Moment js is awesome

moment.js

$(function() {

        $('#patient_age').on('change', function() {
                var birth_year = moment().subtract('years', $(this).val());

                birth_year.startOf('year');

                $('#date_of_birth').val(birth_year.format('YYYY-MM-DD'));
        });

        $('#date_of_birth').on('change', function() {
                var date_of_birth = moment($(this).val());

                var years = moment().diff(date_of_birth, 'years');

                $('#patient_age').val(years);
        }).change();

});