Getting an element's inner height

var style = window.getComputedStyle(document.getElementById("Example"), null);
style.getPropertyValue("height");

The above version will work in modern browsers. Please check currentStyle for IE browsers.

clientHeight - give the height including padding but without the borders.

getComputedStyle - a way to tap into the CSS rules of an element and retrieve a property's value (padding)

Using parseInt is a way to strip away units and leave only the numeric value (which is in pixels)
parseFloat can also be used for more precise sub-pixel measurements

Note that all values will automatically be converted by the DOM API to pixels

function getInnerHeight( elm ){
  var computed = getComputedStyle(elm),
      padding = parseInt(computed.paddingTop) + parseInt(computed.paddingBottom);

  return elm.clientHeight - padding
}

DEMO:

// main method
function getInnerHeight( elm ){
  var computed = getComputedStyle(elm),
      padding = parseInt(computed.paddingTop) + parseInt(computed.paddingBottom);
  
  return elm.clientHeight - padding
}

// demo utility function
function printInnerHeight( selector ){
  console.clear()
  console.log(
    getInnerHeight( document.querySelector(selector) )
  )
}

body{ display: flex; padding:0; margin: 0; }
div{ flex: 1; }

.demo1{
  padding-top: 2vh;
  padding-bottom: 1vh;
  margin: 30px;
  border: 10px solid salmon;
  box-sizing: border-box;
  outline: 1px solid red;
}

.demo2{
  padding-top: 2vh;
  padding-bottom: 4vh;
  margin: 30px;
  border: 10px solid salmon;
  border-bottom-width: 0;
  height: 150px;
  outline: 1px solid red;
}


p::before{
  content: '';
  display: block;
  height: 100%;
  min-height: 50px;
  background: lightgreen;
}

<div>
  <h2>inner height should be ~50px</h2>
  <button onclick="printInnerHeight('.demo1')">Get Inner Height</button>
  <p class='demo1'></p>
</div>
<div>
  <h2>inner height should be ~150px</h2>
  <button onclick="printInnerHeight('.demo2')">Get Inner Height</button>
  <p class='demo2'></p>
</div>

EDIT from comments:

http://jsfiddle.net/hTGCE/1/ (a bit more code then expected)

in the internet you find functions like this:

  function getRectangle(obj) {

          var r = { top: 0, left: 0, width: 0, height: 0 };

          if(!obj)
             return r;

          else if(typeof obj == "string")
             obj = document.getElementById(obj);


          if(typeof obj != "object")
             return r;

          if(typeof obj.offsetTop != "undefined") {

             r.height = parseInt(obj.offsetHeight);
             r.width  = parseInt(obj.offsetWidth);
             r.left = r.top = 0;

             while(obj && obj.tagName != "BODY") {

                r.top  += parseInt(obj.offsetTop);
                r.left += parseInt(obj.offsetLeft);

                obj = obj.offsetParent;
             }
          }
          return r;
       }

if you want to subtract the padding / border-width is set in the css-file and not dynamic in the style attribute:

    var elem = document.getElementById(id);
    var borderWidth = 0;

          try {
             borderWidth = getComputedStyle(elem).getPropertyValue('border-top-width');

             } catch(e) {

             borderWidth = elem.currentStyle.borderWidth;
          } 
    borderWidth = parseInt(borderWidth.replace("px", ""), 10);

and with the padding the same. then you calculate it.