Sexagenary Cycle Lookup: Find a Pair and Move Forward or Back

Why are there sixty pairs, not 120?

The ten stems and twelve branches advance together by one position. Jia-Zi is followed by Yi-Chou; neither list moves alone. Sixty is the smallest number of steps that returns both lists to their starting points. Pairs with mismatched odd/even positions, such as Jia-Chou (甲丑), never occur in this sequence.

Choose a pair and move around the cycle

Enable JavaScript to select stems, branches and step counts. Default example: position 1 甲子 +1 step → position 2 乙丑. The full table below works without scripts.

Check the arithmetic by hand

This page labels Jia-Zi as position 1. One step after position 10, Gui-You (癸酉), is position 11, Jia-Xu (甲戌): only the stems have restarted. One step after position 60, Gui-Hai (癸亥), returns to position 1. For arithmetic, subtract one from the displayed position, add the step count, wrap within sixty positions, then add one again.

Negative steps and a full turn

One step back from Jia-Zi gives Gui-Hai. Adding or subtracting sixty steps returns any pair to itself; zero steps also leaves it unchanged. The tool accepts whole steps from −600 to 600. Programming languages handle negative remainders differently, so the calculation normalizes them to 0–59.

A position does not identify a birthday

A step here is a position in the cycle, not a conversion between years, months, dates or hours. A pair alone cannot uniquely identify a birth year. Date comparisons additionally need the original calendar, a reference date, year/day boundaries and a stated clock convention.

Sources and reproducibility

HKO Table 2 supplies the reference sequence numbered 1–60. This tool calculates using remainders of the two lists; it requests no birth details and sends no tool inputs to a server.

Compare with HKO Table 2 · Site calculation conventions