Calculating Chinese Year, Month, and Day with the Celestial Stem & Terrestrial Branch Algorithm

Celestial Stem (天干) and Terrestrial Branch (地支) are traditional Chinese ordering symbols. There are ten stems – 甲, 乙, 丙, 丁, 戊, 己, 庚, 辛, 壬, 癸 – and twelve branches – 子, 丑, 寅, 卯, 辰, 巳, 午, 未, 申, 酉, 戌, 亥 – each used cyclically.

Symbolic meanings

Stem 甲: grass breaking through soil, armor metaphor.

Stem 乙: tender new growth.

Stem 丙: bright sun.

Stem 丁: robust growth.

Stem 戊: flourishing vegetation.

Stem 己: rising.

Stem 庚: renewal after harvest.

Stem 辛: newness, sharp flavor.

Stem 壬: gestation of yang.

Stem 癸: hidden sprouting.

Branch 子: beginning of yang.

Branch 丑: sprouting in soil.

Branch 寅: spring emergence.

Branch 卯: flourishing under east sun.

Branch 辰: vibration and rise.

Branch 巳: pure yang after yin fades.

Branch 午: fullness of yang.

Branch 未: ripe fruit.

Branch 申: completed growth.

Branch 酉: retreat and contraction.

Branch 戌: decay.

Branch 亥: extreme yin.

60‑year cycle (甲子)

01.甲子 02.乙丑 03.丙寅 04.丁卯 05.戊辰 06.己巳 07.庚午 08.辛未 09.壬申 10.癸酉 11.甲戌 12.乙亥 13.丙子 14.丁丑 15.戊寅 16.己卯 17.庚辰 18.辛巳 19.壬午 20.癸未 21.甲申 22.乙酉 23.丙戌 24.丁亥 25.戊子 26.己丑 27.庚寅 28.辛卯 29.壬辰 30.癸巳 31.甲午 32.乙未 33.丙申 34.丁酉 35.戊戌 36.己亥 37.庚子 38.辛丑 39.壬寅 40.癸卯 41.甲辰 42.乙巳 43.丙午 44.丁未 45.戊申 46.己酉 47.庚戌 48.辛亥 49.壬子 50.癸丑 51.甲寅 52.乙卯 53.丙辰 54.丁己 55.戊午 56.己未 57.庚申 58.辛酉 59.壬戌 60.癸亥

Year calculation

Celestial Stem = (Year – 3) Mod 10
Terrestrial Branch = (Year – 3) Mod 12

Using arrays indexed from 0, the stem index 0 corresponds to 癸, 1 to 甲, …, 9 to 壬; the branch index 0 corresponds to 亥, 1 to 子, …, 11 to 戌.

Example: Year = 2010 → Stem index = (2010‑3) Mod 10 = 7 → 庚; Branch index = (2010‑3) Mod 12 = 3 → 寅; therefore 2010 is 庚寅.

Month calculation (first month)

First‑month stem = 2 × YearStem − 4 ± 5, where +5 is used if YearStem < 5, otherwise − 5.

First‑month branch = Year branch.

YearStem = 7 (for 2010, >5) → FirstMonthStem = 2×7‑4‑5 = 5 → 戊
FirstMonth = 戊寅

Day calculation

Let C = first two digits of year, Y = last two digits, M = month number, D = day, I = 0 for odd month, 6 for even month. [] denotes integer part.

DayStemTotal G = 4*C + [C/4] + [5*Y] + [Y/4] + [3*(M+1)/5] + D – 3
DayBranchTotal Z = G + 4*C + 10 + I
DayStem = G Mod 10
DayBranch = Z Mod 12

Example for 2010‑10‑07 (C=20, Y=10, M=10, D=7, I=6):

G = 4*20 + [20/4] + 5*10 + [10/4] + [3*(10+1)/5] + 7 – 3 = 147
Z = 147 + 4*20 + 10 + 6 = 243
DayStem = 147 Mod 10 = 7 → 庚
DayBranch = 243 Mod 12 = 3 → 寅
Result: 庚寅

24‑hour to 12‑shichen mapping

子: 23‑01

丑: 01‑03

寅: 03‑05

卯: 05‑07

辰: 07‑09

巳: 09‑11

午: 11‑13

未: 13‑15

申: 15‑17

酉: 17‑19

戌: 19‑21

亥: 21‑23