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Sexagenary Cycle Calculator (干支)

Converts a year to its sexagenary name (干支 ganzhi: heavenly stem 天干 + earthly branch 地支) or a ganzhi name back to the matching years, with the stem element, yin/yang, zodiac animal, nayin (纳音), position in the 60-year cycle and the full 60-entry table.

When to use

You need the ganzhi of a year (e.g. 2026 = 丙午), the years that carry a given name such as 甲子 or 辛亥, or the whole 60-year cycle with its nayin elements.

Do not use when: You need the ganzhi of a day, month or hour for a date (use lunar-calendar-converter or chinese-hour), or the zodiac for a birth date near Chinese New Year (use chinese-zodiac).

Formula

index = (year − 4) mod 60 (0 = 甲子); stem = index mod 10; branch = index mod 12; cycle_position = index + 1; cycle_start_year = year − index; matching years = year₀ + 60·k

The cycle has run continuously since antiquity, so any year number maps to one of the 60 names; 4 CE was a 甲子 year, 1984 began the current cycle. Names are valid only when stem and branch share the same polarity (60 of 120 combinations). Traditional calendar/cultural reference calculation; not a prediction, medical, legal or financial advice.

Inputs

ParameterTypeUnitRequiredDescription
yearintegernoYear number to name (proleptic Gregorian/astronomical year; the ganzhi year is counted from Chinese New Year or 立春). Give year or ganzhi. Range: ≥ 1, ≤ 2999
ganzhistringnoSexagenary name to look up: characters (丙午) or pinyin (Bingwu, bing wu). Give year or ganzhi.
range_startintegerdefault 1900First year of the range searched for matching years. Range: ≥ 1, ≤ 2999
range_endintegerdefault 2100Last year of the range searched for matching years. Range: ≥ 1, ≤ 2999

Outputs

OutputTypeUnitDescription
ganzhistringSexagenary name, e.g. 丙午.
pinyinstringPinyin of the name, e.g. Bingwu.
stemstringStem with pinyin, element and polarity, e.g. 丙 (Bing) – Yang Fire.
branchstringBranch with pinyin and zodiac animal, e.g. 午 (Wu) – Horse (马).
year_englishstringStem element and animal, e.g. Fire Horse.
nayinstringNayin melodic element of the pair, e.g. 天河水 · Milky-way Water.
cycle_positioninteger1 (甲子) to 60 (癸亥).
year_usedintegerThe year the position and cycle refer to (the input year, or the first matching year in the range).
cycle_start_yearintegerYear of 甲子 that begins the 60-year cycle containing year_used.
cycle_end_yearintegerLast year (癸亥) of that cycle.
matching_yearsnumber_listYears with this ganzhi between range_start and range_end.
sexagenary_tablelist60 rows: position, ganzhi, pinyin, element (stem), animal, nayin, year (in the cycle containing year_used).

Example

2026 → 丙午: {"year":2026} → {"ganzhi":"丙午","pinyin":"Bingwu","cycle_position":43,"cycle_start_year":1984,"year_english":"Fire Horse","nayin":"天河水 · Milky-way Water","matching_years":[1906,1966,2026,2086]}

甲子 years 1900–2100: {"ganzhi":"甲子","range_start":1900,"range_end":2100} → {"matching_years":[1924,1984,2044],"cycle_position":1,"year_english":"Wood Rat","nayin":"海中金 · Sea Metal"}

GET https://tttkmbb.com/api/v1/calculate/sexagenary-cycle?year=2026

Machine access

Sources

FAQ

When does a ganzhi year start?

Not on 1 January: the lunar calendar switches at Chinese New Year and Bazi practice at 立春 (about 4 February). A January date usually belongs to the previous ganzhi year; use chinese-zodiac or lunar-calendar-converter for a specific date.

Why is 甲丑 rejected?

Stems and branches advance together, so an odd (yang) stem always meets an odd (yang) branch: only 60 of the 120 pairings occur. 甲 pairs with 子, 寅, 辰, 午, 申, 戌.

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