How to Calculate a BaZi Chart by Hand:
Year, Month, Day and Hour

A woman was born on August 15, 1990, in Moscow, at half past two in the afternoon. Her birth certificate gives the date; in her head she is "probably a Leo, Year of the Horse." For BaZi (八字, bā zì, "eight characters") that is enough to write out four pillars: year 庚午, month 甲申, day 壬子, hour 丙午. Below we take this one example all the way from zero, and you can repeat every step with a pencil or a spreadsheet.

Why calculate by hand when calculators exist? First, to understand where the result comes from, and why it is sometimes "not what my friend's practitioner said." Second, to catch mistakes. A wrong pillar rarely comes from the arithmetic. It usually comes from the input: the date and time themselves. We'll get to that in the last section.

If you'd rather skip the hand work, the online BaZi calculator builds the same chart in a minute, with true solar time, the Ten Gods and the Luck Pillars. It's also a handy way to check your own result.

1 Time first: true solar time

The Hour Pillar is tied to the Sun over your city. The clock on the kitchen wall shows zone time, and that can differ noticeably from solar time. The correction has two parts: longitude (4 minutes for every degree between your city and the meridian the clocks actually followed, including any daylight-saving or other added hour) and the equation of time (the seasonal drift of the Sun against an even clock, up to ±16 minutes).

For our example all of this has to be pieced together from history. In August 1990 Moscow ran on UTC+4: the "decree hour" added in 1930, plus summer time. The meridian of that zone is 60° E, and Moscow sits at 37.6° E, a gap of about 22.4° × 4 ≈ 90 minutes. The equation of time in mid-August adds roughly another 4 minutes. The site's engine gives the total: −93.7 minutes. So 2:30 pm on the clock was 12:56 by the Sun.

That difference decides the hour. 12:56 falls into the two-hour window of 午 (11:00–13:00), while 14:30 "by the clock" would land in the window of 未 (13:00–15:00). Someone who skipped this step would get the hour 丁未 instead of 丙午. How the Hour Pillar itself works is covered in The Hour Pillar, and why the minute of birth matters in Exact Time of Birth.

Clock history is full of traps. Moscow alone added a "decree hour" in 1930, dropped it in spring 1991 and brought it back in January 1992; it used summer time from 1981 to 2011, stayed on UTC+4 all year from 2011 to 2014, and has been on UTC+3 since autumn 2014. Other countries have their own stories: the United States kept year-round "War Time" from 1942 to 1945, Britain ran double summer time during the Second World War, and China observed summer time from 1986 to 1991. For any other city and year, look up the clock offset in a time zone database before you correct the hour.

2 Step 1: the Year Pillar

The BaZi year doesn't start on January 1, and not at Chinese New Year either. It starts at the moment of 立春 (lì chūn, "Start of Spring"), around February 4. By this count, someone born on January 20, 1990, still belongs to 1989. Our example was born in August, so we stay in 1990.

The stem and branch come from two remainders. Subtract 4 from the year, then divide by 10 (for the stem) and by 12 (for the branch):

1990 − 4 = 1986. 1986 mod 10 = 6, which is 庚 (gēng, Yang Metal). 1986 mod 12 = 6, which is 午 (wǔ, the Horse). The Year Pillar is 庚午. Had the person been born on January 20, 1990, we would use 1989: 1985 mod 10 = 5 → 己, 1985 mod 12 = 5 → 巳, giving 己巳. The year and its element get a closer look in our article on your element by birth year.

3 Step 2: the Month Pillar, by solar terms, not by the calendar

BaZi months are tied to twelve terms called 節 (jié, the "nodes" of the solar year), each of which opens a month. The cycle begins with 寅 in February, so the "March" month here is 卯, the second one. The dates below are approximate (based on 2027; they shift by up to a day from year to year), so for a birth right at a boundary you need the exact minute of the term.

A birth on August 15 comes after 立秋: in 1990 it fell on August 8, Beijing time (late evening of the 7th in Moscow). The month branch is 申 (the Monkey). The branch is the easy part. The month stem comes from the rule 五虎遁 (wǔ hǔ dùn, "five tigers"). It tells you which stem opens the 寅 month in a year with a given stem; after that, stems and branches simply run in order.

Our year is 庚, so 寅 is 戊寅. Walk the chain to the seventh month (申 is seventh from 寅): 戊寅, 己卯, 庚辰, 辛巳, 壬午, 癸未, 甲申. A check with another year: 2027 is a 丁 year, its 寅 month is 壬寅, which matches the site's engine.

4 Step 3: the Day Pillar, the only one that needs a reference date

The year and the month have formulas. The day doesn't: the sixty-day cycle has run without a break for thousands of years, and the only way to count it is from a known reference date. We'll use January 7, 2000: that day is 甲子, number 0 in the cycle of 60. To check yourself: January 1, 2000, is 戊午, and October 1, 1949 (the day the People's Republic of China was proclaimed) is again 甲子.

The procedure: count the number of days D between the reference date and the birth date (for earlier dates it comes out negative). Take the remainder of D divided by 60, always as a non-negative number; that is N. The stem is N mod 10 and the branch is N mod 12, using the same lists as in Step 1.

For August 15, 1990: D = −3432. The remainder of −3432 modulo 60 is 48. 48 mod 10 = 8, which is 壬; 48 mod 12 = 0, which is 子. The Day Pillar is 壬子.

In Google Sheets or Excel this is one formula: =MOD(DATE(1990,8,15)-DATE(2000,1,7),60) (some locales use semicolons instead of commas). With a positive divisor, MOD returns a non-negative result even when the difference is negative, so the formula works for 1990 too and returns 48. If the cell suddenly shows a date, switch its format to Number. Excel doesn't handle dates before 1900; Google Sheets does. Then take N and convert it to a stem and branch by hand.

The day stem is the Day Master (日主, rì zhǔ): the point from which everything else in the chart is read. What it means is covered in detail in Day Master, and if you're curious what all sixty day pillars look like, see the 60 Day Pillars.

Two subtle points. First, the day is set by true solar time, so if the solar-time correction from the first section pushes the birth across midnight, the date changes too. Second, the Rat hour from 23:00 to 01:00. In the site's calculation the day changes at midnight, and the hour stem for 23:00–00:00 is taken from the next day (the so-called "late Rat hour"). Other schools change the day already at 23:00. If you were born in that window, keep both versions in mind and don't panic if two practitioners give you different Day Pillars.

5 Step 4: the Hour Pillar

The twelve branches are laid out over two-hour windows of true solar time:

Our 12:56 gives 午. The hour stem comes from the rule 五鼠遁 (wǔ shǔ dùn, "five rats"), which works like the "five tigers," except the count starts from the 子 hour and depends on the day stem:

Our day is 壬, so the 子 hour is 庚子. 午 is the seventh hour from 子. Count: 庚子, 辛丑, 壬寅, 癸卯, 甲辰, 乙巳, 丙午. Had we forgotten the solar-time correction, we would have 丁未: a different stem, a different branch, and with them different hidden stems and gods in the Hour Pillar.

6 Steps 5 and 6: hidden stems and the Ten Gods

Each branch holds one, two or three stems inside it. These are the 藏干 (cáng gān, "hidden stems"), and they come from a fixed table. The percentages are each stem's weight in the site's calculation; classical texts may split them differently, but the order "main, middle, residual" is much the same everywhere.

In our example, 午 carries 丁 (70%) and 己 (30%); 申 carries 庚 (60%), 壬 (30%) and 戊 (10%); 子 carries a single 癸 (100%). More on this layer in Hidden Stems.

Now each stem needs a role relative to the Day Master. These roles are the Ten Gods (十神, shí shén), and one rule produces all of them. First see how the stem's element relates to the Day Master's element, then compare polarity (Yang or Yin):

• Same element, same polarity: 比肩 (bǐ jiān, Shoulder to Shoulder).
• Same element, opposite polarity: 劫財 (jié cái, Rob Wealth).
• The Day Master produces this element: same polarity is 食神 (shí shén, Eating God), opposite is 傷官 (shāng guān, Hurting Officer).
• The Day Master controls this element: same polarity is 偏財 (piān cái, Indirect Wealth), opposite is 正財 (zhèng cái, Direct Wealth).
• This element controls the Day Master: same polarity is 七殺 (qī shā, Seven Killings), opposite is 正官 (zhèng guān, Direct Officer).
• This element produces the Day Master: same polarity is 偏印 (piān yìn, Indirect Resource), opposite is 正印 (zhèng yìn, Direct Resource).

The producing cycle: Wood produces Fire, Fire produces Earth, Earth produces Metal, Metal produces Water, Water produces Wood. The controlling cycle: Wood → Earth, Earth → Water, Water → Fire, Fire → Metal, Metal → Wood. Other books and apps use different English names for some of these (Friend or Companion for 比肩, Seal for 印), but the logic is the same.

Our Day Master is 壬, Yang Water. Apply the rule:

• 庚 (Yang Metal) produces Water, same polarity → 偏印.
• 甲 (Yang Wood) is produced by Water → 食神.
• 丙 (Yang Fire) is controlled by Water → 偏財; its Yin partner 丁 → 正財.
• 己 (Yin Earth) controls Water, opposite polarity → 正官; its Yang partner 戊 → 七殺.
• 癸 (Yin Water) → 劫財.

Each god is covered in detail in The Ten Gods of BaZi.

7 Step 7: the Luck Pillars, which direction and from what age

The 大運 (dà yùn, "great luck") are ten-year periods that run along the sixty-cycle starting from the Month Pillar. You need two decisions: direction and starting age.

Direction. A Yang year (year stem 甲, 丙, 戊, 庚 or 壬) for a man and a Yin year for a woman run forward through the cycle; the other combinations run backward. Our year 庚 is Yang and the chart is a woman's, so we go backward from 甲申.

Start. Count the days from birth to the nearest 節 term in the direction of travel (forward: to the next one; backward: to the previous one) and divide by 3: three days equal one year of life. From 立秋 (the term fell on August 7–8, 1990) to the birth is about 7.6 days, so the start is around age 2.5. Her Luck Pillars: 癸未, 壬午, 辛巳, 庚辰, 己卯, 戊寅.

A man born at the very same moment runs forward, to 白露 (September 8), about 23.5 days away, so his start is around age 7.8 and his pillars are 乙酉, 丙戌, 丁亥 and onward. That's why sex is part of the input data in BaZi, just like the date. How to read the pillars themselves is covered in Luck Pillars and the Ten Gods in your Luck Pillar.

8 The finished chart

Here is everything in one table: four pillars, hidden stems, and the god of each visible stem relative to the Day Master 壬.

Now check yourself: enter the same data into the free chart by date of birth. The Day Master, the four pillars and the balance of the five elements should match the table.

Look at the hidden stems and you'll see that the 午 branches hold 丁 and 己, Fire and Earth, which for a 壬 Day Master are 正財 and 正官. From 申 come 庚 (偏印), 壬 (比肩) and 戊 (七殺); from 子 comes 癸 (劫財). Whether the chart is strong or weak is a separate question, and arithmetic alone won't answer it. A good place to start is How to Read a BaZi Chart.

9 Where people most often go wrong

• January and early February. If you were born before 立春, you need the previous year. That shifts the year stem and branch, and the month stem along with them.
• Counting months by the calendar. "August is the eighth month, so it's the eighth branch from 寅, which is 酉" is a classic slip. Until the 8th, August is still 未; after that it's 申. The month boundary is set by the 節 term.
• Forgotten daylight saving or a historical extra hour. The time shifts by an hour or two, and the Hour Pillar easily slides into the next window. For older dates, check the zone time and any shifts in a reference.
• A lunar date instead of a solar one. BaZi is calculated on the solar calendar. If your passport date is an ordinary Gregorian one, there's no issue, but Chinese and other East Asian horoscopes sometimes work with lunar dates.
• Born between 23:00 and 01:00. If you were born between 23:00 and midnight, schools disagree about the Day Pillar: some have already moved to the next day, others (including this site) haven't. Find out how your tool counts and keep both versions in mind.
• A term boundary on your birthday. If a 節 falls on your day, the minute decides: before it you're still in the previous month, after it you're in the next. "Around the 8th" isn't good enough here; you need an exact table of terms. If your birth time is only approximate, rectification can help.

A chart describes conditions and periods that deserve attention. Hand calculation is for understanding the mechanics; conclusions about a person come from the whole chart.

10 Frequently asked questions

How do I calculate the four pillars of BaZi myself?

The Year Pillar counts from 立春 (around February 4), the month follows the 節 solar terms, the day is counted from the reference date January 7, 2000 (甲子) as a remainder of division by 60, and the hour follows two-hour windows of true solar time.

How do I find my Day Pillar and Day Master?

Count the days from January 7, 2000, to your date and take the remainder of division by 60. The remainder by 10 then gives the stem, and by 12 the branch. For August 15, 1990, the result is 壬子.

Why doesn't the Hour Pillar match my watch?

The Hour Pillar is calculated by true solar time at the place of birth. That includes longitude, the equation of time and any daylight-saving or extra hour, and in Moscow on August 15, 1990, they moved 14:30 back to 12:56.

Which year do I use if I was born in January or early February?

The BaZi year changes at the moment of 立春, around February 4. If you were born between January 1 and that moment, use the previous year.

Can I calculate a BaZi chart without a birth time?

The Year, Month and Day Pillars don't need the hour; only the fourth pillar is missing. For that case the site has a separate Three-Pillar Reading.