow.

Phaladīpikā reads fertility from Bīja and Kṣetra Sphuṭa

Mantreśvara's Phaladīpikā (chapter 12) adds three planets to judge the capacity for children. For a man, the Sun, Venus and Jupiter are added, a sum called Bīja Sphuṭa (seed), and an odd sign in an odd navāṁśa shows strength. For a woman, the Moon, Mars and Jupiter make Kṣetra Sphuṭa (field), and an even sign in an even navāṁśa does. A mixed result, he writes, brings children only after effort.

Nila's Kṣetra Sphuṭa falls in the last degree of Scorpio, an even sign, and its navāṁśa is Pisces, also even. To see any sphuṭa's navāṁśa in Mạghā, switch the Planetary ledger's chart menu from D1 to D9, and every row moves to its place in that chart.

A young woman on temple-tank steps sits with a palm-leaf book as a waxing Moon rises over a gateway tower and the Sun sets across the water.

Tithi and Yoga sphuṭas turn the almanac's arithmetic into points

Three of the fifteen appear in P. V. R. Narasimha Rao's Jagannatha Hora program, which defines Tithi Sphuṭa as the Moon minus the Sun, Yoga Sphuṭa as the Moon plus the Sun and Rāhu Tithi Sphuṭa as Rāhu minus the Sun.

The first two hold the numbers behind the Pañchāṅga. Each 12° of the Moon's lead over the Sun is one lunar day (tithi), and each 13°20′ of their sum is one of the 27 yogas. Nila's Tithi Sphuṭa, at Cancer 27°34′, lies 117°34′ from the start of Aries, so nine whole tithis had passed and she was born on the tenth, Śukla Daśamī. Her Yoga Sphuṭa, at 110°55′, falls in the ninth yoga, Śūla. Both agree with the Pañchāṅga of her birth.

Yoga Sphuṭa (Sun + Moon) Cancer 20°55′

+ 93°20′

Yogi Sphuṭa Libra 24°15′ · Viśākhā · lord Jupiter

+ 186°40′

Avayogi Sphuṭa Taurus 0°55′ · Kṛttikā · lord Sun

Yogi and Avayogi points

Yogi Sphuṭa adds 93°20′ to Sun plus Moon; Avayogi adds another 186°40′. De Fouw and Svoboda describe this pair in Light on Relationships. Their nakṣatra lords traditionally signify fortune and obstacles. Some teachers use another Avayogi rule, so check the method.

Nila's Yogi Sphuṭa is at Libra 24°15′ in Viśākhā, a nakṣatra ruled by Jupiter, and her Avayogi Sphuṭa at Taurus 0°55′ in Kṛttikā, ruled by the Sun. Mạghā shows each point with its nakṣatra and pāda; the two planets follow from the nakṣatra lords.

Rāhu Libra 22°09′

Moon Capricorn 24°15′

Arc 92°06′ forward from Rāhu

Half 46°03′

Bhṛgu Bindu Sagittarius 8°12′ · Mūla

Shorter-arc rule: opposite side only when the arc exceeds 180°.

Bhṛgu Bindu halves the arc from Rāhu to the Moon

Bhṛgu Bindu comes from Nāḍī astrology, not the classical horā texts, and is often traced to C. S. Patel's books on the Nāḍīs. Measure forward from Rāhu to the Moon, halve the distance and add it to Rāhu. Nāḍī readers then watch slow planets, Jupiter and Saturn above all, as they cross the point.

Nila's Moon is 92° ahead of Rāhu, so her Bhṛgu Bindu falls 46° past Rāhu, at Sagittarius 8°12′ in Mūla. Mạghā always counts forward from Rāhu. Some programs take the shorter arc between the two instead. The results agree whenever the Moon is less than 180° ahead, as Nila's is, and fall exactly opposite each other when it is further.

An astrologer sets a brass marker on a plain wooden disc at a teak desk beside a laptop and an open palm-leaf manuscript.

Mạghā adds all fifteen as rows in your Planetary ledger

Select all fifteen Sphuṭas & Bindus or individual points in the Planetary ledger. Rows include sign/degree, whole-sign house and nakṣatra/pada; D1 overlays allow five markers.

The seven Praśna Mārga sphuṭas use Mạghā's start-of-Saturn-part Gulika. Raman's reading identifies Gulika with a later Māndi moment, so strict text-based calculations differ. These points also respond quickly to birth time: four minutes moves Nila's Prāṇa Sphuṭa about 5°.

Questions about sphuṭas and Bhṛgu Bindu

What is a sphuṭa in astrology?

Sphuṭa means a true longitude: the exact position of a planet or point along the zodiac, in degrees. The derived sphuṭas on this page are new points made from other longitudes by adding, subtracting, multiplying or halving them. Each family has its own purpose, from Praśna Mārga's questions about illness to Phaladīpikā's fertility rule, so read each by the text that defines it.

How do you calculate Bhṛgu Bindu?

Take the sidereal longitudes of Rāhu and the Moon, counted from 0° Aries. Subtract Rāhu from the Moon, adding 360° if the result is negative, then halve it and add the half to Rāhu. For Nila: Rāhu 202.16°, Moon 294.25°, difference 92.09°, half 46.05°, total 248.21°, which is Sagittarius 8°12′. Mạghā gives the result with its nakṣatra.

What is the Avayogi planet?

In modern teaching, it is the lord of the nakṣatra that holds the Avayogi point, 186°40′ beyond the Yogi point. In Mạghā, read the nakṣatra on the Avayogi Sphuṭa row and take its lord. Nila's Avayogi Sphuṭa is in Kṛttikā, a nakṣatra ruled by the Sun, so her Avayogi planet is the Sun. Teachers differ on the Avayogi rule, so confirm which one a book follows.