Semi-square: the 45° minor aspect in a birth chart

A semi-square is an aspect between two planets that stand 45° apart along the ecliptic. It is half a square and one eighth of the circle, which is why it is also called an octile. The semi-square is a minor aspect, but not a random one: together with the sesquiquadrate it forms a family of hard aspects that grows out of dividing the circle by four and by eight.

Geometry: half a square

Where the square divides the circle into four, the semi-square divides it into eight. Hence the direct link: two planets in semi-square stand as a planet does to the midpoint of a square. Add 90° to 45° and you get 135°, the sesquiquadrate. Together with the conjunction (0°), square (90°) and opposition (180°), these angles form the series of multiples of 45°. Astrologers who work with harmonics call it the eighth harmonic and read it as an axis of tension and action.

A distance of 45° equals a sign and a half, so the semi-square, unlike the major aspects, is not tied to a pair of signs. A planet at 5° Aries is in semi-square to one at 20° Taurus, while a planet at 25° Aries is in semi-square to one at 10° Gemini. The signs may be neighbours or one sign apart, and nothing about element or modality can be said in advance.

Where the aspect comes from

Ptolemy did not know the semi-square. Aspects in multiples of 45° entered practice with the other minor aspects, once the angle between planets came to be measured exactly rather than by sign. Two 20th-century schools gave them particular weight.

The Hamburg School, founded by Alfred Witte early in the century, and the cosmobiology of Reinhold Ebertin that grew out of it, worked with a 90° dial. On such a dial the conjunction, square and opposition fall on one point, while the semi-square and sesquiquadrate land exactly opposite. For these schools the 45° series was the main working tool, and in their practice a semi-square weighs almost as much as a square.

The orb of a semi-square

In ordinary natal practice the semi-square gets a narrow orb: 1-2°, up to 2-3° with the Sun or Moon. The schools that use the 90° dial are stricter still, often allowing no more than 1-1.5°. With a wide orb, every chart holds several semi-squares and the aspect stops meaning anything.

How to read a semi-square

The semi-square shares the character of the square, only weaker and less visible from outside. A square often describes an open conflict the person knows about. A semi-square describes friction that builds up little by little: irritation, impatience, a sense that two parts of life get in each other's way, with no open crisis. Modern writers also link it to motivation: a small tension that keeps a person from standing still.

The order of reading is the usual one:

• Planets. Which functions are under tension. A semi-square of the Sun to Mars speaks of will and action; one of Mercury to Uranus, of thinking and sudden change.
• Signs. How each planet acts. Since the signs can be any, look at each planet on its own rather than searching for a shared element.
• Exactness. A semi-square within 1° deserves attention, especially if a luminary takes part.

Like any minor aspect, the semi-square should not be the basis of a conclusion about a chart. It refines rather than defines.

Example: the semi-square in Zendaya's chart

In Zendaya's chart the Sun is at 9°50′ Virgo and Mars at 25°04′ Cancer. The angle between them is about 44°46′, an orb of 0°14′. Cancer and Virgo are one sign apart, so by sign they form a sextile, yet the exact angle gives a semi-square: a good illustration that eighth-harmonic aspects ignore sign boundaries.

The Sun forms an almost identical semi-square to Venus at 24°33′ Cancer, with an orb of 0°16′. Tradition would read such a pair as tension between will and desire that does not surface as open conflict but asks for constant small corrections. This describes a link between functions of the chart, not a judgement of the person.

How to find a semi-square in your own chart

Most software leaves minor aspects out of its tables, so a semi-square often has to be found by hand. Convert the planets' positions to absolute degrees: Aries 0-30°, Taurus 30-60°, Gemini 60-90° and on around the circle to Pisces at 330-360°. Zendaya's Sun at 9°50′ Virgo becomes 159°50′, her Mars at 25°04′ Cancer becomes 115°04′.

For each pair, subtract the smaller number from the larger; if the result is over 180°, subtract it from 360°. An angle within 1-2° of 45° is a semi-square. You cannot spot it by sign: 45° is a sign and a half, so the two planets' degrees within their signs differ by about 15°. If one planet sits at 10° of a sign, look for a semi-square partner near 25° of the next sign, or near 25° of the sign two places back.

Semi-squares in configurations

On their own, semi-squares rarely build well-known figures. The nearest relative is the figure known as Thor's hammer or the fist of God: two planets in square and a third in sesquiquadrate to both. The point opposite the apex of this figure lies at the midpoint of the square and stands in semi-square to both its ends, so the whole figure is built from multiples of 45°. The section has no separate page for it yet. The classic configurations made of major aspects are covered under aspect patterns.

In celebrity charts

The tightest examples among the published charts.

• Neymar: Moon semi-square Uranus, orb 0°01′
• Ariana Grande: Sun semi-square Venus, orb 0°01′
• Emmanuel Macron: Mercury semi-square Uranus, orb 0°02′

Calculate your chart