When we inspect element on chrome browser its shows height and width of that element. So my question is that can we get that calculated height and width using any scripting language like javascript or any external api?

When we inspect element on chrome browser its shows height and width of that element. So my question is that can we get that calculated height and width using any scripting language like javascript or any external api?

You can use
var height = document.getElementById(<id of the element>).offsetHeight;
var width = document.getElementById(<id of the element>).offsetWidth;
in a JavaScript file, embedded on that page if that is what you are searching for.
Ondra is right,
you need to include jQuery and the following code will get you started (based on the element you've highlighted (The first function() line is to make sure your document is ready:
<script>
$(function() {
width = $('div#t8_2').width();
height = $('div#t8_2').height();
});
</script>
Edit: Seems to me like you're trying to calculate Text width and not an element's width.
I'm taking the answer from this question from philfreo:
Here's his jsFiddle: http://jsfiddle.net/philfreo/MqM76/
That should work.