The centre of the matrix: what point E means and how to calculate it

What is the centre of the matrix?

The matrix begins with a diamond of four points: A on the left, B at the top, C on the right and D at the bottom. At the intersection of its diagonals is point E, the centre. Each point represents one of the 22 Major Arcana.

The centre comes from the sum of the whole diamond. In the calculator we describe it as what feels natural when nobody expects anything of you: your usual pace, how you regain balance and the things you do without thinking. The other points describe different sides of life; the centre brings them together.

This is material for self-reflection, not a verdict. The arcanum at the centre offers questions and settles nothing. Simply set aside anything that does not fit you.

How to calculate point E

The whole calculation follows one rule: each point must be between 1 and 22, the number of Major Arcana. When a sum exceeds 22, add its digits. We call this reduction. For example, 44 becomes 4 + 4 = 8, and 38 becomes 3 + 8 = 11.

First calculate the four points of the diamond:

• A is the day of birth. Days 1⁠–⁠22 stay unchanged; reduce days 23⁠–⁠31 (29 gives 2 + 9 = 11).
• B is the month, from 1 to 12.
• C is the sum of the year’s digits, reduced if necessary.
• D is A + B + C, reduced if necessary.

The centre is the sum of all four points: E = A + B + C + D. Reduce a result above 22.

Two examples step by step

For 15 June 1990: A = 15, B = 6, C = 19, D = 4, E = 44, or 4 + 4 = 8, Justice.

In the second example reduction is needed at the start. Take 29 December 1985.

• A = 29, or 2 + 9 = 11.
• B = 12, because December is the twelfth month.
• C = 1 + 9 + 8 + 5 = 23, or 2 + 3 = 5.
• D = A + B + C = 11 + 12 + 5 = 28, or 2 + 8 = 10.
• E = A + B + C + D = 11 + 12 + 5 + 10 = 38, or 3 + 8 = 11.

The centre here is Strength. The calculator uses the same formulas.

Not every arcanum can appear at the centre

Point D is already the sum of A, B and C, so these three numbers count twice at the centre. If A + B + C is at most 11, no reduction is needed and the centre is simply twice that sum: an even number no greater than 22. For sums from 12 to 22, doubling gives 24 to 44, which reduces to 3 through 11. For sums above 22, the reduced result is no greater than 14. The centre therefore always contains an arcanum from 3⁠–⁠14 or one of 16, 18, 20 and 22. Arcana 1, 2, 15, 17, 19 and 21 never appear at the centre.

We checked every day from 1 January 1900 to 31 December 2026: 46,386 dates. Arcana 5 through 11 are most common, each appearing for roughly one in nine dates. The Emperor (4) and the Hanged Man (12) occur in about 6.5% of dates, and the Empress (3) and Death (13) in about 4⁠–⁠5%. The other five are rare: the Fool appears on 214 days, Temperance on 151, Judgement on 149, the Moon on 98 and the Tower on just 55. The Tower, Moon, Judgement and Fool arise only by doubling a small sum, when A + B + C is between 8 and 11. This happens with an early day and month in a year with a small C, such as 1985 (C = 5), 2000⁠–⁠2007 or 2020⁠–⁠2025.

One such rare date is 1 January 2007: A = 1, B = 1, C = 9, D = 11 and E = 1 + 1 + 9 + 11 = 22.

Where to find the other six

You can find these six arcana in other points, most simply A, B and C:

• The Magician (1): A for those born on the 1st; B for those born in January.
• The High Priestess (2): A for the 2nd; B for February; C for 2000.
• The Devil (15): A for the 15th; C for 1905, 1914, 1923, 1932, 1941 and 1950.
• The Star (17): A for the 17th; C every nine years from 1907 to 1970.
• The Sun (19): A for the 19th; C every nine years from 1909 to 1990.
• The World (21): A for the 21st; C every nine years from 1929 to 1992.

In the example matrix for 15 June 1990, the Devil is at A, the Sun at C and the World in the upper left corner (point F).

What the arcanum at the centre means

Here are short descriptions. Each arcanum’s page has the full text, including its gift, shadow and first step.

• The Empress (3). Even when nobody asks, you care for someone or something: people, plants or others’ ideas. You feel best seeing something grow under your care. Check whether you give yourself the same attention.
• The Emperor (4). Even on a day off you start by putting things in order: a plan, a drawer, a list. You find your footing when you know how things depend on one another. Disorder tires you more quickly than it tires others.
• The Hierophant (5). Familiar things restore your calm: shared customs and conversations where one person teaches and another learns. You explain how things work without thinking twice.
• The Lovers (6). Relationships set your usual pace: you instinctively consider how decisions affect loved ones. You lose balance when you choose only to avoid disappointing anyone, and regain it when the decision is yours again.
• The Chariot (7). You rest best in motion, on a journey or working on something you can finish. Knowing your destination gets you moving. Without a goal you may go in circles, so choosing the next stop helps you find direction.
• Justice (8). Before judging, you weigh both sides without being asked. You feel at ease when things are settled fairly. Take care not to judge yourself more harshly than others.
• The Hermit (9). Given time to yourself, you choose quiet: a closed door, a solitary walk, a phone put away. This is how you recover after a day among people. Answers often come when nobody is asking.
• Wheel of Fortune (10). A change of plans does not throw you off because your natural pace is changeable. When things shift, you instinctively look for a new arrangement.
• Strength (11). In a tense moment you slow down and lower your voice before you have time to think; people around you often calm down too. You treat yourself similarly: gently, without rushing.
• The Hanged Man (12). When something stalls, your first move is to pause, step back and look from another angle. Consider: how do you know when the pause has gone on too long?
• Death (13). Despite its alarming name, this card concerns closing chapters. You instinctively finish what has run its course and make room for something new. Tidying, saying goodbye and changing habits come more easily to you than to many people.
• Temperance (14, rare). You regain balance in small steps: a little of this and a little of that until the proportions feel right. You instinctively soften extremes, your own and others’.
• The Tower (16, rare). Rather than patching what is breaking down, you prefer to start again on firmer ground. Rebuilding from the foundations reassures you more than it tires you.
• The Moon (18, rare). A free moment quickly becomes a story, an image or a melody. You sense moods before anyone names them. When uncertainty lasts, writing down what you know and what you are assuming can help.
• Judgement (20, rare). You instinctively return to what you see as your task. You like taking stock: what worked, what to leave behind and where to begin again. When something unsettles you, asking why you do it helps restore order.
• The Fool (22, rare). Curiosity and lightness are natural to you. On a free day you choose an unfamiliar road or a new place. Starting something from scratch, even something small, helps release tension.

How to use point E

Start by calculating your own centre, on paper with the formula or in the calculator, which also shows where each number came from. Then read your arcanum’s page and compare it with the last day when nobody wanted anything from you: what did you find yourself doing naturally?

A useful exercise is to compare the centre with point A. Point A, personality, describes your first instinct: what you bring into new places and conversations (see Point A and the day of birth). If the same arcanum appears in both, your first instinct matches what comes naturally. If they differ, consider when each feels closer to you. People born on the 1st, 2nd, 15th, 17th, 19th or 21st always have two different arcana here, because their point A arcanum cannot appear at the centre.

The centre is one of sixteen points and says the most alongside the rest. See your full matrix in the calculator and the calculation for each point in How to calculate the matrix.