# Chinese Solar Equivalent date for any Western Date 2

How to Calculate the Chinese Solar Equivalent date (Ba Zi) for any western dates without using the Ten Thousand Year Calendar? Part 2 of 2

by Henry Fong

In the last article, we learnt how to calculate the year and month pillar without referring to the ten thousand year calendar.

In this article, we will learn a method to do the same for the day and hour pillar. There are at least a few mathematics formulas to calculate the heavenly stem and earthly branch for the day but here is the one that I feel is the easiest to learn and use.
The first step is to derive the ‘Number’ using the following formula.

Number = 5 (x-1) + (x-1)/4 + 15 + y

Where x is the last two digit of the year and y is the number of days from the 1st of Jan to the day in question.

Example: 15th June 1957.
x = 57 (last two digit of the year 1957)

(For the new millennium you must add 100 to the last two digits.
Example: 12th March 2004.
x = 104 (last two digit of 2004 plus 100)

To calculate the value for ‘y’ we need to know if the year is a leap year or not. This is very straightforward. Any Shen (Monkey), Zi (Rat) and Chen (Dragon) year is a leap year and has 29 days in the month of February! The rest have 28 days in February.

Example: 15th June1957
1957 is a You (Rooster) year. It is not a leap year and February has 28 days.

Example: 12th March 2004
2004 is a Shen (Monkey) year. It is a leap year and February has 29 days.

From Calendar101 we know that Jan, Mar, May, July, Aug, Oct and Dec has 31 days while the other remaining months except Feb has 30 days.

Therefore to calculate the number of days from the 1st of Jan to the date in question we simply add them up.

Example: 15th June 1957
Y = No of days in Jan + No of days in Feb + …… + 15 days in June
Y = 31 (Jan) +28 (Feb) +31 (Mar) +30 (Apr) +31 (May) +15 (Jun)
Y = 166
(Note: Since 1957 is not a leap year, February has 28 days)

Example: 12th March 2004
Y = No of days in Jan + No of days in Feb + 12 days in March
Y = 31 (Jan) +29 (Feb) +12 (Mar)
Y = 72
(Note: Since 2004 is a leap year, February has 29 days)

Let’s calculate the ‘Number’ for both the examples.

Example: 15th June 1957

Num = 5(x-1) + (x-1)/4 + 15 + y
Num = 5(57-1) + (57-1)/4 + 15 + 166
Num = 5(56) + 56/4 + 15 + 166
Num = 280 + 14 + 15 + 166
Num = 475

Example: 12th March 2004

Num = 5(x-1) + (x-1)/4 + 15 + y
Num = 5(104-1) + (104-1)/4 + 15 + 72
Num = 5(103) + 103/4 + 15 + 72
Num = 515 + 25.75 + 15 + 72
Num = 627.75
Num = 627 (take the absolute value)

To derive the Heavenly Stem of the day, we calculate the remainder of the ‘Number’/10.

In the example of the 15th June 1957, the ‘Number is 475. When we divide this number by 10 we get 47 and a remainder of 5. From the table 5 is ‘wu’ 戊which is the Heavenly Stem of the day (Also known as Day Master in Ba Zi)

In the example of the 12th March 2004, the ‘Number’ is 627. When we divide this number by 10 we get 62 and a remainder of 7. From the table 7 is ‘geng’庚 which is the Heavenly Stems of the day.

To derive the earthly branch of the day, calculate the remainder of the Num/12 and compare against the table below.

In the example of the 15th June 1957, the remainder of 475/12 is 7 which is equivalent to the earthly branch ‘wu 午’. Thus the stem and branch combination of the 15th June 1957 is Wu Wu (戊午).

In the example of the 12th March 2004, the remainder of 627/12 is 3 which is equivalent to the earthly branch of ‘Yin 寅’. Thus the stem and branch combination of the 12th March 2004 is Geng Yin (庚寅)

Calculating the stem and branch of the hour pillar is much simpler.

From BaZi 101 we know that Zi hour is between 11 to 1 am, Chou is between 1 am to 3 am and so on. Please refer to the table below for the rest of the hours.

If you are born at 10 am, it is Si hour, if you are born at 9.15 pm it is Hai hour and so on.

This is the easy part. What about the heavenly stem of the hour? For this we need to look at the day master. Let’s take the example from above of someone born on the 15th Jun 1957 at 4.30 am.

We know that the stem of the day (or day master) is ‘wu’ and we know from the above table that 4.30 am noon is ‘yin’ hour.

If we know the heavenly stem at Zi hour, we can derive the stem at any other hour by just moving forward in the heavenly stems sequence. For example if the stem at Zi hour is Jia, then the stem at Chou is Yi (a step forward), the stem Yin is Bing (another step forward in the sequence of the heavenly stems) and so on.

To derive the stem at the first (Zi) hour all you need to do it remember the table below.

(Note: You may observe that the stem of the first or ‘Zi’ hour is always an ‘odd number’ or ‘yang’ stem.)

Let’s get back to the example of the 15th Jun 1957 (Day Master ‘wu’) at 4.30 am.

From the table above, we see that the stem of the first or ‘Zi’ hour is Ren. For the next hour which is Chou the stem is simply ‘Gui’ (the next stem in the sequence of heavenly stem). Chou is followed by ‘Yin’ and the next stem in the sequence is ‘Jia’. Hence the stem branch combination of Yin hour on the 15th June 1957 is ‘Jia Yin’.

Let’s take another example, 12th Mar 2004, this time at ‘Wei’ hour.

We know from the calculation above that this is a ‘Geng’ day. From the table above, the stem of the first hour is ‘Bing’. The stem branch combination is ‘Bing Zi’. The second hour is thus Ding Chou, the next hour is Wu Yin, followed by Ji Mao, Geng Chen, Xin Si, Ren Wu and finally arriving at Gui Wei.

The above method is normally used in conjunction with the finger counting method. All you need to know is the stem of the ‘Zi’ hour and you simply run the sequence of the heavenly stems until you reach the desired hour!