I solved my problem with lots and lots of testing things out.
Apparently my FormData Object was not correct.
Doing these changes to my code worked:
$('#xml').on('submit', function(e) {
e.preventDefault();
var form_data = new FormData(this);
form_data.append('action', 'calculate_xml');
$.ajax({
url : ajaxurl,
type: "POST",
data : form_data,
processData: false,
cache: false,
contentType: false,
success:function(response){
$('#response').html(response);
},
error: function(response){
$('#response').text('error');
}
});
});