Lunisolar Calendar

Lunisolar Calendar is used in many cultures. Its months are based on moon phases, while the years are roughly aligned with the solar calendar. It is a lunar calendar, but with a leap month every two or three years.

Chinese Calendar

Also known as the Agricultural Calendar (農曆 Nóng Lì), is believed to be the origin of some lunisolar calendar variants in the region.

Apart from the month and dates, the Chinese Calendar follow a sexagenary cycle, the Gān Zhī (干支) system. It's a repeating cycle of 10 Heavenly Stems (十天干) and 12 Earthly Branches (十二枝) that form 60 pairs or terms. Odd-even and Even-odd numbered pairing are not included, resulting in only 60 combinations instead of 120. These terms are cycled independently on years, months, days and hours. The 4 terms are referred to as the Four Pillars (四柱), which consist of 4 pairs of Heavenly Stem and Earthly Branch. This is also referred to as the Bā Zì (八字), literally meaning 8 characters. There are also elements are associated with each heavenly stem and zodiac animals associated with each earth branch.

10 Heavenly Stems (十天干)

#	Heavenly Stem		Element
1	甲	Jiǎ	木	Mù	Wood
2	乙	Yǐ	木	Mù	Wood
3	丙	Bǐng	火	Huǒ	Fire
4	丁	Dīng	火	Huǒ	Fire
5	戊	Wù	土	Tǔ	Earth
6	己	Jǐ	土	Tǔ	Earth
7	庚	Gēng	金	Jīn	Metal
8	辛	Xīn	金	Jīn	Metal
9	壬	Rén	水	Shuǐ	Water
10	癸	Guǐ	水	Shuǐ	Water

12 Earthly Branches (十二枝)

#	Earthly Branch		Zodiac Animal
1	子	Zǐ	鼠	Shǔ	Rat
2	丑	Chǒu	牛	Niú	Ox
3	寅	Yín	虎	Hǔ	Tiger
4	卯	Mǎo	兔	Tù	Rabbit
5	辰	Chén	龙	Lóng	Dragon
6	巳	Sì	蛇	Shé	Snake
7	午	Wǔ	马	Mǎ	Horse
8	未	Wèi	羊	Yáng	Goat
9	申	Shēn	猴	Hóu	Monkey
10	酉	Yǒu	鸡	Jī	Chicken
11	戌	Xū	狗	Gǒu	Dog
12	亥	Hài	猪	Zhū	Pig

Sexagenary cycle - Gān Zhī (干支) system

#	Gānzhī (干支)		Element-Zodiac
1	甲子	Jiǎ Zǐ	木鼠	Wood Rat
2	乙丑	Yǐ Chǒu	木牛	Wood Ox
3	丙寅	Bǐng Yín	火虎	Fire Tiger
4	丁卯	Dīng Mǎo	火兔	Fire Rabbit
5	戊辰	Wù Chén	土龙	Earth Dragon
6	己巳	Jǐ Sì	土蛇	Earth Snake
7	庚午	Gēng Wǔ	金马	Metal Horse
8	辛未	Xīn Wèi	金羊	Metal Goat
9	壬申	Rén Shēn	水猴	Water Monkey
10	癸酉	Guǐ Yǒu	水鸡	Water Chicken
11	甲戌	Jiǎ Xū	木狗	Wood Dog
12	乙亥	Yǐ Hài	木猪	Wood Pig
13	丙子	Bǐng Zǐ	火鼠	Fire Rat
14	丁丑	Dīng Chǒu	火牛	Fire Ox
15	戊寅	Wù Yín	土虎	Earth Tiger
16	己卯	Jǐ Mǎo	土兔	Earth Rabbit
17	庚辰	Gēng Chén	金龙	Metal Dragon
18	辛巳	Xīn Sì	金蛇	Metal Snake
19	壬午	Rén Wǔ	水马	Water Horse
20	癸未	Guǐ Wèi	水羊	Water Goat
21	甲申	Jiǎ Shēn	木猴	Wood Monkey
22	乙酉	Yǐ Yǒu	木鸡	Wood Chicken
23	丙戌	Bǐng Xū	火狗	Fire Dog
24	丁亥	Dīng Hài	火猪	Fire Pig
25	戊子	Wù Zǐ	土鼠	Earth Rat
26	己丑	Jǐ Chǒu	土牛	Earth Ox
27	庚寅	Gēng Yín	金虎	Metal Tiger
28	辛卯	Xīn Mǎo	金兔	Metal Rabbit
29	壬辰	Rén Chén	水龙	Water Dragon
30	癸巳	Guǐ Sì	水蛇	Water Snake
31	甲午	Jiǎ Wǔ	木马	Wood Horse
32	乙未	Yǐ Wèi	木羊	Wood Goat
33	丙申	Bǐng Shēn	火猴	Fire Monkey
34	丁酉	Dīng Yǒu	火鸡	Fire Chicken
35	戊戌	Wù Xū	土狗	Earth Dog
36	己亥	Jǐ Hài	土猪	Earth Pig
37	庚子	Gēng Zǐ	金鼠	Metal Rat
38	辛丑	Xīn Chǒu	金牛	Metal Ox
39	壬寅	Rén Yín	水虎	Water Tiger
40	癸卯	Guǐ Mǎo	水兔	Water Rabbit
41	甲辰	Jiǎ Chén	木龙	Wood Dragon
42	乙巳	Yǐ Sì	木蛇	Wood Snake
43	丙午	Bǐng Wǔ	火马	Fire Horse
44	丁未	Dīng Wèi	火羊	Fire Goat
45	戊申	Wù Shēn	土猴	Earth Monkey
46	己酉	Jǐ Yǒu	土鸡	Earth Chicken
47	庚戌	Gēng Xū	金狗	Metal Dog
48	辛亥	Xīn Hài	金猪	Metal Pig
49	壬子	Rén Zǐ	水鼠	Water Rat
50	癸丑	Guǐ Chǒu	水牛	Water Ox
51	甲寅	Jiǎ Yín	木虎	Wood Tiger
52	乙卯	Yǐ Mǎo	木兔	Wood Rabbit
53	丙辰	Bǐng Chén	火龙	Fire Dragon
54	丁巳	Dīng Sì	火蛇	Fire Snake
55	戊午	Wù Wǔ	土马	Earth Horse
56	己未	Jǐ Wèi	土羊	Earth Goat
57	庚申	Gēng Shēn	金猴	Metal Monkey
58	辛酉	Xīn Yǒu	金鸡	Metal Chicken
59	壬戌	Rén Xū	水狗	Water Dog
60	癸亥	Guǐ Hài	水猪	Water Pig

24 Solar Terms (二 十 四 節 氣)

The chinese use 24 terms to align with the seasons. These seasons are related to the Earth's orbit around the Sun, which make them fall on the same Gregorian dates (may vary by a day) every year. These Solar Terms are also mapped to 12 seasons, which are used for computing Ba Zi Month Pillar instead of the Lunisolar month.

Type	Solar Term		Month/Season Number	Start (Gregorian Date)
Major 中氣	立春 Lì Chūn	Beginning of Spring	1	2/4
Minor 節氣	雨水 Yǔ Shuǐ	Rain Water	1	2/19
Major 中氣	惊蛰 Jīng Zhé	Awakening of Insects	2	3/6
Minor 節氣	春分 Chūn Fēn	Spring Equinoz	2	3/21
Major 中氣	清明 Qīng Míng	Pure Brightness	3	4/5
Minor 節氣	谷雨 Gǔ Yǔ	Grain Rain	3	4/20
Major 中氣	立夏 Lì Xià	Beginning of Summer	4	5/6
Minor 節氣	小满 Xiǎo Mǎn	Grain Buds	4	5/21
Major 中氣	芒种 Máng Zhòng	Grain in Ear	5	6/6
Minor 節氣	夏至 Xià Zhì	Summer Solstice	5	6/21
Major 中氣	小暑 XiǎoShǔ	Minor Heat	6	7/7
Minor 節氣	大暑 Dà Shǔ	Major heat	6	7/23
Major 中氣	立秋 Lì Qiū	Beginning of Autumn	7	8/8
Minor 節氣	处暑 Chǔ Shǔ	End of Heat	7	8/23
Major 中氣	白露 Bái Lù	White Dew	8	9/8
Minor 節氣	秋分 Qiū Fēn	Autumn Equinox	8	9/23
Major 中氣	寒露 Hán Lù	Cold Dew	9	10/8
Minor 節氣	霜降 Shuāng Jiàng	Frost's Descent	9	10/23
Major 中氣	立冬 Lì Dōng	Beginning of Winter	10	11/7
Minor 節氣	小雪 Xiǎo Xuě	Minor Snow	10	11/22
Major 中氣	大雪 Dà Xuě	Major Snow	11	12/7
Minor 節氣	冬至 Dōng Zhì	Winter Solstice	11	12/22
Major 中氣	小寒 Xiǎo Hán	Minor Cold	12	1/6
Minor 節氣	大寒 Dà Hán	Major Cold	12	1/20

Bā Zì (八字) Formula

The following are formulas to compute Ba Zi for a given date. You'll need both the Lunisolar Date, Gregorian Date and Corresponding Solar Term Month/Year. Refer to the tables above to map the # to the character. The formulas are zero-based (i.e. row 1 is 0).

Bā Zì (八字)	Formula	Notes
Year Heavenly Stem #	(Lunisolar Year + 6)%10	Lunisolar 1900: 6 as initial value; No need to subtract 1900 since mod 10
Year Earthly Branch #	(Lunisolar Year-1900)%12	Lunisolar 1900: 0 as initial value; Plus 12 to result if negative
Month Heavenly Stem #	(Solar Term Year*12 + Solar Term Month # + 3)%10	Lunisolar Jan 1900: 4 as initial value; +3 = -1 + 4 No need to subtract 1900 since mod 10; Note that Solar Term Year should be the previous lunar year if the Gregorian Date is less than the first cut off (i.e. Feb 4)
Month Earthly Branch #	Solar Term Month # + 1	Lunisolar Jan 1900: 2 as initial value; +1 = -1 +2
Day Heavenly Stem #	(Gregorian days since Jan 31, 1900)%10	Gregorian Date Jan 31, 1900; 0 being the initial value; Plus 10 to result if negative
Day Earthly Branch #	((Gregorian days since Jan 31, 1900)+4)%12	Gregorian Date Jan 31, 1900; 4 as initial value; Plus 12 to result if negative
Hour Heavenly Stem #	((Day Heavenly Stem #%5)*2 + Floor((Military Hour + 1)/2))%10	60-term cycles every 5 days (10 across 12 terms a day), with the next day +2 stems, both initial values are 0; +1 hour so that 11pm-1am/23 to 1 is 0
Hour Earthly Branch #	Floor((Military Hour + 1)/2)%12	+1 hour so that 11pm-1am/23 to 1 is 0

The above formulas use Lunisolar Date Jan 1, 1900 / Gregorian Date Jan 31, 1900 as anchor. Below are the Year, Month and Day terms for the said date:

Pillar	Term	Heavenly Stem #	Earthly Branch #
Year	庚子 Gēng Zǐ	6	0
Month	戊寅 Wù Yín	4	2
Day	甲辰 Jiǎ Chén	0	4

You may also use different anchor dates for each entry to futher simplify the formulas. Leap months do not factor in the formulas as the Solar Term Months are aligned with the Gregorian Calendar (i.e. 12 months a year).