Dated Determination: Converting from the Julian Calendar to the Gregorian
Date: 02/09/2011 at 14:07:56 From: William Subject: Converting a Julian calendar date to a Gregorian date Hi! How do you convert a Julian calendar date (e.g., 1987 Dec 14) to the corresponding Gregorian date (in this case, 1987 Dec 27) and vice versa? Are there any algorithms for this? I get the general idea, but would really like to see a thorough, worked example of the conversion, both from Julian to Gregorian and Gregorian to Julian. From what I understand so far, you'd have to first convert the Julian calendar date to the Julian Day Number and then to a Gregorian date (same strategy in the other direction). Is there a "better" way? Thanks, William
Date: 02/10/2011 at 16:15:23 From: Doctor Vogler Subject: Re: Converting a Julian calendar date to a Gregorian date Hi William, Thanks for writing to Dr. Math. Frankly, I rather like the strategy you described, because I think that using a number-of-days figure is very useful for many other purposes. But there is a different way of doing the conversion which you might consider simpler: you just compute how many days off the two dates are. The difference between the Julian and Gregorian calendars is that the Julian one has a leap year every fourth year, while the Gregorian one skips leap years on century years (like 1900) that are not divisible by 400. So the Gregorian calendar gains a day at the end of every February in a century year that is not divisible by 400. So you take the year number of the last 1st of March before your date (in other words, use the previous year if your date is in January or February), divide by 100 and round down. Then divide that same year by 400 and round down, and subtract the two quotients. Subtract two because the two calendars are aligned in the A.D. 200s. Then add that many days of offset to your Julian date. If you have any questions about this or need more help, please write back and show me what you have been able to do, and I will try to offer further suggestions. - Doctor Vogler, The Math Forum http://mathforum.org/dr.math/
Date: 02/11/2011 at 05:14:42 From: William Subject: Converting a Julian calendar date to a Gregorian date Thanks for the reply; it really helped! I'm just wondering about the algorithm you described in the last paragraph: "So you take the year number of the last 1st of March before your date...." Does that algorithm have any limits? In other words, does it only work up until a certain date, say, year 2500? Also, what is it called? I'm doing this for a programming exercise that converts between the two calendars, and it would be nice if I could refer to the algorithm by some name. William
Date: 02/12/2011 at 00:39:59 From: Doctor Vogler Subject: Re: Converting a Julian calendar date to a Gregorian date Hi William, Thanks for writing to Dr. Math. This method for date conversion works for any year, and is called "the conversion between Julian and Gregorian calendars"! Of course, the Gregorian calendar might not be in common use in the year 2500. But then the Julian calendar isn't in common use today, and yet here we are invoking it in exercises for computer programming -- a technology that did not exist when it was! - Doctor Vogler, The Math Forum http://mathforum.org/dr.math/
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