As mentioned above, the cycle first started to be used for indicating years during the Han dynasty, but it also can be used to indicate earlier years retroactively. Since it repeats, by itself it cannot specify a year without some other information, but it is frequently used with the
Chinese era name (; ) to specify a year. The year starts with the new year of whoever is using the calendar. In China, the cyclic year normally changes on the Chinese
Lunar New Year. In Japan until recently it was the Japanese lunar new year, which was sometimes different from the Chinese; now it is January 1. So when calculating the cyclic year of a date in the Gregorian year, one has to consider what their "new year" is. Hence, the following calculation deals with the Chinese dates
after the Lunar New Year in that Gregorian year; to find the corresponding sexagenary year in the dates before the Lunar New Year would require the Gregorian year to be decreased As for example, the year 2697 BC (or −2696, using the
astronomical year numbering), traditionally the first year of the reign of the legendary
Yellow Emperor, was the first year (甲子;
jiǎzǐ) of a cycle. 2700 years later in 4 AD, the duration equivalent to 45 60-year cycles, was also the starting year of a 60-year cycle. Similarly 1980 years later, 1984 was the start of a new cycle. Thus, to find out the
Gregorian year's equivalent in the sexagenary cycle use the appropriate method below. • For any year number greater than 4 AD, the equivalent sexagenary year can be found by subtracting 3 from the Gregorian year, dividing by 60 and taking the
remainder. See example below. • For any year before 1 AD, the equivalent sexagenary year can be found by adding 2 to the Gregorian year number (in BC), dividing it by 60, and subtracting the remainder from 60. • 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle. • The formula for years AD is and for years BC is . The result will produce a number between 0 and 59, corresponding to the year order in the cycle; if the remainder is 0, it corresponds to the 60th year of a cycle. Thus, using the first method, the equivalent sexagenary year for 2012 AD is the 29th year (壬辰;
rénchén), as (i.e., the remainder of (2012–3) divided by 60 is 29). Using the second, the equivalent sexagenary year for 221 BC is the 17th year (庚辰;
gēngchén), as (i.e., 60 minus the remainder of (221+2) divided by 60 is 17).
Examples Step-by-step example to determine the sign for 1967: • 1967 – 3 = 1964 ("subtracting 3 from the Gregorian year") • = 32 ("divide by 60 and discard any fraction") • 1964 – (60 × 32) = 44 ("taking the remainder") • Show one of the Sexagenary Cycle tables (the following section), look for 44 in the first column (No) and obtain Fire
Goat (丁未;
dīngwèi). Step-by-step example to determine the cyclic year of first year of the reign of
Qin Shi Huang (246 BC): • 246 + 2 = 248 ("adding 2 to the Gregorian year number (in BC)") • = 4 ("divide by 60 and discard any fraction") • 248 – (60 × 4) = 8 ("taking the remainder") • 60 – 8 = 52 ("subtract the remainder from 60") • Show one of the Sexagenary Cycle table (the following section), look for 52 in the first column (No) and obtain Wood
Rabbit (乙卯;
yǐmǎo).
Equivalent lookup method Start from the AD year (1967), take directly the remainder mod 60, and look into column AD of the
table "Sexagenary years" (just above). • 1967 = 60 × 32 + 47. • Remainder is therefore 47 and the AD column says 'Fire
Goat' as it should be. For a BC year: take the remainder of the year mod 60 and look into column BC. Applied to year 246 BC, this gives: • 246 = 60 × 4 + 6. • Remainder is therefore 6 and the BC column of table "Sexagenary years" (just above) gives 'Wood
Rabbit'. When doing these conversions, year 246 BC may be treated as −245 AD as in astronomical year numbering, but never as −246 AD, due to the lack of a year 0 in the Gregorian AD/BC system.
Recent cycles ==Sexagenary months==