□ Free T-Square Calculator: Is There a T-Square in Your Chart?

Umbriel's free T-square calculator checks your birth chart for a T-square, an opposition with a third planet square to both ends, and shows the apex planet and the exact orb of every aspect.

A T-square is two planets about 180° apart, an opposition, with a third planet about 90° from both of them, a square to each end. On the wheel the three points make a right-angled triangle, the shape of a carpenter's T-square, and the planet at the right angle is the apex. The empty point opposite the apex is the missing fourth corner of a cross.

The usual reading is that the opposition is a tug between two sides, and the apex planet is where the strain is felt and acted out: the pressure point. Because the apex carries the tension, astrologers read it as an engine as much as a difficulty, tension with an outlet. The lesson on aspect patterns suggests starting with the apex, not the opposition.

T-squares are the most common of the figures on these pages, partly because they need only three planets and the orbs are generous. If a fourth planet sits on the empty corner, the figure is a Grand Cross and Umbriel reports the Grand Cross instead.

Each aspect is judged on its own orb. Nothing is added up, the Sun and Moon get no extra orb, and the limits are the same for every planet. Every limit is at or below the orb the chart's own aspect lines use, so each aspect in a figure is also a line on your chart. Umbriel never widens an orb to produce a result. If nothing fits, the answer is none, and a figure that is only just outside an orb is shown on its own, marked as not counted.

In Umbriel's collection of 4,135 famous charts (born 1600 to 2014), cast for noon on the birth date with the Sun to Pluto and the Moon left out, because the collection holds no birth times, 637 have at least one T-square at these orbs: 15.4 per cent.

At the wider orbs of the chart's own aspect lines (opposition 8°, trine and square 7°, sextile 5°, quincunx 3°), 899 would have one: 21.7 per cent instead of 15.4. The orb choice alone moves the answer, which is why this page prints its own.

That is a count of famous people, not of births: the collection leans towards the twentieth century, and because Jupiter to Pluto move slowly, a whole birth cohort can share a figure made of them. A fair sample of everyone would differ.

Umbriel casts the ten planets, Sun to Pluto, for the moment of birth with the same engine as the rest of the app, then tests every combination of planets against the shape. A figure counts only if every aspect in it is inside its own orb: opposition 6°, and square 6°. Each aspect is judged on its own orb. Nothing is added up, the Sun and Moon get no extra orb, and the limits are the same for every planet. Every limit is at or below the orb the chart's own aspect lines use, so each aspect in a figure is also a line on your chart.

The Ascendant and Midheaven are left out because they need an exact birth time and place; the lunar nodes, Chiron and the asteroids are left out to keep one clear rule. Adding any of them would find more patterns, and every pattern found that way depends on a choice that is not made here. Umbriel never widens an orb to produce a result. If nothing fits, the answer is none, and a figure that is only just outside an orb is shown on its own, marked as not counted.

The place of birth does not matter for this, because the planets stood at the same longitudes wherever you were born. What turns your clock time into a moment is the time zone, which is why the form asks for a UTC offset and not a city. Use the offset that was in force on the birth date, daylight saving included. The place of birth does not change where the planets were, so Umbriel asks for the time zone, not the town.

With no birth time the Moon is the first thing to move. The Moon travels about 13° a day, so with no birth time it could have stood anywhere in a span of about 26°, and any figure that includes it depends on the hour. The Ascendant and Midheaven need an exact time and place, so Umbriel does not use them here at all.

A real chart: Elizabeth II, born 21 April 1926. The page in Famous charts casts the chart for noon, because the records those pages come from hold no birth time, and this example does the same and leaves the Moon out. Cast that way, the nine planets from the Sun to Pluto make a T-square: Jupiter, Neptune and Saturn.

Jupiter 22°34′ Aquarius, Neptune 22°02′ Leo, Saturn 24°25′ Scorpio.

• Jupiter opposite Neptune0°32′ from exact, limit 6°
• Saturn square to Jupiter1°51′ from exact, limit 6°
• Saturn square to Neptune2°23′ from exact, limit 6°

The apex is Saturn, squared by the opposition of Jupiter and Neptune.

With the Moon left out this is the chart of nine planets, and the figure is the same whatever the hour, so it is as firm as an example can be without a birth time.