Here is an example:

$(function() {

  $('#test').change(function() {

    $('#length').html($('#test').val().length)

  })

})

<script src=https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js></script>

<textarea id=test maxlength=10></textarea>

length = <span id=length>0</span>

Fill textarea with lines (one character at one line) until browser allows.
When you finish, leave textarea, and js code will calculate characters too.

So in my case I could enter only 7 characters (including whitespaces) before chrome stopped me. Although value of maxlength attribute is 10: