Moment.js – two dates difference in number of days

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From the moment.js docs: format('E') stands for day of week. thus your diff is being computed on which day of the week, which has to be between 1 and 7.

From the moment.js docs again, here is what they suggest: 

var a = moment([2007, 0, 29]);
var b = moment([2007, 0, 28]);
a.diff(b, 'days') // 1

Here is a JSFiddle for your particular case: 

$('#test').click(function() {
  var startDate = moment("13.04.2016", "DD.MM.YYYY");
  var endDate = moment("28.04.2016", "DD.MM.YYYY");

  var result="Diff: " + endDate.diff(startDate, 'days');

  $('#result').html(result);
});
#test {
  width: 100px;
  height: 100px;
  background: #ffb;
  padding: 10px;
  border: 2px solid #999;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.12.0/moment.js"></script>

<div id='test'>Click Me!!!</div>
<div id='result'></div>

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