How can I calculate the number of years between two dates?

Probably not the answer you're looking for, but at 2.6kb, I would not try to reinvent the wheel and I'd use something like moment.js. Does not have any dependencies.

The diff method is probably what you want: http://momentjs.com/docs/#/displaying/difference/

Sleek foundation javascript function.

 function calculateAge(birthday) { // birthday is a date
   var ageDifMs = Date.now() - birthday;
   var ageDate = new Date(ageDifMs); // miliseconds from epoch
   return Math.abs(ageDate.getUTCFullYear() - 1970);
 }