{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"sexagenary-cycle"},"result":{"entity_type":"calculator","id":"sexagenary-cycle","calculator_id":"sexagenary-cycle","canonical_url":"https://tttkmbb.com/lunar/sexagenary-cycle","name":"Sexagenary Cycle Calculator (干支)","title":"Sexagenary Cycle Calculator – Ganzhi (干支) Year Name, Cycle Position, Nayin and the 60-Year Table","category":"lunar","category_name":"Chinese Calendar","tool_name":"convert_sexagenary_year","featured_mcp_tool":false,"description":"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.","use_when":"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).","inputs":[{"name":"year","label":"Year","type":"integer","required":false,"min":1,"max":2999,"description":"Year number to name (proleptic Gregorian/astronomical year; the ganzhi year is counted from Chinese New Year or 立春). Give year or ganzhi.","example":2026},{"name":"ganzhi","label":"Ganzhi name","type":"string","required":false,"description":"Sexagenary name to look up: characters (丙午) or pinyin (Bingwu, bing wu). Give year or ganzhi.","example":"丙午"},{"name":"range_start","label":"Search from year","type":"integer","required":false,"default":1900,"min":1,"max":2999,"description":"First year of the range searched for matching years.","example":1900},{"name":"range_end","label":"Search to year","type":"integer","required":false,"default":2100,"min":1,"max":2999,"description":"Last year of the range searched for matching years.","example":2100}],"outputs":[{"name":"ganzhi","label":"Ganzhi (干支)","type":"string","decimals":4,"description":"Sexagenary name, e.g. 丙午."},{"name":"pinyin","label":"Pinyin","type":"string","decimals":4,"description":"Pinyin of the name, e.g. Bingwu."},{"name":"stem","label":"Heavenly stem (天干)","type":"string","decimals":4,"description":"Stem with pinyin, element and polarity, e.g. 丙 (Bing) – Yang Fire."},{"name":"branch","label":"Earthly branch (地支)","type":"string","decimals":4,"description":"Branch with pinyin and zodiac animal, e.g. 午 (Wu) – Horse (马)."},{"name":"year_english","label":"Element + animal","type":"string","decimals":4,"description":"Stem element and animal, e.g. Fire Horse."},{"name":"nayin","label":"Nayin (纳音)","type":"string","decimals":4,"description":"Nayin melodic element of the pair, e.g. 天河水 · Milky-way Water."},{"name":"cycle_position","label":"Position in cycle","type":"integer","decimals":0,"description":"1 (甲子) to 60 (癸亥)."},{"name":"year_used","label":"Year used","type":"integer","decimals":0,"description":"The year the position and cycle refer to (the input year, or the first matching year in the range)."},{"name":"cycle_start_year","label":"Cycle start (甲子 year)","type":"integer","decimals":0,"description":"Year of 甲子 that begins the 60-year cycle containing year_used."},{"name":"cycle_end_year","label":"Cycle end (癸亥 year)","type":"integer","decimals":0,"description":"Last year (癸亥) of that cycle."},{"name":"matching_years","label":"Matching years","type":"number_list","decimals":0,"description":"Years with this ganzhi between range_start and range_end."},{"name":"sexagenary_table","label":"60-year table","type":"list","decimals":4,"description":"60 rows: position, ganzhi, pinyin, element (stem), animal, nayin, year (in the cycle containing year_used)."}],"input_schema":{"type":"object","properties":{"year":{"description":"Year number to name (proleptic Gregorian/astronomical year; the ganzhi year is counted from Chinese New Year or 立春). Give year or ganzhi.","type":"integer","minimum":1,"maximum":2999,"examples":[2026]},"ganzhi":{"description":"Sexagenary name to look up: characters (丙午) or pinyin (Bingwu, bing wu). Give year or ganzhi.","type":"string","examples":["丙午"]},"range_start":{"description":"First year of the range searched for matching years.","type":"integer","minimum":1,"maximum":2999,"default":1900,"examples":[1900]},"range_end":{"description":"Last year of the range searched for matching years.","type":"integer","minimum":1,"maximum":2999,"default":2100,"examples":[2100]}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"ganzhi":{"description":"Sexagenary name, e.g. 丙午.","type":"string"},"pinyin":{"description":"Pinyin of the name, e.g. Bingwu.","type":"string"},"stem":{"description":"Stem with pinyin, element and polarity, e.g. 丙 (Bing) – Yang Fire.","type":"string"},"branch":{"description":"Branch with pinyin and zodiac animal, e.g. 午 (Wu) – Horse (马).","type":"string"},"year_english":{"description":"Stem element and animal, e.g. Fire Horse.","type":"string"},"nayin":{"description":"Nayin melodic element of the pair, e.g. 天河水 · Milky-way Water.","type":"string"},"cycle_position":{"description":"1 (甲子) to 60 (癸亥).","type":"integer"},"year_used":{"description":"The year the position and cycle refer to (the input year, or the first matching year in the range).","type":"integer"},"cycle_start_year":{"description":"Year of 甲子 that begins the 60-year cycle containing year_used.","type":"integer"},"cycle_end_year":{"description":"Last year (癸亥) of that cycle.","type":"integer"},"matching_years":{"description":"Years with this ganzhi between range_start and range_end.","type":"array","items":{"type":"number"}},"sexagenary_table":{"description":"60 rows: position, ganzhi, pinyin, element (stem), animal, nayin, year (in the cycle containing year_used).","type":"array"}}},"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","method":"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.","sources":[{"name":"Sexagenary cycle (Wikipedia)","url":"https://en.wikipedia.org/wiki/Sexagenary_cycle","type":"reference","retrieved_at":"2026-09-24"},{"name":"Chinese calendar (Wikipedia) – calendar rules as standardised in GB/T 33661-2017","url":"https://en.wikipedia.org/wiki/Chinese_calendar","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"2026 → 丙午","inputs":{"year":2026},"expected":{"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]},"url":"https://tttkmbb.com/api/v1/calculate/sexagenary-cycle?year=2026"},{"name":"甲子 years 1900–2100","inputs":{"ganzhi":"甲子","range_start":1900,"range_end":2100},"expected":{"matching_years":[1924,1984,2044],"cycle_position":1,"year_english":"Wood Rat","nayin":"海中金 · Sea Metal"},"url":"https://tttkmbb.com/api/v1/calculate/sexagenary-cycle?ganzhi=%E7%94%B2%E5%AD%90&range_start=1900&range_end=2100"}],"faq":[{"q":"When does a ganzhi year start?","a":"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."},{"q":"Why is 甲丑 rejected?","a":"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."}],"tags":["sexagenary cycle","ganzhi","干支","heavenly stems earthly branches","60 year cycle","jiazi"],"related":[{"calculator_id":"chinese-zodiac","reason":"Zodiac sign and relationships for a birth date with the year boundary handled."},{"calculator_id":"lunar-calendar-converter","reason":"Ganzhi of the year, month and day for a given date."},{"calculator_id":"chinese-hour","reason":"Ganzhi of the double-hour for a time of day."}],"links":{"html":"https://tttkmbb.com/lunar/sexagenary-cycle","markdown":"https://tttkmbb.com/lunar/sexagenary-cycle.md","json":"https://tttkmbb.com/lunar/sexagenary-cycle.json","api":"https://tttkmbb.com/api/v1/calculate/sexagenary-cycle","schema":"https://tttkmbb.com/api/v1/calculators/sexagenary-cycle","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T08:35:02Z"}