Converting string to Date and DateTime

Use strtotime() on your first date then date('Y-m-d') to convert it back:

$time = strtotime('10/16/2003');

$newformat = date('Y-m-d',$time);

echo $newformat;
// 2003-10-16

Make note that there is a difference between using forward slash / and hyphen - in the strtotime() function. To quote from php.net:

Dates in the m/d/y or d-m-y formats are disambiguated by looking at the separator between the various components: if the separator is a slash (/), then the American m/d/y is assumed; whereas if the separator is a dash (-) or a dot (.), then the European d-m-y format is assumed.

To avoid potential ambiguity, it's best to use ISO 8601 (YYYY-MM-DD) dates or DateTime::createFromFormat() when possible.

You need to be careful with m/d/Y and m-d-Y formats. PHP considers / to mean m/d/Y and - to mean d-m-Y. I would explicitly describe the input format in this case:

$ymd = DateTime::createFromFormat('m-d-Y', '10-16-2003')->format('Y-m-d');

That way you are not at the whims of a certain interpretation.