A CodePen by Mohit Aneja. Proportionate Window and Element Heights - Tried this for responsive design. Check it out and let me know if any improvements can be done.

Proportionate Window and Element Heights

<h2>Resize the window to see it working!</h2>
<div id="test">
	<div class="log margin-10-bottom">Window Height: </div>
	<div class="log1 margin-10-bottom">Element Height: </div>
</div>

script.js

height_fix('#test', window);

function height_fix(element, parent){
  var woh = $(parent).height();
  var eoh = $(element).height();
  $(window).resize(function(){
    var eh = $(element).height();
    var wh = $(parent).height();
    var wdiff = wh / woh;
    var nh = Math.round((eoh * wdiff));
    $(element).height(nh);
    
    $('.log').text('Window Height: '+wh+'px');
    $('.log1').text('Element Height: '+nh+'px');
    
  })
}

style.css

body{
  margin:40px;
}
#test{
		width: 100%;
		height: 100px;
		background: #444;
		color: #fff;
}
h2{
  text-align:center;
  margin:0 0 10px 0;
  font-weight:bold;
  color:red;
}

Added info as users couldn't understand how to see it in action ;)