How a bazi chart is cast
Eight characters, four pillars, and a short chain of arithmetic that can be checked against public astronomical data. This page sets out what the chart is and how each part of it is arrived at.
What the eight characters are
A completed chart is eight characters.
They read as four columns, and each column is called a pillar: the year pillar, then the month, the day and the hour.
Every pillar has two parts. The upper character is one of the ten Heavenly Stems, 天干. The lower is one of the twelve Earthly Branches, 地支. Ten and twelve run together in a repeating cycle of sixty pairs — the 六十甲子 — which has been used to number days in China without a break since the Shang oracle bones, and is the longest continuously operating dating system anywhere.
The upper character of the day pillar is called the Day Master, 日主, and it is the subject of the entire reading. The other seven characters describe the conditions it stands in.
The month pillar is set by a solar term, not by a calendar date. The year animal is read off the branch of the year pillar — one character out of eight, and of the eight it carries the least.
This section states what the chart is. There is no interpretation in it.
The full calculation trace
This is the full trace, so that any of it can be checked against a source you choose.
Step 1 — the instant. The birth date and clock time are converted to a single UTC instant using the time zone in force at the birthplace on that date, including any daylight saving then in effect.
Step 2 — true solar time. Longitude and the equation of time are each stated in minutes, and their sum gives true solar time against the clock reading. Where the adjustment does not cross a branch boundary, no pillar moves.
Step 3 — year and month. The year and month pillars are set by solar terms, not by calendar dates. The page names the term governing the month. Term instants are computed from the sun's apparent ecliptic longitude at fifteen-degree intervals; the table covers 1899 to 2100 and was checked against an independent ephemeris across 4,704 terms, agreeing on all but seven, every one of those inside twelve minutes of local midnight.
Step 4 — day and hour. The day pillar comes from the continuous sixty-pair count, which has run without interruption since the Shang and is therefore an ordinal, not a calculation. The hour pillar follows from the solar-time branch and the day stem. Step 5 — decades: direction from year-stem polarity and sex, starting age by counting to the adjacent solar term at three days to the year.
Every number above is reproducible. Nothing in it depends on us.
Cast the chart this page describes
The four pillars, the Day Master, the five-phase count, the day’s almanac read against the chart and the true solar time working — about 2,700 words — are free and need no account. The chart is computed in the browser; nothing about the birth is sent anywhere.