Midpoint
Calculator

A midpoint is the degree halfway between two points in a chart. Your Sun at 10° Aries and your Moon at 10° Gemini have their midpoint at 10° Taurus. The degree opposite, 10° Scorpio, is the far midpoint, and the two together make the midpoint axis.

A midpoint on its own is just a degree. It becomes something to read when a third point stands on it. Astrologers write that as Point = A/B: Mars = Sun/Jupiter means Mars sits on the Sun/Jupiter midpoint, and the three are read together as one combination, Mars bringing its action to whatever the Sun and Jupiter share. Such a combination is called a planetary picture or midpoint picture. The idea is that a planet can be tied to two others with no ordinary aspect between it and either of them, simply by being equidistant from both.

Midpoint work goes further than the conjunction. A point square or opposite a midpoint, or 45° or 135° from it, counts as well. Those are the aspects of the 45° series, the 8th harmonic, and they all coincide on the 90° dial, the working tool of the Hamburg School and of Reinhold Ebertin's cosmobiology. The calculator searches for all of them.

It starts from your birth chart, cast with the Swiss Ephemeris for the moment of birth in Universal Time (the methodology page explains how). The midpoint work then runs in six steps:

1. The points. The ten planets, the true North Node, Chiron, and the exact Ascendant and Midheaven, 14 points in all. The angles are the degrees rising and culminating at birth, never house cusps.
2. The midpoints. For each of the 91 pairs, the halfway point along the shorter arc, and the far midpoint opposite it. Two points 350° and 10° along the zodiac have their midpoint at 0° Aries, not 0° Libra.
3. The pictures. Every other point is tested against each midpoint at eight positions 45° apart: the midpoint itself, 45°, 90°, 135° and 180° from it, on either side. A point within 1°30′ of one of them is listed, with the aspect and the orb. A pair's own two points are never tested against their midpoint.
4. The dial. Each point's longitude modulo 90°, sorted, and drawn around a circle.
5. The trees. For each point, the midpoints it stands on, tightest first.
6. Display. Degrees and orbs drop the arc-seconds rather than rounding them.

The calculator's orb is 1°30′. Published practice varies from about 1° to 2°; with every orb shown, you can apply a tighter limit by reading down the list.

Prince William was born in London at 9:03 PM (UTC+1:00) on June 21, 1982, the time given in the official birth announcement. His 14 points and their places on the 90° dial are below, and a separate run of the Swiss Ephemeris, outside the API, reproduces every number.

With a 1°30′ orb the calculator finds 75 pictures: 3 by conjunction, 8 by opposition, 19 by square, 22 by semi-square and 23 by sesquiquadrate. The 45° aspects outnumber the rest because there are four positions for them around each midpoint and only two for the conjunction and opposition. 27 of the 75 are within 0°30′. The ten tightest:

The tightest, Mercury = Saturn/Midheaven, is 0°00′ from an exact sesquiquadrate. The second, Midheaven = Venus/Mars, involves the Midheaven, and like every picture with an angle it depends on the recorded minute of birth: the Midheaven moves about a degree every four minutes, so a time a few minutes out would loosen it past the orb or bring other pictures in.

Of the 91 midpoints, the one people most often look up on its own is the Sun/Moon midpoint, the halfway point between the two lights. It is read like any other midpoint, by the points that stand on its axis, and it is also used between charts: someone else's planet on your Sun/Moon midpoint. The calculator gives it its own box above the pictures, with any point on its axis.

Prince William was born with the Sun at 0°06′ Cancer and the Moon at 4°57′ Cancer, 4°51′ apart, so his Sun/Moon midpoint is 2°32′ Cancer and its far point 2°32′ Capricorn. On the 90° dial it sits at 2°32′, the dashed line on the drawing. No other point is within 1°30′ of that axis by any aspect of the 45° series; the nearest is his Ascendant, 5°03′ from the far midpoint. So he has no Sun/Moon picture, and that is not unusual: with 12 other points and a 1°30′ orb, chance alone leaves about 44% of midpoints with no point on them.

To find yours by hand, write both lights as longitudes from 0° Aries (Taurus starts at 30°, Gemini at 60°, and so on), add them and halve the sum; if they are more than 180° apart, add 180° to land on the shorter arc. The FAQ below works it through for Prince William.

A midpoint tree lists, for one point, every midpoint it stands on. The calculator builds one for each of the 14 points. Prince William's fullest is the North Node, with 8 midpoints; his sparsest is Mercury, with 4. The full set:

Two trees show how a reading starts. His Midheaven stands on Venus/Mars, 0°01′ from an exact square, then on Mercury/Neptune and Mars/Chiron. His Sun stands on Moon/Neptune, 0°08′ from an exact square. In each case the reading combines the meaning of the point with the meaning of the pair: what the Midheaven stands for (aims, standing, public role) colored by what Venus and Mars share, or the Sun colored by the Moon and Neptune together. The calculator prints a short reading for the pictures and pairs it has text for, written for this site rather than taken from Ebertin.

A picture names three points: the one on the midpoint and the two whose midpoint it is. The usual way in is to read the pair first, as what the two share, and then the point standing on it as the part of life where that shows. With the plain keywords for each point, Prince William's three tightest read like this:

• Mercury = Saturn/Midheaven (sesquiquadrate, 0°00′): duty, limits and structure joined with aims, standing and public role, brought out through thinking, speech and plans.
• Midheaven = Venus/Mars (square, 0°01′): affection and taste joined with drive and action, brought out through aims, standing and public role.
• Chiron = Moon/Saturn (square, 0°02′): feelings and habits joined with duty, limits and structure, brought out through old hurts and how they are handled.

The Ascendant/Midheaven midpoint deserves a mention of its own, since it depends on the birth time and place as well as the date. Prince William's Saturn stands on it, 0°32′ from an exact semi-square. Pictures like that are the personal ones: anyone born on the same day shares most of the pictures among the planets, apart from those with the Moon, but not the ones with the angles.

Midpoint lists are long, and it helps to know why. 14 points make 91 midpoints, and each midpoint is tested against the 12 points not in its pair: 1,092 tests. Each test has eight target positions, 45° apart, and a 1°30′ orb either side of them covers 3° in every 45°, one fifteenth of the circle. Scattered at random, a chart would show about 72.8 pictures.

Real charts come out close to that. Casting a chart for London at 12:00 UT every 7 days from 1950 to 1999, 2,609 charts in all, the Swiss Ephemeris gives an average of 72.8 pictures and a median of 73. Eight charts in ten have between 62 and 83; the range runs from 37 to 186. The highest counts come mostly from charts with several planets close together, whose midpoints pile up near the same degrees. Prince William's 75 sits above 59% of them, an ordinary count.

So the number of pictures says little about a chart. What stands out is a very tight picture, a picture involving the Sun, the Moon or an angle, or a point that turns up again and again, as the North Node does in Prince William's trees. Narrow the orb to 0°30′ and his list drops to 27; at 1° it is 51.

The same arithmetic works across two charts. The composite chart puts each planet at the midpoint of two people's positions and casts a chart from the results. Midpoint users also look for one person's planet standing on the other person's midpoints, the Sun/Moon midpoint above all, which the synastry calculator does not do. This calculator works within one chart; to compare two, take each person's midpoints from the full list in the result and check the other's positions against them, or compare the two 90° dials, where a planet of one chart on the other's midpoint shows as a point halfway between two others.

Transits are read the same way: a transiting planet reaching a natal midpoint, or a point 45° or 90° from it, is read as a picture made for the time it lasts. Because the dial folds the 45° series together, a slow transit touches the same midpoints eight times on its way around the zodiac.

The earlier version had two faults. It took the Ascendant and Midheaven from the first and tenth Whole Sign house cusps, which sit at 0° of a sign. For Prince William that put the “Ascendant” at 0°00′ Sagittarius instead of 27°28′ Sagittarius, and the “Midheaven” at 0°00′ Virgo instead of 2°27′ Scorpio, 62°27′ away in a different sign. 7 of its pictures existed only because of those false angles.

It also showed only conjunctions and oppositions to a midpoint, 15 of them for Prince William. It computed the squares, another 19, without showing them, and never looked at the semi-square or sesquiquadrate. A calculator that describes the 90° dial has to count everything the dial puts together, so it now searches all five aspects of the 45° series with the true angles: 75 pictures for the same chart.

Midpoint analysis in its modern form comes from Alfred Witte (1878–1941), a Hamburg surveyor and astrologer, and the circle around him that became the Hamburg School, founded as an association in 1925. Witte revived the use of midpoints and worked with planetary pictures more generally: formulas that add and subtract positions, such as A + B − C, of which the midpoint picture is the simplest. His rules were published as Regelwerk für Planetenbilder (1929), with an introduction by his colleague Ludwig Rudolph, and in English as Rules for Planetary Pictures (1939). The school also added hypothetical planets of its own, which this calculator does not use.

Reinhold Ebertin (1901–1988) took the midpoints and the 90° dial into the school known as cosmobiology, and left out the hypothetical planets. His Kombination der Gestirneinflüsse (1940), translated as The Combination of Stellar Influences (1972), gives readings for planetary pairs and for the points that stand on them, and its chart form, the cosmogram, comes from the Hamburg dial. In English, Michael Munkasey's Midpoints: Unleashing the Power of the Planets (1991) is a later book-length treatment.

• Alfred Witte, Regelwerk für Planetenbilder (Witte-Verlag, Hamburg, 1929; English translation, Rules for Planetary Pictures, 1939).
• Reinhold Ebertin, Kombination der Gestirneinflüsse (Ebertin-Verlag, Aalen, 1940); The Combination of Stellar Influences (Ebertin-Verlag, 1972; later American Federation of Astrologers editions).
• Witte-Verlag's history of the Hamburg School, for Ludwig Rudolph's 90° and 45° dials (1931).
• Michael Munkasey, Midpoints: Unleashing the Power of the Planets (ACS Publications, 1991).
• Every position comes from the Swiss Ephemeris (Astrodienst); the picture counts for London charts were computed with it.

Pictures with the Ascendant or Midheaven need a birth time good to a few minutes, and pictures with the Moon a time good to an hour or so; those among the slower planets hold for a day or more. The calculator finds the geometry. It makes no claim about what a picture means for a person; the short readings in the result are a starting point, and Ebertin's book is the place to go further.