Sun-Moon Midpoint: How to Calculate It, Near and Far

A Sun-Moon midpoint is a degree of the zodiac, not a body: the place exactly halfway between the Sun’s longitude and the Moon’s. Two numbers go in and one comes out, yet the same birth can still be given two different answers, because a circle has two halfway points and a careless average picks the wrong one. This page shows the arithmetic, works three charts through it, and counts, over a hundred years of sky, which sign the point tends to land in and how much a birth-time error moves it.

Two Midpoints, 180° Apart

Any two points on a circle split it into two arcs, a shorter one and a longer one, and each arc has a middle. The two middles always face each other across the circle. On this page the middle of the shorter arc is called the near midpoint and the other the far midpoint; “the midpoint” on its own means the near one, and the page says “far” whenever it means the other. The near midpoint is never more than 90° from either body, and it is the same distance from both. Only when the Sun and Moon stand exactly opposite are the two arcs equal, and then neither midpoint is nearer.

A calculator you compare against may follow a different rule, so check which of the two it prints: the near and far answers share the same degree within their signs and sit in opposite signs, six apart.

Where the Technique Comes From

The English Wikipedia article on midpoints in astrology gives a short history. It says Ptolemy used midpoints as “half-sums” in the second century, tied to the first and second harmonics, and that midpoints went into the calculation of the Arabic lots, such as the Part of Fortune. It names Guido Bonatti as using them in the thirteenth century to refine timing in event charts. In its account Alfred Witte investigated midpoints with movable dials, and with Ludwig Rudolph and Herman Lefeldt formed the Hamburg School, whose Uranian astrology added trans-Neptunian points; Reinhold Ebertin later dropped those points and simplified the method, and the American authors Aren Ober and Eleanor Kimmel popularised it further. That is the article’s history, reported as it stands; the interpretations those schools attach to midpoints are outside this page.

The Calculation, Step by Step

Write both longitudes in the same zodiac as degrees from 0° Aries, 0° to 360°. Then:

1. Find the Moon’s lead over the Sun, the elongation: Moon − Sun, adding 360° if the result is negative.
2. If the elongation is under 180°, the near midpoint is the Sun plus half the elongation.
3. If it is over 180°, the Moon is really behind the Sun, and the near midpoint is the Moon plus half of what is left of the circle: Moon + (360° − elongation) ÷ 2.
4. If the answer is 360° or more, take 360° off. Every 30° is a sign, counted from Aries.
5. The far midpoint is the near one plus 180° (less 360° if needed).

Three Charts Worked Through

The three birth times below are illustrations, chosen to show the three situations that arise; they are not anyone’s chart. The longitudes are sidereal, Lahiri ayanamsa, from the same ephemeris code as the site’s free kundli, and the Sun and Moon columns print them as that tool does, whole degrees and sixtieths of a degree.

20 August 1980, the simple case. In decimals the Sun is at 123.74° and the Moon at 228.22°. The elongation is 228.22 − 123.74 = 104.48°, under 180°, so the midpoint is 123.74 + 52.24 = 175.98°, which is Virgo 25°58′. Notice that the point is in neither body’s sign: the Sun is in Leo, the Moon in Scorpio, and the midpoint falls in Virgo, one of the two signs between them.

1 April 1987, the wrap past 360°. The Sun is at 347.26°, late in Pisces, and the Moon at 19.92°, in Aries. Moon − Sun is negative, so add 360°: the elongation is 19.92 − 347.26 + 360 = 32.66°. Half of it is 16.33°, and 347.26 + 16.33 = 363.59°; taking 360° off leaves 3.59°, Aries 3°35′. The point has crossed 0° Aries with the Moon.

12 July 1985, the Moon behind the Sun. The Sun is at 86.06° and the Moon at 18.78°. Moon − Sun + 360 gives an elongation of 292.72°, over 180°: the shorter way from the Sun to the Moon runs backwards. What is left of the circle is 360 − 292.72 = 67.28°, half of that is 33.64°, and the midpoint is 18.78 + 33.64 = 52.42°, Taurus 22°25′, again a sign between the two bodies.

Tropical or Sidereal

The history above belongs to Western astrology, where the convention in modern practice is to count longitudes in the tropical zodiac; the site’s kundli counts them in the sidereal. Both bodies shift by the same ayanamsa between the two, so their elongation is unchanged and the midpoint shifts by exactly that ayanamsa too: tropical midpoint = sidereal midpoint + ayanamsa. The code behind this page checks that identity for each example and at every sampled moment of the census below. The sign can still change. For 12 July 1985 the ayanamsa is 23.655°, and the midpoint moves from Taurus 22°25′ to Gemini 16°04′; for 20 August 1980 it moves from Virgo 25°58′ to Libra 19°33′. Why the offset is about 24° and growing is set out on the Lahiri ayanamsa page.

The Plain Average Gives the Wrong Half

Adding the two longitudes and halving them ignores the circle. For 1 April 1987 it gives (347.26 + 19.92) ÷ 2 = 183.59°, Libra 3°35′: the far midpoint, half a zodiac from both bodies. The plain average is right whenever the two numbers differ by less than 180°, and lands on the far midpoint whenever they differ by more. Across every pair of whole-degree positions of the Sun and Moon, that happens for 24.9% of pairs, about one in four. The same trap, for the midpoint of the Moon and Rahu, is the subject of the Bhrigu Bindu calculation page.

Which Sign the Midpoint Falls In

The site’s ephemeris was sampled every 3 hours from 1 January 1950 to 1 January 2050, IST: 292,200 moments, a share of time rather than of people. For each one the near midpoint’s sign was compared with the Sun’s and the Moon’s.

About three moments in four put the midpoint in a sign that holds neither body, and each of the other three rows is roughly one in twelve. When the Sun and Moon share a sign the midpoint is always in it as well, since it lies between them. Otherwise it is always in a sign along the shorter way from the Sun’s sign to the Moon’s, never beyond either. The two zodiacs give the same shares to within a tenth of a percentage point, even though they put the midpoint in different signs at 79.5% of the moments themselves, about four in five.

How Fast It Moves, and What an Hour Does

Because the midpoint is half the Moon’s longitude plus half the Sun’s, it moves at half the Moon’s speed plus half the Sun’s. The Sun’s share is small and steady (the Sun itself covered 0.95° to 1.02° a day across the sample); the Moon’s varies, and with it the midpoint ran at 6.36° to 8.20° a day, 7.08° on average. Per hour that is 0.27° to 0.34°, between a quarter and a third of a degree.

So a birth time an hour out moves the midpoint by that much, and at 1.0% of the sampled moments, about one in a hundred, the moment an hour later had the sidereal midpoint in a different sign, not counting the jump described next. There is one place where an hour does far more. As the elongation passes 180°, at full moon, the shorter arc changes sides and the near midpoint jumps to the opposite point of the zodiac. In the sample, 0.14% of moments, one in 732, were close enough to full moon for that jump to fall inside the next hour. For a birth that close to full moon the near and far midpoints are nearly equally near, and the birth time decides which is which.

The Tithi and the Yoga Inside the Midpoint

The elongation that fixes the midpoint is the same angle that fixes the tithi, the lunar day of the panchang: each 12° of elongation is one tithi, counted from Shukla Pratipada at 0°. In the bright half (Shukla paksha) the near midpoint sits half the elongation ahead of the Sun, so each tithi carries it 6° further on, from beside the Sun at the start of Shukla Pratipada to 90° ahead at the end of Purnima. In the dark half (Krishna paksha) it sits behind the Sun and closes back to it by the end of Amavasya. The first example was born in Shukla Navami, the second in Shukla Tritiya and the third in Krishna Dashami; the birth tithi page works that side of the arithmetic, and what moon phase was I born under names the phases the same angle defines.

The panchang’s yoga comes from the other combination, the sum of the two sidereal longitudes, cut into 13°20′ steps. Twice either midpoint is that sum, so each yoga covers 6°40′ of midpoint, and the 27 yogas fill half the circle and repeat on the far side. The three examples fall in Vaidhriti, Vishkambha and Dhriti yoga, and the code behind this page checks both read-offs, tithi and yoga, against the site’s panchang function at all 292,200 sampled moments. Doubling a longitude is the second harmonic, and the harmonic chart page sets out what multiplying a longitude does in general; doubled, the near and far midpoints become one point.

Getting the Two Longitudes

Unlike the ascendant, neither input depends on the birthplace, only on the instant. The free kundli, once you are signed in, prints the Moon’s and the Sun’s sidereal longitudes as whole degrees and sixtieths, like the table above, along with the ayanamsa it used; add that ayanamsa for the tropical figures. It does not print a midpoint, so the steps above are yours to apply. The Part of Fortune is another point built from the same two bodies, with the ascendant added.

What This Page Does Not Give

There is no meaning here for the midpoint in a sign or house, or for a planet that sits on it, because a longitude can be checked and a meaning cannot. A midpoint between two people’s charts, as used in composite or synastry work, belongs to relationship astrology, and this page stays with the arithmetic of one birth chart.

In Brief

• Two answers: the near and far midpoints, 180° apart; this page means the near one
• Formula: elongation under 180°: Sun + elongation ÷ 2; over 180°: Moon + (360° − elongation) ÷ 2
• Plain average: gives the far midpoint whenever the two numbers differ by more than 180°
• Zodiacs: tropical midpoint = sidereal midpoint + ayanamsa; the sign can differ
• Sign: in a sign holding neither body at 75.3% of sampled moments
• Precision: a quarter to a third of a degree per hour of birth time; near full moon an hour can swap near and far
• Panchang link: the elongation gives the tithi, twice the midpoint gives the yoga