Learn saju · Chapter 2: How a chart is built · Lesson 1 of 5
How a saju chart is actually calculated (the real math)
2026-07-10 · 6 min read · Ioreum
A saju (BaZi) chart looks mystical — eight Chinese characters, five elements, a cycle of sixty. But the chart itself is pure calendar math: deterministic, reproducible, and checkable against a printed almanac. Here is how the calculation really works, and the three boundary problems where most tools quietly get it wrong.
Four pillars, one counting system
Traditional East Asia tracked time on a repeating cycle of sixty: ten heavenly stems paired with twelve earthly branches. Every year, month, day and hour carries one stem-branch pair — so your birth moment pins down four pairs, eight characters total. That is the entire chart. No interpretation has happened yet; this part is arithmetic.
The day pillar — the one your Day Master and your 60-character identity come from — simply counts the sixty-day cycle, unbroken for centuries. Given the same calendar date, every honest calculator on earth must produce the same day pillar.
Boundary problem #1 — the year and month change with the sun, not the calendar
Here is the first place tools go wrong: in saju, the year does not begin on January 1st, and months do not begin on the 1st. Both follow the twenty-four solar terms — precise moments in the Earth’s orbit. The saju year begins at Ipchun (start of spring, around February 4th), and each saju month begins at a solar term that lands mid-calendar-month, at a specific hour and minute.
Someone born on February 3rd belongs to the previous saju year. Someone born six hours before a solar term has a different month pillar than someone born six hours after. Round the boundary to a whole day — as many quick calculators do — and everyone born on a boundary day gets a coin-flip chart.
Boundary problem #2 — the 11 pm question
The traditional day is divided into twelve two-hour branches, and the first one — the zi hour — starts at 11 pm, before midnight. So a birth at 11:30 pm sits inside the next day’s first hour while the clock still says today. Schools differ on how to resolve this, and a serious calculator has to pick a convention and state it, not ignore the problem.
This is also why a missing birth time matters less than people fear for the day pillar, but a great deal for the hour pillar — the pillar that governs later life and inner ambition in classical reading.
Boundary problem #3 — your birthplace bends the clock
Clock time is political; solar time is physical. Charts are traditionally cast by the sun’s actual position at your birthplace, so an honest engine corrects your birth time by longitude and the equation of time — a shift that can reach tens of minutes. Born near an hour-branch boundary in, say, New York or Kuala Lumpur, that correction can move your hour pillar.
This is why the same person can get different charts from different sites. The disagreement is almost never about tradition — it is about whether the tool did the astronomy.
Why chatbots get this wrong
Large language models predict plausible text; they do not run calendars. Ask a chatbot for your Four Pillars twice and you can receive two different charts, each presented with full confidence. The failure is invisible because the interpretation still reads beautifully — an ornate essay built on the wrong eight characters.
ioreum’s answer is architectural: a deterministic engine — locked by golden tests for solar-term boundaries, the zi hour, leap months and true solar time — computes every number first. The AI writes the interpretation afterward and is structurally unable to change a digit. The full architecture, with a worked example chart, is public at ioreum.com/en/methodology.
Frequently asked questions
Can my chart be calculated without a birth time?
Yes — the year, month and day pillars don’t need it, and the day pillar carries your Day Master. The hour pillar is skipped rather than guessed, and the reading says so honestly.
Why do two calculators give me different charts?
Almost always one of the three boundary problems: solar terms rounded to whole days, the 11 pm zi hour handled differently, or the birthplace’s true solar time skipped entirely.
Is the calculation something I can verify myself?
Yes. Pillars are calendar facts — a printed manseryeok (Korean almanac) or any rigorous almanac lists them. Same birth data, same eight characters, every time.