Last revised: 2026-10-18
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Five-field matrix of 52 Chinese calendars
This page expands the 52 calendars in the “Chronology of calendrical reforms” of the Chinese Calendar Public Dataset into five fields of calendrical mechanism: year-beginning (岁首), solar-term method (节气法), lunar-month method (朔法), intercalation (置闰) and year length (岁实).
The chronology itself gives the calendar name, the years in use, the year-beginning and the year length, together with the record of each reform. The values in the solar-term method, lunar-month method and intercalation columns are derived on this page from those records, following the general practice of calendrical history. Every cell carries its provenance in a bracket; where a source is lacking, nothing is entered and the cell reads 尚未考定.
How to read the table
Each cell is followed by a bracketed tag. Only three provenances occur.
- [A] Attested — taken directly from an existing entry in the dataset’s chronology. 91 cells.
- [I] Inferred — inferred from the general practice of calendrical history; the grounds are the three rules below. 158 cells.
- [U] Unattested — no source yet, not yet established. 11 cells, all in the year-length column.
Term names are given in Chinese with an English gloss, the convention used throughout this site’s English pages; the provenance tags are English letters, the Chinese codes 〔载〕〔推〕〔未〕 being reserved for the Chinese page. A year-beginning written 建寅, and so on, means the year begins in the 寅 month.
The three rules:
- Solar-term method. The Shixian calendar (1645) was the first to enter true solar terms into the almanac. The Huangji calendar devised true solar terms, and the Dayan calendar held that “entering them into the almanac follows the mean terms”; hence rows 1–50 use mean terms, and rows 51 onward use true terms.
- Lunar-month method. The Wuyin yuan calendar (619, row 22) was the first to use the true new moon. Mean new moons were used before it, and later calendars followed it.
- Intercalation. The six pre-Qin calendars, and the Qin Zhuanxu calendar, placed the intercalary month at the end of the year, the latter as a “second ninth month”. The Taichu calendar (104 BCE, row 7) established that “the month without a mid-term is the intercalary month”, and later calendars followed it. From the adoption of true solar terms onward, the intercalary year must first be full (13 synodic months between two winter-solstice months), and within it the first month that has no mid-term is taken as intercalary, the second is not.
The matrix
| No. | Calendar | Dynasty / polity | In use | Year-beginning | Solar-term method | Lunar-month method | Intercalation | Year length |
|---|---|---|---|---|---|---|---|---|
| 1 | 黄帝历 (Huangdi calendar) | Antiquity (the six ancient calendars) | — | 建子 (the year begins in the zi month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 岁终置闰 (intercalary month at the end of the year)[I] | 365.25[I] |
| 2 | 颛顼历 (Zhuanxu calendar) | Antiquity (the six ancient calendars) · Qin | 221–104 BCE | 建亥 (the year begins in the hai month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 岁终置闰 (intercalary month at the end of the year)[I] | 365.25[I] |
| 3 | 夏历 (Xia calendar) | Xia (the six ancient calendars) | — | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 岁终置闰 (intercalary month at the end of the year)[I] | 365.25[I] |
| 4 | 殷历 (Yin calendar) | Shang (the six ancient calendars) | — | 建丑 (the year begins in the chou month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 岁终置闰 (intercalary month at the end of the year)[I] | 365.25[I] |
| 5 | 周历 (Zhou calendar) | Zhou (the six ancient calendars) | — | 建子 (the year begins in the zi month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 岁终置闰 (intercalary month at the end of the year)[I] | 365.25[I] |
| 6 | 鲁历 (Lu calendar) | Lu, Spring and Autumn (the six ancient calendars) | — | 建子 (the year begins in the zi month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 岁终置闰 (intercalary month at the end of the year)[I] | 365.25[I] |
| 7 | 太初历 (Taichu calendar) | Western Han | 104–7 BCE | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[A] | 365.2502[A] |
| 8 | 三统历 (Santong calendar) | Western Han | 前7—85 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2502[A] |
| 9 | 四分历（后汉） (Sifen calendar (Later Han)) | Eastern Han | 85–236 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.25[A] |
| 10 | 乾象历 (Qianxiang calendar) | Late Eastern Han · Eastern Wu | 206–280 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2462[A] |
| 11 | 景初历 (Jingchu calendar) | Cao Wei | 237–442 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2469[A] |
| 12 | 元嘉历 (Yuanjia calendar) | Liu Song | 443–462 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2467[A] |
| 13 | 大明历（祖冲之） (Daming calendar (Zu Chongzhi)) | Southern Qi | 463–520 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2428[A] |
| 14 | 正光历 (Zhengguang calendar) | Northern Wei | 523–539 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2437[A] |
| 15 | 兴和历 (Xinghe calendar) | Eastern Wei | 540–549 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2442[A] |
| 16 | 天保历 (Tianbao calendar) | Northern Qi | 550–565 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2446[A] |
| 17 | 天和历 (Tianhe calendar) | Northern Zhou | 556–578 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 18 | 大象历 (Daxiang calendar) | Northern Zhou | 579–583 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 19 | 开皇历 (Kaihuang calendar) | Sui | 584–596 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 20 | 皇极历 (Huangji calendar) | Sui | 604–617 | 建寅 (the year begins in the yin month)[A] | 平气（注历）(mean solar terms, entered into the almanac)[A] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2445[A] |
| 21 | 大业历 (Daye calendar) | Sui | 597–618 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 平朔 (mean new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 22 | 戊寅元历 (Wuyin yuan calendar) | Tang | 619–665 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[A] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2446[A] |
| 23 | 麟德历 (Linde calendar) | Tang | 666–728 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2448[A] |
| 24 | 大衍历 (Dayan calendar) | Tang | 728–761 | 建寅 (the year begins in the yin month)[A] | 平气（注历）(mean solar terms, entered into the almanac)[A] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2444[A] |
| 25 | 五纪历 (Wuji calendar) | Tang | 762–784 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2448[A] |
| 26 | 正元历 (Zhengyuan calendar) | Tang | 785–821 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2447[A] |
| 27 | 宣明历 (Xuanming calendar) | Tang | 822–892 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2446[A] |
| 28 | 崇玄历 (Chongxuan calendar) | Tang → Later Zhou | 893–955 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2445[A] |
| 29 | 钦天历 (Qintian calendar) | Later Zhou | 956–959 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2444[A] |
| 30 | 应天历 (Yingtian calendar) | Northern Song | 960–980 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 31 | 乾元历 (Qianyuan calendar) | Northern Song | 981–1000 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 32 | 仪天历 (Yitian calendar) | Northern Song | 1001–1023 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2446[A] |
| 33 | 崇天历 (Chongtian calendar) | Northern Song | 1024–1063 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2446[A] |
| 34 | 明天历 (Mingtian calendar) | Northern Song | 1064–1073 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 35 | 奉元历 (Fengyuan calendar) | Northern Song | 1074–1091 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 36 | 观天历 (Guantian calendar) | Northern Song | 1092–1102 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 37 | 占天历 (Zhantian calendar) | Northern Song | 1103–1105 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 38 | 纪元历 (Jiyuan calendar) | Northern Song | 1106–1126 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 39 | 大明历（杨级） (Daming calendar (Yang Ji)) | Jin | 1127–1179 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 40 | 统元历 (Tongyuan calendar) | Southern Song | 1135–1160 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 41 | 乾道历 (Qiandao calendar) | Southern Song | 1167–1175 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 42 | 重修大明历 (Revised Daming calendar) | Jin | 1180–1280 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 43 | 淳熙历 (Chunxi calendar) | Southern Song | 1177–1198 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2436[A] |
| 44 | 统天历 (Tongtian calendar) | Southern Song | 1199–1206 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2425[A] |
| 45 | 开禧历 (Kaixi calendar) | Southern Song | 1207–1250 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2431[A] |
| 46 | 淳祐历 (Chunyou calendar) | Southern Song | 1251–1252 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 47 | 会天历 (Huitian calendar) | Southern Song | 1253–1270 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 尚未考定 (not yet established)[U] |
| 48 | 成天历 (Chengtian calendar) | Southern Song | 1271–1276 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2427[A] |
| 49 | 授时历 (Shoushi calendar) | Yuan | 1281–1644 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2425[A] |
| 50 | 大统历 (Datong calendar) | Ming | 1368–1644 | 建寅 (the year begins in the yin month)[A] | 平气 (mean solar terms)[I] | 定朔 (true new moon)[I] | 无中气置闰 (the month without a mid-term is intercalary)[I] | 365.2425[A] |
| 51 | 崇祯历书·时宪历 (Chongzhen lishu · Shixian calendar) | Qing | 1645–1911 | 建寅 (the year begins in the yin month)[A] | 定气 (true solar terms)[A] | 定朔 (true new moon)[I] | 无中气置闰（闰岁内取首个无中气月，第二个不置闰）(the intercalary year must first be full; within it the first month without a mid-term is intercalary, a second is not)[I] | 365.2422[A] |
| 52 | 公历（格里高利历） (Gregorian calendar) | China (era-counting in parallel use) | from 1912 | 不适用 (not applicable — the Gregorian calendar has no year-beginning substitution)[I] | 不适用 (not applicable)[I] | 不适用 (not applicable)[I] | 不适用 (not applicable)[I] | 365.2425[A] |
The 11 cells not yet established
The year lengths of the remaining 11 calendars are still empty in the dataset, and are left empty here as well: 17 Tianhe calendar, 18 Daxiang calendar, 19 Kaihuang calendar, 21 Daye calendar, 30 Yingtian calendar, 31 Qianyuan calendar, 35 Fengyuan calendar, 37 Zhantian calendar, 39 Daming calendar (Yang Ji), 46 Chunyou calendar, 47 Huitian calendar.
These year lengths were re-checked one calendar at a time in October 2026 against the “stepping of the qi and new moons” sections of the official dynastic histories (18 works, from the Han shu to the Qing shi gao): of the 35 cells originally missing, 24 yielded a value, each with its book and chapter. Each value divides the calendar’s own year-length dividend by the day divisor it records; nothing is extrapolated.
This page was originally left blank throughout because the circulating transcription of the Song shi was found on test to contain missing characters: computing from the numerators and denominators it lists gives 22.45 for the Yingtian calendar, 228.5 for the Qianyuan calendar and 36.52 for the Yitian calendar, none of which is a tropical-year length. Reading the original sources recovered 365.2446 for Yitian. The 11 cells still blank each have their own reason: the history states the method is not preserved (Fengyuan, Huitian); only denominators unrelated to the year length are recorded (Yingtian, Qianyuan); no day divisor is stated, so the conversion is not unique (Tianhe, Daxiang, Kaihuang); the numbers given are internally inconsistent (Daye); or the method is simply not recorded (Zhantian, Chunyou, the Yang Ji Daming calendar). All are left blank, with no estimate given.
The 41 cells that are filled (35 attested, 6 inferred) are marked cell by cell in the table; the 11 that are not are left blank.
Source and licence
This page is a derivative of the Chinese Calendar Public Dataset, expanding row by row its “Chronology of calendrical reforms” (52 rows). The dataset is licensed CC BY 4.0, DOI 10.5281/zenodo.22788686.
The five field names follow epochType / solarTermMethod / lunarMonthMethod / intercalationRule / yearLength; the machine-readable definition of the intercalation rule is given in the Chinese calendrical terminology namespace.
本页由邝楚嘉搜集整理。 Compiled and maintained by Chujia Kuang.