How the Calendar Is Calculated

Every reading and calendar on Yorozu Goyomi is calculated inside your browser. Here we set out the basis of the calculations and how accurate they are. All times are Japan Standard Time.

On this page

1.The 24 solar terms and setsuiri

Using an astronomical calculation library, we find the moments when the Sun’s apparent ecliptic longitude (its position as seen from Earth) reaches a multiple of 15 degrees for every year from 1900 to 2100, and keep them in a table. The table below compares our values with those in the Rekiyōkō, the official calendar published by the National Astronomical Observatory of Japan.

2.The old lunar calendar and rokuyō

We calculate the moment of each new moon and make the day of the new moon (in Japan time) the first day of the lunar month. The month containing the winter solstice is the eleventh month. When there are thirteen months from one winter solstice to the next, the first month that contains no principal term (Usui, Shunbun, Kokuu and so on) becomes a leap month. This follows the usual present-day rules, based on the Tenpō calendar (2033 is treated, as is common, as having a leap eleventh month). The rokuyō is set by the remainder of (lunar month + day) ÷ 6.

3.The eto and Nine Star Ki

• The year’s eto and Nine Star Ki star change at the moment of Risshun, and the month’s eto at the moment of each setsuiri.
• The day’s eto is calculated from the Julian day number (1 January 2000 = Tsuchinoe-uma 戊午). The day changes at midnight.
• For the hour pillar, the 11 pm hour is treated as the Rat hour of the next day, and the hour stem is found from the next day’s day stem (the day pillar stays on the same day).
• The day’s Nine Star Ki star counts forwards from One White Water starting on the Kinoe-ne day nearest the winter solstice, and backwards from Nine Purple Fire starting on the Kinoe-ne day nearest the summer solstice. Schools differ on how to switch in years when the solstice and the Kinoe-ne day are far apart; this site always uses “the nearest Kinoe-ne day”.

4.Lucky and unlucky days (almanac notes)

• Tenshabi, Ichiryū-manbai-bi and Sanrinbō are judged by the solar month, and the day of a setsuiri is treated as part of the new solar month.
• Fujōjubi is judged by the date in the old lunar calendar.
• The dates of almanac notes can differ between traditions.

5.Astrology

• The ecliptic longitudes of the Sun and Moon are found with the formulas in Jean Meeus’s Astronomical Algorithms (the Moon is accurate to within 0.05 degrees).
• The ascendant is calculated from the latitude and longitude of the prefectural capital of your birthplace.
• The ayanamsa used for Indian astrology is an approximation of the Lahiri method.