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### Calculating Using Dates AD and BC

```Date: 11/25/2003 at 09:17:56
From: Theodore
Subject: How do you work the BC & AD math problems

How do you calculate how many years there are between dates where one
is given in years B.C. and the other is in years A.D.?  For example,
how many years were there from 15 B.C. to 63 A.D.?

B.C. amount, then add the A. D. amount.  Is that correct?

```

```
Date: 11/25/2003 at 12:21:14
From: Doctor Peterson
Subject: Re: How do you work the BC & AD math problems

Hi Theodore.

Thanks for writing to Dr. Math.  As discussed here

Year 0
http://mathforum.org/library/drmath/view/52475.html

there was no year 0; that forces us to make an adjustment when we
compare A.D. and B.C. dates.  If there were a year 0, the time line
would look like this:
__________________________________
/                                  \
<-+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-->
-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

(I've put the numbers between the marks because a given year spans
the time from Jan 1 one year to Jan 1 the next.)

Then you could find the time from, say, June 1, 5 B.C. to June 1, 7
A.D. by subtracting a negative number:

7 - -5 = 7 + 5 = 12 years

That amounts to what you do: there are 5 years before 0, and 7 years
after, making a total of 12.

But in fact there was no year zero, because the people who invented
the B.C./A.D. system didn't know about the number zero yet.  (That
was, of course, long after the year zero, but still a long time ago!)
So reality looks like this:
_______________________________
/                               \
<-+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-->
-9 -8 -7 -6 -5 -4 -3 -2 -1  1  2  3  4  5  6  7  8  9

To make that, I just deleted one year's worth from a copy of the
first version--and that's all you have to do to find the difference
between dates.  After you subtract the first date from the second, you
subtract one year if the non-existent year zero would have been
between them.

(7 - -5) - 1 = 12 - 1 = 11 years.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/

```

```
Date: 11/25/2003 at 20:29:40
From: W. Theodore
Subject: Thank you (How do you work the BC &amp; AD math problems)

Dr. Math, I would like to say thank you for your help.  I am home-
schooled and my text has nothing to say about that topic.

Thanks again!
```
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