UPDATE:
Many browser inconsistencies have been fixed since my original answer. Now the clientHeight
property of a DOM element is reliable.
var height = element.clientHeight;
The Element.clientHeight read-only property is zero for elements with no CSS or inline layout boxes, otherwise it's the inner height of an element in pixels, including padding but not the horizontal scrollbar height, border, or margin.
clientHeight can be calculated as CSS height + CSS padding - height of horizontal scrollbar (if present).
Note: This property will round the value to an integer. If you need a fractional value, use element.getBoundingClientRect().
Source: https://developer.mozilla.org/en-US/docs/Web/API/Element/clientHeight
Original answer:
If you use the jQuery JS library, you can just do this:
var computed_height = $('#my_div').height();
If you use the Prototype JS library, it's similar:
var computed_height = $('my_div').getHeight();
Using a library is often the easiest & most cross-browser way to do something. Getting computed styles with vanilla js is unreliable because the properties are different across browsers.