Calculator Form
Example Data Table
| Example Year | Cycle Number | Stem Branch | Element | Animal | Common Reading |
|---|---|---|---|---|---|
| 1984 | 1 | 甲子 / Jia-Zi | Yang Wood | Rat | Start of a modern 60-year cycle. |
| 2024 | 41 | 甲辰 / Jia-Chen | Yang Wood | Dragon | Wood Dragon cycle year. |
| 2025 | 42 | 乙巳 / Yi-Si | Yin Wood | Snake | Wood Snake cycle year. |
| 2026 | 43 | 丙午 / Bing-Wu | Yang Fire | Horse | Fire Horse cycle year. |
Formula Used
The calculator uses the sexagenary cycle. It has ten heavenly stems and twelve earthly branches. The least common multiple is sixty. Each cycle pair advances by one step.
Year cycle: cycleIndex = (effectiveYear - 4) mod 60. The year 4 gives the first pair, Jia-Zi. The stem is cycleIndex mod 10. The branch is cycleIndex mod 12.
Month cycle: solar month branches start from Tiger near February 4. The first month stem depends on the year stem. The formula is firstMonthStem = ((yearStem mod 5) × 2 + 2) mod 10.
Day cycle: the Julian day number is shifted by the selected offset. The default formula is dayIndex = (JulianDay + 49) mod 60.
Hour cycle: each branch covers two hours. Zi covers 23:00 to 00:59. The hour stem starts from the day stem group.
How to Use This Calculator
- Select a Gregorian date.
- Enter the local time for the hour pillar.
- Choose how the calculator should treat the year boundary.
- Add a custom cutover date when needed.
- Use manual year override for special calendar research.
- Keep the default day offset unless your source uses another table.
- Press calculate to show the result above the form.
- Download the result as CSV or PDF.
Understanding Heavenly Stems and Earthly Branches
What the Cycle Means
The heavenly stems and earthly branches form a repeating system of sixty pairs. It is often called the sexagenary cycle. Each pair combines one stem with one branch. The stem adds element and polarity. The branch adds an animal sign. Together they create a compact time marker. This marker can describe a year, month, day, or hour.
Why the Calculator Has Several Layers
A single year sign is useful. Yet traditional timing often uses more detail. The year layer gives the broad cycle. The month layer adds seasonal context. The day layer gives a daily pair. The hour layer adds a two-hour period. This creates a four-level view. It can support study, naming, record keeping, and symbolic planning.
About Year Boundaries
Year boundaries can vary by method. Some users prefer January first. Others use a lunar new year date. Some systems use the solar term near early February. This calculator includes flexible controls for those cases. You may enter a custom cutover date. You may also override the year manually. That makes the tool useful for mixed references.
About Month, Day, and Hour Results
Month results use approximate solar-term starts. These boundaries are practical for general use. Exact almanac work can require precise solar-term times. Day results use a Julian day number. The offset field lets advanced users match a preferred table. Hour results follow the twelve traditional double-hours. Zi starts at 23:00. Each next branch covers another two-hour block.
Best Use
Use this calculator as a clear reference tool. Check the main cycle number first. Then compare the stem, branch, element, polarity, and animal. Export your result when you need records. For formal calendar work, compare results with a specialized almanac.
FAQs
1. What are heavenly stems?
Heavenly stems are ten repeating symbols. They carry element and polarity meanings. The calculator shows the stem character, pinyin, element, and yin or yang quality.
2. What are earthly branches?
Earthly branches are twelve repeating symbols. They are commonly linked with zodiac animals. The calculator shows the branch character, pinyin, and animal sign.
3. Why are there sixty cycle numbers?
Ten stems and twelve branches repeat together. Their full pattern returns after sixty steps. Each step creates one valid stem and branch pair.
4. Does the year always start on January first?
No. Some systems use a lunar or solar boundary. This tool lets you use the Gregorian year, a custom cutover date, or a manual year.
5. What is the day cycle offset?
The day offset aligns the Julian day number with a sexagenary cycle table. Keep the default value unless your source requires another offset.
6. What is a double-hour branch?
A double-hour branch covers two clock hours. Zi covers 23:00 to 00:59. The next branch then starts at 01:00.
7. Can I download my result?
Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.
8. Is this suitable for formal almanac work?
It is useful for study and general calculations. Formal almanac work may need exact lunar dates, solar terms, location, and specialist references.