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How a BaZi chart is calculated

Most BaZi calculators give you four pillars and stop there. This page documents every rule behind ours — which boundary we use for the year, how the hour is corrected for longitude, how hidden stems are weighted, and what the percentages on the result page actually measure.

Algorithm version 1.3Updated 19 October 2026Engine lunar-javascript (MIT), self-hosted

1. From clock time to the chart's clock

A birth certificate records civil time: the reading on a clock in a particular place, under whatever time zone and daylight-saving rules were in force that day. A BaZi chart is traditionally built on local solar time — when the sun actually crossed the local meridian. Two corrections are needed.

Longitude correction

Each time zone is anchored to a central meridian (15° of longitude per hour of offset). If you were born away from that meridian, your local noon is not the same as the zone's noon. The correction is four minutes per degree:

Someone born in Lisbon (about 9°W) under a 0-offset zone is roughly 36 minutes behind zone time; someone born in Warsaw (about 21°E) is roughly 24 minutes ahead.

Equation of time

Because Earth's orbit is elliptical and its axis is tilted, apparent solar time drifts by up to about ±16 minutes across the year. We apply the standard approximation:

The two corrections are added to the civil time you enter, and the result is the time used for the hour pillar and for locating the birth moment against the solar terms.

2. The year turns at Li Chun

The sexagenary year does not begin on 1 January, and it does not begin at Chinese New Year either. In the BaZi tradition the year changes when the sun reaches 315° of solar longitude, the term Li Chun (Beginning of Spring), which falls around 3–5 February.

This produces the mismatch that confuses people most often. In 2000, Li Chun arrived on 4 February at about 20:40 China time. A birth on 4 February at 20:00 still belongs to the previous year, Ji Mao (己卯); twenty minutes later the year becomes Geng Chen (庚辰) — even though Chinese New Year that year was 5 February. Our regression tests pin exactly this pair of cases.

Practically: if you were born in the first week of February, the year pillar is the part of your chart most likely to be wrong elsewhere.

3. Months follow solar terms, not lunar months

BaZi months are defined by the twelve jie (节), the odd-numbered solar terms that mark roughly every 30° of solar longitude. The month pillar's branch is fixed by that term, and its stem is derived from the year stem by the Five Tigers rule (五虎遁):

Notice that Spring begins in February and that 辰, 未, 戌 and 丑 — the "earth" branches — close each season rather than opening one. That is why the month branch, not the month number, sets the seasonal weighting in section 7.

4. The day pillar and the 23:00 boundary

The day pillar runs on an unbroken 60-day cycle counted from a fixed reference date, so it needs no astronomical input — but it does need a decision about when a day ends. Two conventions are in use:

• 23:00 boundary (晚子时 school): the day changes at the start of the Zi hour. A birth at 23:30 belongs to the next day's pillar.
• 00:00 boundary (早子时 school): the day changes at midnight, so 23:30 still belongs to the current day.

Aveni uses the 23:00 boundary, which is the convention in the classical texts we cite. If another calculator disagrees with ours by exactly one day pillar for a late-night birth, this is almost always the reason.

5. The hour pillar

Hours are grouped into twelve double-hours, each named by a branch. The Zi hour spans 23:00–01:00, and the sequence then follows the branches. The hour stem is derived from the day stem by the Five Rats rule (五鼠遁):

Because the hour pillar depends on solar time, the corrections in section 1 can change it. A birth recorded at 12:55 in a city 20° west of its zone meridian can fall in the previous double-hour once longitude and the equation of time are applied — which is exactly the kind of edge case that silently flips a chart.

6. Hidden stems

Each earthly branch contains one to three stems, traditionally described as main qi (本气), middle qi (中气) and residual qi (余气). These hidden stems are what make a chart's element balance meaningful; counting only the four visible stems loses most of the information.

Other schools weight differently — some give three hidden stems equal shares, some use 0.6 / 0.3 / 0.1. The choice shifts percentages by a few points but rarely changes which element leads. What matters is that the numbers are stated rather than hidden.

7. Seasonal weighting

This is the step most simple calculators skip: they count stems and branches equally and report an average-looking chart. In practice a Fire element born in midwinter and a Fire element born at midsummer are not in the same condition. Traditional theory describes five states — 旺 prosperous, 相 strong, 休 resting, 囚 trapped, 死 dead — relative to the season set by the month branch.

Each state carries a multiplier, applied after the raw weights are summed:

The full model, in order:

1. Each visible stem adds 1.0 to its element.
2. Each branch adds its hidden stems at 1.0 / 0.4 / 0.2.
3. The branch itself adds 0.3 as structural support — 0.5 when it is the month branch.
4. Everything inside the month branch is multiplied by 1.6, because the month command carries the season.
5. Every element total is multiplied by its seasonal factor from the table above.
6. The five totals are normalised to 100%.

Day Master support

The result page also reports one derived figure: the share of the chart that supports the Day Master versus the share that drains it.

Bands: 62% and above — Strong Day Master; 45–61% — Balanced; below 45% — Gentle. These thresholds are ours, chosen to be legible rather than authoritative; classical texts describe the same idea qualitatively.

8. Ten Gods

Every stem in a chart is classified by its relation to the Day Master: the five element relations, each split by polarity. This is what the labels above each pillar on the result page mean.

Hidden stems receive the same classification, which is why each pillar on the result page shows a short list such as Seven Killings · main beneath the branches.

9. Luck pillars

The ten-year luck pillars (大运) sequence the chart's month pillar forward or backward. Direction follows the year stem's polarity and the sex recorded at birth:

• Yang year stem + male, or Yin year stem + female → forward through the sexagenary cycle.
• Yin year stem + male, or Yang year stem + female → backward.

The starting age comes from the distance to the adjacent solar term: count the days from birth forward to the next jie (forward sequence) or backward to the previous one, then convert at three days per year, one day per four months. The example chart above starts its sequence at 5 years 6 months 20 days, opening with 壬午.

We display eight pillars, marking the one that contains the current year. Sex at birth is used for this calculation only; it is not stored with your chart.

10. What this calculator does not do

• No predictions. Nothing here forecasts events, outcomes, health, money or relationships. The output is a symbolic map offered as a prompt for reflection.
• No "good" or "bad" charts. A missing element is not a deficit, and a "strong" Day Master is not a compliment. The bands describe balance under one model.
• No silent guessing. If the birthplace cannot be geocoded, the calculation stops and says so rather than defaulting to a time zone.
• Known approximations. The equation of time is a standard approximation, not an ephemeris lookup. Historical time zone data comes from the IANA database and is reliable for major cities, less so for small towns before 1970.
• Schools differ. Where they do — day boundary, hidden-stem weights, strength thresholds — this page states our choice instead of presenting it as the only reading.

Sources and further reading

• 渊海子平 (Yuan Hai Zi Ping), attributed to Xu Ziping — the foundational compilation of the Four Pillars method, including the year boundary and the Ten Gods system.
• 三命通会 (San Ming Tong Hui), Wan Minying, 1578 — the encyclopaedic Ming-dynasty reference for hidden stems, seasonal states and luck pillars.
• 穷通宝鉴 (Qiong Tong Bao Jian) — the classical treatment of seasonal preference (调候) that informs the weighting model here.
• 子平真诠 (Zi Ping Zhen Quan), Shen Xiaozhan, 1739 — the standard text on structure and usefulness (格局用神).
• Ho Peng Yoke, Chinese Mathematical Astrology: Reaching Out to the Stars, Routledge, 2003 — scholarly context for the calendar and solar-term mathematics.
• lunar-javascript (MIT licence), self-hosted — the sexagenary cycle, solar-term and sexagenary-hour tables used by this page's engine.

Corrections are welcome and credited: [email protected].

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