12-Hour and 24-Hour Time

Date: 04/25/2002 at 15:40:57
From: Becky Jarrard
Subject: 12 hour time and 24 hour time

If it is 00:46 on the clock, what would the time be for 12-hour time?
Please explain the steps for finding the solution. Also, when you are 
trying to find 24-hour time, what are the rules?

Date: 04/25/2002 at 23:15:25
From: Doctor Peterson
Subject: Re: 12 hour time and 24 hour time

Hi, Becky.

To convert from 24 hour time to 12 hour time:

  A. If the hour is 13 or more, subtract 12 from the hours 
     and call it P.M. Otherwise it is A.M.

  B. If the hour is 12, leave it unchanged, but call it P.M.

  C. If the hour is 0, make it 12 and call it A.M.

  D. Otherwise, leave the hour unchanged and call it A.M.

To convert from 12-hour time to 24-hour time:

  A. If the P.M. hour is from 1 through 11, add 12.

  B. If the P.M. hour is 12, leave it as is.

  C. If the A.M. hour is 12, make it 0.

  D. Otherwise, leave the hour unchanged.

  Then drop the A.M. or P.M., of course.

In both directions, the minutes are not changed.

The conversions look like this:

    24 hour     12 hour
    -------     -------
    00:xx       12:xx AM -- rule C
    01:xx        1:xx AM \
    ...         ...       | rule D
    11:xx       11:xx AM /
    12:xx       12:xx PM -- rule B
    13:xx        1:xx PM \
    ...         ...       | rule A
    23:xx       11:xx PM /

This answer from our archives may also help:

   Military Time
   http://mathforum.org/library/drmath/view/58434.html 

There is a two-step method that is easier in some respects, though a 
bit tricky to think about. This time, the numbers refer to two steps 
to do one after the other; the letters as before refer to the two 
possible cases at each step.

To convert from 24-hour time to 12 hour time:

  1. A. If the hour is 12 or more, subtract 12 from the hours
        and call it P.M.
     B. Otherwise call it A.M.

  2. A. If the hour is 0, change it to 12.
     B. Otherwise leave it alone.

To convert from 12-hour time to 24-hour time:

  1. A. If P.M., add 12 to the hour.
     B. Otherwise, leave it alone.

  2. A. If the hour is 12 or 24, subtract 12.
     B. Otherwise, leave it alone.

   Then drop the A.M. or P.M.

In both directions, the minutes are not changed.

The conversions look like this:

    24 hour     12 hour     rules
    -------     -------     -----
    00:xx       12:xx AM -- 1B, 2A
    01:xx        1:xx AM \
    ...         ...       | 1B, 2B
    11:xx       11:xx AM /
    12:xx       12:xx PM -- 1A, 2A
    13:xx        1:xx PM \
    ...         ...       | 1A, 2B
    23:xx       11:xx PM /

You can choose whichever method fits your style of thinking better.

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