Lunisolar Calendar (農曆)

stembranch computes the Chinese lunisolar calendar from first principles using astronomical new moon calculations and solar term interpolation.

How It Works

The Chinese calendar (農曆) is lunisolar — lunar months reconciled with the solar year:

• Months start at each new moon (朔日)
• Year boundaries are aligned with the solar cycle via intercalary (leap) months
• Month numbering is determined by which major solar term (中氣) falls within each lunar month

Step 1: New Moon Calculation

New moon moments are computed using Meeus Ch. 49 (Jean Meeus, Astronomical Algorithms):

1. Estimate the lunation number k from the target date
2. Compute the approximate new moon JDE using a polynomial in k
3. Apply 14 planetary correction terms and 25 additional periodic terms
4. Convert from TT to UT via ΔT

Step 2: Solar Term Mapping

The 12 中氣 (major solar terms at 30° intervals) determine month numbers:

中氣	Longitude	Month Number
雨水	330°	1 (正月)
春分	0°	2
穀雨	30°	3
小滿	60°	4
夏至	90°	5
大暑	120°	6
處暑	150°	7
秋分	180°	8
霜降	210°	9
小雪	240°	10
冬至	270°	11
大寒	300°	12

A lunar month is assigned the number of the 中氣 that falls within it.

Step 3: Intercalary Month Detection

When a lunar month contains no 中氣, it becomes an intercalary (leap) month (閏月). It takes the number of the preceding month with a 閏 prefix.

This is the No-Zhongqi Rule (無中氣置閏法), the standard rule used since the Qing dynasty Shíxiàn calendar (時憲曆, 1645).

The 2033 Problem

In some years, multiple lunar months lack a 中氣, creating ambiguity about which month is intercalary. The most notable case is 2033, where the standard algorithm would place the leap month incorrectly without the Winter Solstice Rule (冬至必在十一月): the month containing 冬至 must be month 11.

stembranch handles this correctly — validated against Hong Kong Observatory data.

API

import { gregorianToLunisolar } from 'stem-branch';

// Gregorian → lunisolar (農曆) date
gregorianToLunisolar(new Date(2024, 1, 10));
// → { year: 2024, month: 1, day: 1, isLeapMonth: false }