Stem and Branch Number Conversion Rules Explained

Mastering the Stem and Branch Number Conversion Rules Explained in He Lu Li Shu is the pivotal technical skill that transforms a standard Four Pillars birth chart into an exact I Ching hexagram map. In traditional Chinese metaphysics, birth timing is recorded using the ten Heavenly Stems (Tian Gan) and twelve Earthly Branches (Di Zhi). While systems like BaZi evaluate these components through seasonal strength, elemental interactions, and ten gods, He Lu Li Shu takes a fundamentally mathematical approach. Every single stem and branch is mapped directly to a specific cosmic integer derived from the primordial He Tu matrix and Luo Shu numerical square. If you are new to this mathematical discipline, reviewing our master guide on He Lu Li Shu birth hexagram conversion will clarify how these raw numerical sums serve as the foundation for life hexagram construction.

When converting a birth chart into numbers, a practitioner must not treat these values as arbitrary counters or superficial tallies. The assigned numbers represent specific polarities of energy. Odd numbers from one to nine embody the creative, active impulse of Heaven (Tian), whereas even numbers from two to ten represent the receptive, structural weight of Earth (Di). By converting all eight characters of the Four Pillars into these integer values, He Lu Li Shu computes two master numbers: the Heaven Raw Sum (Tian Shu) and the Earth Raw Sum (Di Shu). Over my three decades in business, running companies, leading cross-border negotiations, and advising corporate executives, I have observed that individuals with highly asymmetrical numerical balances in their charts display distinct strategic behaviors. A founder whose chart generates an overwhelmingly dominant Heaven sum tends to possess extraordinary visionary drive but may struggle with operational execution. Conversely, a director with a heavy Earth sum excels at risk mitigation and institutional building but may hesitate when swift innovation is required.

To execute this conversion flawlessly, every practitioner must internalize the precise conversion tables, understand the subtle differences between stem and branch valuation mechanics, and know how positional weights operate. In this comprehensive guide, we will systematically examine every conversion rule, break down the numerical values of all ten stems and twelve branches, explore edge cases, and analyze complete worked examples step by step.

The Numerical Architecture of the Ten Heavenly Stems

The ten Heavenly Stems represent pure cosmic energies operating in the higher realm. In He Lu Li Shu, assigning numerical values to the Heavenly Stems relies on the primordial Yellow River Map (He Tu) paired with five-element completion rules. Unlike systems that assign simple sequential numbers from one to ten, He Lu Li Shu assigns numbers that reflect whether a stem represents a generating force (Sheng Shu) or a completing force (Cheng Shu) within its elemental sector.

To understand why specific stems carry specific numbers, consider the five elemental pairings of the He Tu diagram. Water is established by one and six in the North; Fire by two and seven in the South; Wood by three and eight in the East; Metal by four and nine in the West; Earth by five and ten in the Center. Each pair consists of one odd Heaven number and one even Earth number. When converting Heavenly Stems, the Yang stem of an element takes the primary generating or completing number, while the Yin stem takes its reciprocal counterpart. Understanding these mathematical foundations is deepened when examining He Tu matrix foundations in He Lu Li Shu, where the interaction of primordial number pairs is fully detailed.

Below is the detailed breakdown of the ten Heavenly Stems and their exact numeric conversion values used in classical He Lu Li Shu chart calculation:

• Jia (甲 – Yang Wood): Takes the value 1 (Heaven Odd Number). Representing primordial Wood initiative, Jia carries the generative Yang Water-Wood impulse in cosmic math.
• Yi (乙 – Yin Wood): Takes the value 2 (Earth Even Number). Representing flexible structural Wood, Yi carries the receptive Earth number associated with Fire generation.
• Bing (丙 – Yang Fire): Takes the value 7 (Heaven Odd Number). Representing radiant solar Fire, Bing takes the completed Yang Fire number located in the Southern sector.
• Ding (丁 – Yin Fire): Takes the value 6 (Earth Even Number). Representing illuminating candle Fire, Ding takes the completed Yin Water-Fire completion balance number.
• Wu (戊 – Yang Earth): Takes the value 5 (Heaven Odd Number). Representing central mountain Earth, Wu takes the primary central Yang Earth pivot number.
• Ji (己 – Yin Earth): Takes the value 10 (Earth Even Number). Representing fertile garden Earth, Ji takes the central completed Yin Earth mass number.
• Geng (庚 – Yang Metal): Takes the value 9 (Heaven Odd Number). Representing unrefined sword Metal, Geng takes the completed Yang Metal number of the Western axis.
• Xin (辛 – Yin Metal): Takes the value 4 (Earth Even Number). Representing refined jewelry Metal, Xin takes the generative Yin Metal number.
• Ren (壬 – Yang Water): Takes the value 1 (Heaven Odd Number). Representing ocean surge Water, Ren takes the primary generative Yang Water number in the North.
• Gui (癸 – Yin Water): Takes the value 6 (Earth Even Number). Representing mist and rain Water, Gui takes the completed Yin Water number in the Northern quadrant.

The reference matrix below synthesizes the complete conversion properties for all ten Heavenly Stems, detailing their element, polarity, numerical assignment, and classification as a Heaven or Earth value.

When analyzing this stem conversion table, note that all five Yang Stems (Jia, Bing, Wu, Geng, Ren) convert into odd numbers: 1, 7, 5, 9, 1. Conversely, all five Yin Stems (Yi, Ding, Ji, Xin, Gui) convert into even numbers: 2, 6, 10, 4, 6. This perfect alignment means that the intrinsic polarity of the Heavenly Stem determines whether its numeric value streams into the Heaven Raw Sum or the Earth Raw Sum.

The Twelve Earthly Branches Numerical Mapping Rules

While Heavenly Stems represent higher cosmic intentions, Earthly Branches represent earthly reality, physical structure, spatial directions, and temporal progression. The twelve Earthly Branches receive fixed numerical values that reflect their position on the compass wheel, their primary element, and their intrinsic spatial geometry.

To establish these branch values, classical He Lu Li Shu aligns the branches with the Luo Shu magic square and the twelve double-hours of the solar day. Understanding how spatial positions dictate these values is enhanced by consulting Luo Shu magic square mechanics for birth calculation, where the nine palaces map directly onto branch positions. Each branch carries a fixed integer value between 1 and 10.

Here is the exhaustive rule set for converting the twelve Earthly Branches in birth chart analysis:

• Zi (子 – Rat / Water): Assigned the value 1 (Heaven Odd Number). Situated in the true North, Zi carries the primordial Yang generative Water impulse.
• Chou (丑 – Ox / Earth): Assigned the value 8 (Earth Even Number). Situated in the Northeast, Chou carries the completed Wood-Earth structural weight.
• Yin (寅 – Tiger / Wood): Assigned the value 3 (Heaven Odd Number). Situated in the East-Northeast, Yin carries the generative Yang Wood vitality.
• Mao (卯 – Rabbit / Wood): Assigned the value 8 (Earth Even Number). Situated in the true East, Mao carries the completed Yin Wood network energy.
• Chen (辰 – Dragon / Earth): Assigned the value 5 (Heaven Odd Number). Situated in the East-Southeast, Chen carries the central Heaven Earth pivot value.
• Si (巳 – Snake / Fire): Assigned the value 2 (Earth Even Number). Situated in the South-Southeast, Si carries the generative Yin Fire value.
• Wu (午 – Horse / Fire): Assigned the value 7 (Heaven Odd Number). Situated in the true South, Wu carries the radiant Yang Fire expansion number.
• Wei (未 – Goat / Earth): Assigned the value 10 (Earth Even Number). Situated in the South-Southwest, Wei carries the central completed Yin Earth mass.
• Shen (申 – Monkey / Metal): Assigned the value 9 (Heaven Odd Number). Situated in the West-Southwest, Shen carries the completed Yang Metal execution value.
• You (酉 – Rooster / Metal): Assigned the value 4 (Earth Even Number). Situated in the true West, You carries the generative Yin Metal structural number.
• Xu (戌 – Dog / Earth): Assigned the value 5 (Heaven Odd Number). Situated in the West-Northwest, Xu carries the secondary central Heaven Earth pivot value.
• Hai (亥 – Pig / Water): Assigned the value 6 (Earth Even Number). Situated in the North-Northwest, Hai carries the completed Yin Water storage number.

The visual diagram below demonstrates how Heavenly Stems and Earthly Branches enter the numerical engine, converting raw character inputs into sorted odd and even streams.

Four Pillars Input 4 Heavenly Stems (Jia, Yi, Bing, etc.) 4 Earthly Branches (Zi, Chou, Yin, etc.)

Conversion Engine He Tu Stem Rules Luo Shu Branch Rules Polarity Sorting Odd (1,3,5,7,9) vs Even (2,4,6,8,10)

Heaven Raw Sum Tian Shu (Sum of Odds)

Earth Raw Sum Di Shu (Sum of Evens)

To compare all twelve Earthly Branches side by side, review the comprehensive reference table below:

Observe the mathematical distribution across the twelve branches: exactly six branches carry odd numbers (Zi=1, Yin=3, Chen=5, Wu=7, Shen=9, Xu=5), and six branches carry even numbers (Chou=8, Mao=8, Si=2, Wei=10, You=4, Hai=6). This balanced division ensures that every birth chart contains a natural mix of Heaven and Earth numeric streams regardless of the season of birth.

Hidden Stems (Cang Gan) and Positional Weighting Protocol

One of the most frequent questions raised by practitioners converting Four Pillars into He Lu Li Shu numbers is whether hidden stems inside Earthly Branches should receive separate numerical additions. In standard BaZi analysis, Earthly Branches store hidden stems (Cang Gan) that represent underlying influence. For instance, the Yin branch contains primary Jia Wood, secondary Bing Fire, and tertiary Wu Earth.

In authentic classical He Lu Li Shu, baseline number conversion applies strictly to the surface Heavenly Stem and the primary Earthly Branch of each pillar. The hidden stems embedded inside the branches are not added directly to the raw integer total during primary chart derivation. Why? Because the Earthly Branch number already encapsulates the entire elemental composite of that branch position. Adding hidden stems on top of the branch number would double-count the elemental energy and distort the delicate 25/30 Heaven and Earth constant ratios.

In He Lu Li Shu conversion math, the Earthly Branch value represents the complete environmental container. We do not extract hidden stems into separate additive integers during primary hexagram derivation, as doing so violates primordial number equilibrium.

However, positional weighting across the four pillars plays a vital role in understanding how numbers manifest in real life. While every pillar converts using the standard stem and branch integer tables, the four pillars represent different operational spheres:

• Year Pillar Stems & Branches: Represent ancestral foundation, childhood environment, macro-industry shifts, and early life opportunities (Ages 1 to 15).
• Month Pillar Stems & Branches: Represent parental influence, career trajectory, operational environment, and young adult development (Ages 16 to 30).
• Day Pillar Stems & Branches: Represent personal core identity, self-worth, marriage partner dynamics, and middle-age execution (Ages 31 to 45).
• Hour Pillar Stems & Branches: Represent legacy, subordinate relationships, late-life investment outcomes, and final achievements (Ages 46 and onward).

From a business leadership perspective, this positional breakdown mirrors how an enterprise evaluates strategic assets. When I advise company founders on corporate restructuring or executive placement, we look at both external market trends (Year/Month equivalent) and internal operational capabilities (Day/Hour equivalent). In He Lu Li Shu, if a birth chart draws its highest concentration of Heaven odd numbers from the Day and Hour pillars, that individual will experience their most potent breakthroughs and personal autonomy in mature adulthood.

Step-by-Step Conversion Protocol: Calculating Heaven and Earth Raw Sums

To convert a Four Pillars birth chart into raw Heaven and Earth sums, follow this four-step mathematical execution protocol. We will demonstrate the complete calculation using a real Four Pillars chart example.

The Four-Step Conversion Method

1. Step 1: Write down the Four Pillars. Identify the Heavenly Stem and Earthly Branch for Year, Month, Day, and Hour.
2. Step 2: Assign numerical values. Using the stem and branch conversion tables above, replace each of the eight characters with its assigned integer value (1 to 10).
3. Step 3: Separate by polarity. Sort all eight numbers into two columns: Odd numbers (1, 3, 5, 7, 9) into the Heaven column, and Even numbers (2, 4, 6, 8, 10) into the Earth column.
4. Step 4: Compute the raw sums. Sum all values in the Heaven column to obtain the Raw Heaven Sum (Tian Shu). Sum all values in the Earth column to obtain the Raw Earth Sum (Di Shu).

To understand how this protocol operates in practice, let us walk through a complete worked chart example.

Worked Example: Complete Four Pillars Numerical Calculation

Consider a male born in a Yang Year with the following Four Pillars birth chart:

• Year Pillar: Jia-Zi (甲子)
• Month Pillar: Bing-Yin (丙寅)
• Day Pillar: Wu-Chen (戊辰)
• Hour Pillar: Geng-Shen (庚申)

Let us perform the character-by-character conversion step by step using the reference rules:

Now, let us aggregate the values into our two target sum buckets:

• Heaven Column (Odd Numbers): 1 (Jia) + 1 (Zi) + 7 (Bing) + 3 (Yin) + 5 (Wu) + 5 (Chen) + 9 (Geng) + 9 (Shen) = 40.
• Earth Column (Even Numbers): No even numbers are present in this specific chart. Therefore, Earth Raw Sum = 0.

In this extraordinary chart example, every single stem and branch converts into an odd Heaven number, yielding a Heaven Raw Sum of 40 and an Earth Raw Sum of 0. This extreme configuration triggers specialized reduction rules where the central 5 or 25 subtraction protocols take effect to derive upper and lower trigrams. Understanding such extreme distributions is illuminated by cross-referencing Wu Xing Ming Li five element destiny analysis, where pure single-polarity charts are evaluated for extreme character drive and specialized career paths.

Solar Terms, Hour Divisions, and Gender-Year Condition Adjustments

Executing accurate stem and branch number conversion requires strict adherence to astronomical timing rules. A common error among novice practitioners is relying on civil calendar midnight or standard clock time without adjusting for solar terms and true solar hour positions.

Solar Month Boundary Rules

In He Lu Li Shu, monthly stems and branches are governed strictly by solar terms (Jie Qi), not by the lunar calendar first day of the month. For instance, the transition from the Chou month (Ox) to the Yin month (Tiger) occurs at the precise solar instant of Spring Begins (Li Chun). If an individual is born on the third day of the lunar first month, but before the exact moment of Li Chun, their Month Pillar remains Chou (Ox = 8) rather than Yin (Tiger = 3). Reclassifying a month branch from Chou to Yin alters the raw sum by subtracting 8 from the Earth column and adding 3 to the Heaven column, causing a massive shift in the downstream hexagram.

Hour Branch and Zi Hour Pivot Rules

The birth hour determines the Hour Pillar stem and branch, contributing two vital numbers to the raw sum. Practitioners must apply true solar time adjustments based on the birth location longitude. Furthermore, the handling of the Zi hour (11:00 PM to 1:00 AM) requires precision:

• Early Zi Hour (Ye Zi – 11:00 PM to midnight): Uses the current day stem with Zi branch. Zi branch contributes 1 to the Heaven sum.
• Late Zi Hour (Zheng Zi – midnight to 1:00 AM): Uses the next day stem with Zi branch. The next day stem may introduce a completely different integer and polarity.

The flowchart below maps the decision tree for verifying timing parameters before locking in stem and branch numbers.

1. Solar Term Audit Confirm Li Chun / Jie Qi exact time