<p>I am trying to figure out the Julian date equation by myself. Unfortunately, there are not many resources I could find which explains in depth. Moreover, there are several variations of the same equation which I have realised after trying my luck with ChatGPT. Here is the first variation.</p>
<pre><code>JD = d - 32075+ (1461*(y+4800+b/4) + 367*(m-2-b/12)/12 - 3*(y+4900+b)/400

Where d = day, y = year, m = month,
b= m-14/12
</code></pre>
<p>Variation 2:</p>
<pre><code>JD= d + (153m + 2)/5 + 365y + y/4 - y/100 + y/400 - 32045

Where
y = year + 4800 - a
m = month + 12a - 3
a = (14 - month)/12
</code></pre>
<p>I understood what <code>153m+2/5</code> is trying to achieve (total average days upto a given month I suppose) but I don't get how it is derived. Is it not 152m/5 instead? Like 30m + (2/5m for additional days), but why is it (30m + 2/5m + m/5 + 2/5) days? And why the adjustment to march as the first month which can be seen in <code>m = month + 12m - 3</code>? Is the Julian date not supposed to be from Jan 1st 12:00 TT of 4800 BCE?</p>
<p>Can someone please help me with the derivation of these two equations (emphasis on equation 2) and elaborate what each component correspondents to get clarity?</p>

CC BY-SA 4.0
2023-10-15T19:54:28.677Z
*ChatGPT*  There's your problem. :-)  Wikipedia has a page on [Julian day](https://en.wikipedia.org/wiki/Julian_day) this with lots of links to more detailed material from more reliable sources that ChatGPT (which, wow, is bad way to do research).  I know some people don't trust Wikipedia, but it's way better than ChatGPT which I suggest you get out of the habit of using.
StephenG - Help Ukraine
CC BY-SA 4.0
2023-10-15T20:00:46.593Z
@StephenG-HelpUkraine Alright. But on wiki there is only the equation from Gregorian to Julian conversion which is the first equation I gave. Is there a step by step derivation article somewhere? I want to have an intuitive understanding of the said equation
Thinker-101
CC BY-SA 4.0
2023-10-15T20:57:46.400Z
The two most popular Julian date conversion algorithms are the one in the "Explanatory Supplement to the Astronomical Almanac", and in "Astronomical Algorithms".  They look quite a bit different than those you posted, so you might have a look at those.  Also consider that the question is much more about counting days in the Gregorian Calendar, and doesn't really have much to do with the Julian Date when searching for references.
Greg Miller
CC BY-SA 4.0
2023-10-15T22:11:58.807Z
I explain the March adjustment here: https://math.stackexchange.com/a/4489149/207316
PM 2Ring
<time><mathematics>
Understanding the Julian Date equation in detail
Thinker-101
# Understanding the Julian Date equation in detail

(Asked by: username_0 on 2023-10-15)

I am trying to figure out the Julian date equation by myself. Unfortunately, there are not many resources I could find which explains in depth. Moreover, there are several variations of the same equation which I have realised after trying my luck with ChatGPT. Here is the first variation.
JD = d - 32075+ (1461*(y+4800+b/4) + 367*(m-2-b/12)/12 - 3*(y+4900+b)/400

Where d = day, y = year, m = month,
b= m-14/12

Variation 2:
JD= d + (153m + 2)/5 + 365y + y/4 - y/100 + y/400 - 32045

Where
y = year + 4800 - a
m = month + 12a - 3
a = (14 - month)/12

I understood what 153m+2/5 is trying to achieve (total average days upto a given month I suppose) but I don't get how it is derived. Is it not 152m/5 instead? Like 30m + (2/5m for additional days), but why is it (30m + 2/5m + m/5 + 2/5) days? And why the adjustment to march as the first month which can be seen in m = month + 12m - 3? Is the Julian date not supposed to be from Jan 1st 12:00 TT of 4800 BCE?
Can someone please help me with the derivation of these two equations (emphasis on equation 2) and elaborate what each component correspondents to get clarity?

**Tags:** time, mathematics
> **Comments:**
> **username_1**: *ChatGPT*  There's your problem. :-)  Wikipedia has a page on [Julian day](https://en.wikipedia.org/wiki/Julian_day) this with lots of links to more detailed material from more reliable sources that ChatGPT (which, wow, is bad way to do research).  I know some people don't trust Wikipedia, but it's way better than ChatGPT which I suggest you get out of the habit of using.  
> **username_0**: @StephenG-HelpUkraine Alright. But on wiki there is only the equation from Gregorian to Julian conversion which is the first equation I gave. Is there a step by step derivation article somewhere? I want to have an intuitive understanding of the said equation  
> **username_2**: The two most popular Julian date conversion algorithms are the one in the "Explanatory Supplement to the Astronomical Almanac", and in "Astronomical Algorithms".  They look quite a bit different than those you posted, so you might have a look at those.  Also consider that the question is much more about counting days in the Gregorian Calendar, and doesn't really have much to do with the Julian Date when searching for references.  
> **username_3**: I explain the March adjustment here: https://math.stackexchange.com/a/4489149/207316  

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