How Is the Five-Element Ratio Actually Calculated?
The percentage on your element bars and the percentage that decides strong or weak are two different sums — and for some charts, that difference flips the verdict.
Bokki Editorial
The short answer
Bokki does not have one number for "how much Fire is in this chart." It has two, and they answer different questions. The bars you see on the element screen come from a straightforward weighted count: every stem in your four pillars counts once, and every branch contributes its hidden stems (地藏干) at their traditional fractional weights — no extra credit for any single pillar. A separate, heavier calculation runs underneath the strong/weak verdict and the favorable-element pick: it takes that same weighted count and then triples the month branch's hidden-stem contribution (because the season a person is born into carries the most weight in judging a chart) and adds a bonus if three or four branches lock into a seasonal or triangular bureau (局). Both numbers are real, both come from the same chart, and they are not required to agree — because they were never built to answer the same question.
The rule — one count for display, a heavier one for judgment
The display count, weightedElementBalance, loops over the year, month, day and hour pillars once: each pillar's visible stem adds one full point to its element, and each pillar's branch spreads roughly one point across its 1-3 hidden stems by a fixed ratio (the dominant hidden stem gets 0.6, a secondary gets 0.3, a minor one gets 0.1 — the classical 정기·중기·여기 split). Four pillars, so the five element totals always sum to exactly 8.0. The judgment count starts from that identical loop, then does two more things before anyone reads a verdict from it. First, it takes the month branch's hidden stems a second time — not replacing the first pass, adding to it — multiplied by three, because in Ziping method the commanding month (월령) is traditionally read as the single heaviest factor in a chart's strength. Second, it checks whether three or four of the chart's branches lock into a 삼합 (trine), 반합 (half-trine) or 방합 (directional trio) bureau; if they do, that bureau's element gets a flat bonus (+1.5 for a half-trine, +3 for a full trine or directional trio) on top of everything else. Only after both of those additions does the engine compute support share — same-element plus generating-element points, divided by the whole — and read strong (>55%), weak (<45%) or balanced.
Worked example — a Metal day master, and Fire that disagrees with itself
Take a real chart: 15 May 1990, 14:30, Seoul — 庚午 辛巳 庚辰 癸未, a Metal (金) day master, the same chart Bokki's pieces on luck cycles (daeun) and the Ten Gods (sipsin) already used. Run the display count first: Fire lands at 20.0% (1.6 of the 8.0 total), Metal at 41.3%, and support (Metal plus its resource element, Earth) comes to 61.3% of the chart — comfortably over the 55% strong threshold. Now run the judgment count on the exact same birth data. The month branch is 巳 (Snake), and its hidden Fire stem gets tripled — adding 1.8 points on top of what the display count already gave it. Then the engine checks for bureaus: the chart's four branches are Horse (午), Snake (巳), Dragon (辰) and Goat (未) — three of which, Snake-Horse-Goat (巳午未), are exactly the directional Fire trio, so a +3 방합(方合) bonus lands on Fire too. Fire's judgment-count share jumps to 45.7% of a new 14.0 total, more than double its display-count share. And because that extra Fire now counts as drain against a Metal day master (Fire controls Metal, 火剋金), support share falls to 43.6% — under the 45% weak threshold. The same birth data, run through two different but equally real Bokki calculations, gives strong from one ruler and weak from the other. Bokki's actual verdict for this chart is weak, because the strength judgment always uses the judgment count, never the display bars.
What this calculation doesn't decide
Neither ruler tells you whether an element is good or bad for you — that is a separate step (용신, the favorable-element pick), which reads the strong/weak verdict and then asks what the chart needs, not merely what it has most of. Neither number is shown to you as a literal score; Bokki keeps the bars visual precisely so no one screenshots "you are 45.7% Fire" as a diagnosis (D-003: no numeric self-worth ratings). The 지장간 weight ratios themselves (0.6 / 0.3 / 0.1) are a documented pedagogical approximation of a classical day-count method called 월률분야(月律分野), not an exact day-by-day proportion — Bokki's own source comments say so plainly, and this article does not claim more precision than that. And the bureau check only looks for the four classical trine/half-trine/directional groups already in Bokki's engine; it does not detect the rarer six-branch or mixed-合 patterns some schools also count.
Closing note — two sums, one chart, and only one of them judges
In short: Bokki's element bars and Bokki's strong/weak verdict are computed from two different weighted sums of the same eight pillar characters, not one number read two ways. The display sum treats every pillar equally; the judgment sum leans hard on the birth month and rewards branches that lock into a seasonal or triangular bureau. For most charts the two sums point in a similar direction and the difference barely registers — but for the Metal day master above, born in a month whose branch forms a Fire trio with two other branches in the chart, the gap is wide enough to turn a 61.3%-strong reading into a 43.6%-weak one. When Bokki tells you your chart runs weak, that judgment already used the heavier calculation — the bars on screen were never meant to carry that verdict alone.