The BaZi chart
Eight characters — a stem and a branch for each of four pillars. Each pillar is derived from a different thing, which is why they can disagree between calculators independently of each other.
Year pillar
Set by where the birth instant falls relative to Li Chun, the first solar term — not Chinese New Year, and not the calendar year. Because the term is a single worldwide instant, the comparison must be made against the absolute time of birth, not any locally corrected clock reading.
Month pillar
Set by the twelve major solar terms. Like the year, it depends on an absolute astronomical instant.
Day pillar
A continuous count through the sixty possible stem-branch pairs — ten stems and twelve branches repeat together on a 60-step cycle. The only question is where the day starts, and schools disagree — see the conventions.
Hour pillar
Derived from the position of the sun at the birthplace, which is why it needs true solar time rather than clock time. At Hong Kong’s longitude the correction runs about −24 minutes: a clock reading of 23:00 is still 22:36 true solar time, and the hour branch is still the previous one.
Why two calculators can disagree
The four pillars above are not derived from one clock reading applied four times. The year and month compare an absolute instant against astronomical events; the hour reads the local sun. Most disagreements between sites come from collapsing those into a single chain — most commonly by running true solar time through the whole chart, which quietly produces the wrong year pillar for anyone born near Li Chun. The solar-term boundary cases in the test corpus show this happening; the conventions state the rule this engine takes.
Cast your own chart — free, no sign-up, with every correction shown. Or read what a Day Master is.