How we calculate.

The Year, Month, Day, and Hour pillars each hold one Heavenly Stem (天干) and one Earthly Branch (地支). Together they form the Eight Characters — 八字. Every pillar is computed from your birth date, your birth time, and the IANA timezone of your birth city. None of it is interpreted at this stage. The arithmetic is fixed; the same inputs always produce the same chart.

The Year pillar turns over at 立春 (Li Chun), not at the Gregorian or Lunar New Year. Li Chun is one of the 24 solar terms — the moment the sun's apparent ecliptic longitude reaches 315°. Flow+ computes that moment with the VSOP87 simplified solar model, accurate to roughly one minute of arc, so the boundary is correct to the minute. A child born twelve hours before Li Chun has the previous year's pillar; a child born twelve hours after has the new one. Most popular calculators use a fixed February 4 cutoff, which fails for births within twenty-four hours of the true term.

The Month pillar turns over at the twelve JIE solar terms — the major terms (立春, 惊蛰, 清明, 立夏, 芒种, 小暑, 立秋, 白露, 寒露, 立冬, 大雪, 小寒). Each JIE marks the start of a BaZi month. The intermediate ZHONG terms (雨水, 春分, and so on) sit inside a month and never change the pillar. The Month Stem is then derived from the Year Stem via the 五虎遁年起月歌 verse — a deterministic table.

The Day pillar is anchored at January 1, 1900 = 甲戌 (the tenth of the sixty Jiazi). Flow+ counts whole days from that anchor in the user's local timezone, then advances by one when the birth time is at or after 23:00 — the Joey Yap and Tin Yat Lai "Early Zi" rule. We surface that rule explicitly because the Taiwan 子正 school disagrees and prefers a midnight boundary; users from that lineage can read their pillar without surprise.

The Hour pillar is selected from the local 时辰 — the twelve two-hour windows around the day — and assigned a Heavenly Stem via the 五鼠遁元歌 table from the Day Stem. The 23:00–00:59 window collapses into a single 子 hour; we do not split 早子 and 晚子, in line with the Joey Yap school.

Two schools, two answers. Chinese metaphysics has long debated how to read the hour pillar when the user's birthplace longitude differs from their timezone's standard meridian. The classical 真太阳时 (True Solar Time) doctrine — taught by Joey Yap, Master Sean Chan, and BaZi Lab — applies a longitude correction (roughly four minutes per degree from the meridian) plus the Equation of Time, on the principle that what matters is where the sun actually was, not what the clock read. The mainstream calculator school — what most 5tools, paokong, Master Tan, and popular Chinese-language sites use — reads the hour pillar directly from the user's wall-clock 时辰, on the principle that civil time is what the person was actually born under, and what their family, doctor, and birth records knew.

Flow+ defaults to wall-clock. Two reasons: (1) it matches what every other calculator the user is likely to consult shows, so the chart they see here is the chart they already know; and (2) classical BaZi practice in Singapore, Malaysia, Taiwan, and mainland China overwhelmingly uses wall-clock — TST is a modern Western-influenced refinement, not the lineage default. For users who want the rigorous Joey Yap-style approach, a True Solar Time toggle in profile settings switches their hour pillar computation. We honor whichever the user prefers.

An Earthly Branch is not a single character. It carries a primary hidden stem and, in most cases, a middle and a residual stem as well. Flow+ uses the canonical weighting from 《三命通会》: the main stem at sixty percent, the middle at thirty percent, the residual at ten percent. Single-stem branches (子, 卯, 酉) carry their stem at full weight. The 午 / 亥 pair use the 70/30 split documented in Joey Yap's Compendium.

From the Day Master and any other stem in the chart, Flow+ derives one of the Ten Gods (十神) — 比肩, 劫财, 食神, 伤官, 偏财, 正财, 七杀, 正官, 偏印, 正印. The mapping is a function of two facts only: the elemental relationship between the two stems (same, generates, generated, controls, controlled), and whether the polarities match (both yang, both yin, or mixed). The result is a single, deterministic key per stem comparison.

Hidden-stem Ten Gods are tagged with their type — 'main', 'middle', or 'residual' — so the dashboard can emphasise the primary and quiet down a ten-percent residual. Reading every hidden stem flat is a common bug in lighter calculators; it inflates noise and obscures the actual structure of the chart.

The Day Stem is the Day Master — the user themselves. Every other stem and branch in the chart either supports or drains that element. Flow+ scores Day Master strength on the classical 子平 trio: 得令 (in season), 得地 (rooted in branches), 得势 (supported by stems). The weights, drawn from 子平真诠 and Tin Yat Lai's published methodology, are 0.50 for the seasonal command of the month branch, 0.25 for branch rooting across the four pillars, and 0.25 for stem support and drain.

Stem support means same-element peers (比肩, 劫财) and producing resource (印). Stem drain comes from the officer pair (七杀, 正官) controlling the Day Master, the wealth pair (正财, 偏财) it controls, and — critically — the output pair (食神, 伤官) it generates. A Day Master surrounded by output stems is being expressed outward, and that depletion belongs in the score. Lighter calculators omit the output drain and produce systematically over-strong readings.

We bucket scores into very_weak / weak / balanced / strong / very_strong using the Joey Yap school cuts of 30 / 45 / 55 / 70. The thresholds are documented in the dashboard's chart-detail panel so the user can see where their score sits relative to a balanced chart. A balanced Day Master between 45 and 55 is the rarest and most flexible profile — most charts lean one way, and the Useful God logic uses that lean as input.

The Useful God (用神) is the single element a chart most needs to function. Pure 扶抑 logic — support if weak, suppress if strong — gets the answer right in mid-season charts, where the climate is moderate. It fails predictably at the extremes. A Day Master born in deep winter or peak summer has a climate problem that overrides the strength calculation.

Flow+ layers 调候 (climate balance) from 《穷通宝鉴》 on top of 扶抑. The classical 30-row lookup, indexed by Day Master and birth-month branch, returns a primary and secondary climate Useful God. For a 庚 (yang metal) Day Master born in 子月 (deep winter), the table specifies 丙 (warm fire) as primary — the metal must be warmed before it can hold its edge. A pure 扶抑 engine would suggest 戊 / 己 (earth) as resource. The classical answer is fire.

The merged logic prefers the climate god in season-extreme months and the support / suppress god in moderate months. Both are surfaced; the user sees which one is doing the work. 通关 (mediator stems) and 病药 (disease and cure) are not yet in production — they are documented in the audit and on the engineering roadmap.

The Twelve Stages of Life (十二长生) trace each Heavenly Stem through a twelve-phase cycle around the Earthly Branches: 长生, 沐浴, 冠带, 临官, 帝旺, 衰, 病, 死, 墓, 绝, 胎, 养. Yang stems walk clockwise from their classical anchor; yin stems walk counter-clockwise. From the Day Master, every other branch in the chart resolves to one of these twelve labels — a precise way to read the rooting and support each pillar gives the Self.

Na Yin (纳音) maps every consecutive pair of the sixty Jiazi to one of thirty named sound-elements. 甲子乙丑 is 海中金 — gold within the sea. 丙寅丁卯 is 炉中火 — fire within the furnace. The lookup is fully deterministic and standard across Joey Yap, Tin Yat Lai, and mainland 子平 schools. Flow+ surfaces the Na Yin of each pillar as a poetic descriptor that complements the abstract element label.

Shen Sha (神煞) are the auspicious and inauspicious stars layered on top of the four pillars. Flow+ implements twenty: 太极贵人, 三奇贵人, 月德贵人, 天德贵人, 国印贵人, 将星, 天医, 天厨贵人, 金舆, 流霞, 孤辰寡宿, 天罗地网, plus the better-known 桃花, 华盖, 天乙贵人, 红艳, 文昌, 魁罡, 羊刃, 驿马. Each one is a table lookup keyed off Day Stem, year branch, or month branch — never invented prose.

Where classical doctrine reads a Shen Sha as fatalistic, Flow+ rewrites the framing. 桃花 is romantic and creative magnetism, not a moral hazard. 华盖 is depth and solitude, not a curse on relationships. 孤辰寡宿 names a tendency toward inwardness, not a sentence to loneliness. The arithmetic stays classical; the language stays constructive.

The four pillars are settled, but practitioners read two more pillars beyond them — 胎元 (Embryo Origin) and 胎息 (Conception Pillar). Both vary by lineage. Flow+ computes and displays both schools side-by-side on every chart so users see whichever value their teacher uses, without having to reconcile the two. The classical 三命通会 method derives 胎元 from the month pillar (stem +1, branch +3) and 胎息 from the day pillar via the 五合 stem partner and 六合 branch partner. The 玄學 lineage — traceable to Master Wilbur Goh and the 悟中源 school in Cantonese / Singapore-Malaysia practice — derives 胎元 from the hour pillar (stem +5, branch +7) and 胎息 from the day pillar (stem +1, branch +7).

The classical method is hour-independent, which makes it the right reading when birth time is unknown. The 玄學 method anchors the gestation pillar to the conception moment relative to the birth hour, encoding the roughly ten lunar-month gestation as a stepwise advance through the sixty-jiazi cycle. Practitioners differ on which lineage is canonical — and Flow+ does not arbitrate. Both values appear on every chart with their lineage citation chip, so a reader trained in either school recognises the value they expect.

Qi Men Dun Jia produces a nine-palace chart — the 洛书 grid — populated with stems, gates, stars, and deities for a given time slice. Flow+ runs two chart types: 时家 (hourly), driven by the Hour Pillar of the present moment, and 日家 (daily), driven by the Day Pillar pinned to local noon. The hourly chart updates every two hours; the daily chart is stable across a calendar day in the user's timezone.

Yang Dun and Yin Dun are selected by solar term: Yang from 冬至 through 芒种, Yin from 夏至 through 大雪. Within each polarity, the Ju (上元 / 中元 / 下元) is selected by 拆补法 — the engine reads the most recent 符头 (jiazi or jisi) day on or before the current solar term, then walks forward. Many engines that label themselves 拆补法 actually implement 置闰法 (days-modulo-fifteen). The classical 拆补法 reads the 符头's branch: 子午卯酉 maps to upper, 寅申巳亥 to middle, 辰戌丑未 to lower. Flow+ has the day-modulo path in production today and the branch-table refinement on the audit-driven roadmap.

The center palace (中5) has no native lodging in the eight-direction grid, so it borrows. Flow+ uses the 古星门 lineage rule: Yang Dun lodges at palace 2 (Kun), Yin Dun lodges at palace 8 (Gen). Other lineages — most notably the popular Joey Yap school — use 阳遁寄坤 for both polarities. We declare our school in the engine header and document the choice here so users can compare.

Gates rotate forward in 转盘 Qi Men regardless of polarity — confirmed by the 烟波钓叟歌. Stars follow the heaven-plate rotation. Deities rotate clockwise in Yang Dun and counter-clockwise in Yin Dun, anchored at 值符. The 旬空 (void branches) are derived from the head of the current 旬 — the start of the ten-day cycle the present pillar belongs to — never from the present pillar itself, a distinction that is easy to invert and that we test against.

Couples mode pairs two BaZi charts and computes pair-element analysis (which elements each chart most needs from the other), Useful God overlap (where one chart is the climate balance the other is missing), and Day Branch interaction across the classical 三合 (triads), 六合 (pairs), 冲 (clash), 害 (harm), 刑 (penalty), and 破 (break) relations. Each interaction is named, sourced, and rendered as a constructive observation, never as a verdict on the relationship.

Family mode extends this to a household — parent and one or more children — and adds child-coaching language drawn from the child's Day Master strength and Useful God. Work mode does the same for a team and overlays Feng Shui Kua (本命卦) directions from 八宅明镜 to recommend seating arrangements. The Kua number is computed from solar Li Chun birth year and gender, mapped to East-Group or West-Group, and resolved into the four favourable directions (生气, 天医, 延年, 伏位) per person.

天乙贵人 cross-chart analysis answers a specific question: who in the group is a noble (贵人) for whom? The classical rule from 《三命通会》 maps each Day Stem to two noble branches; when a second person's chart contains one of those branches, that person carries noble effect for the first. The relation is not symmetric — A may be a noble for B without B being a noble for A — and Flow+ surfaces both directions independently.

Flow+ does not predict death, disaster, or hopelessness. Every difficult chart factor — a heavy 七杀, a 流霞 day, a clash year — is reframed as a growth edge or a timing window. Master Xie, the AI mentor who narrates Realign and the daily reading, is built on a system prompt that forbids fear language at the model layer. A safety filter (`lib/ai/safety-filter.ts`) catches anything the model produces that crosses the line.

The voice guard regression test runs every BaZi composer over canonical fixtures and asserts the generated prose contains zero forbidden patterns: no Singlish particles, no cushioning fillers, no fatalistic openers. The static editorial copy on this page is held to the same standard. If a contributor reintroduces a rejected pattern anywhere in a phrase inventory, the test fails before the change can ship.

We hold this line because the audience matters. Founders and professionals making meaningful decisions do not need a horoscope app to scare them. They need a calm, accurate reading and a clear next step. The constraint is the product.

Flow+ ships a 39-kilobyte calculation audit alongside the source code. The headline finding: "Overall accuracy assessment: ~85% production-correct on the actively-used Tang Yang Wu Qi Men path before today's fixes." The audit names every methodology choice, compares Flow+ against Joey Yap, Tin Yat Lai, and classical 子平, and grades each domain — pillars, hidden stems, Day Master strength, Useful Gods, luck pillars, annual pillars, Qi Men Ju selection, palace lodging, void branches.

Where Flow+ is correct, the audit says so. Where Flow+ has chosen a school different from the most popular alternative — center-palace lodging, the 子时 split, 天禽 lodging when 中5 borrows — the audit names the tradeoff and the lineage. Where Flow+ has shipped an approximation, the audit names the gap and the fix. The document is updated on every methodology change and is the canonical reference for engineering, not a marketing artifact.

Reading the audit is a fair way to evaluate any calculation tool. We invite the comparison.