How to calculate the XPath position of an element using Javascript?

Firebug can do this, and it’s open source (BSD) so you can reuse their implementation, which does not require any libraries.

3rd party edit

This is an extract from the linked source above. Just in case the link above will change. Please check the source to benefit from changes and updates or the full featureset provided.

Xpath.getElementXPath = function(element)
{
    if (element && element.id)
        return '//*[@id="' + element.id + '"]';
    else
        return Xpath.getElementTreeXPath(element);
};

Above code calls this function.
Attention i added some line-wrapping to avoid horizontal scroll bar

Xpath.getElementTreeXPath = function(element)
{
    var paths = [];  // Use nodeName (instead of localName) 
    // so namespace prefix is included (if any).
    for (; element && element.nodeType == Node.ELEMENT_NODE; 
           element = element.parentNode)
    {
        var index = 0;
        var hasFollowingSiblings = false;
        for (var sibling = element.previousSibling; sibling; 
              sibling = sibling.previousSibling)
        {
            // Ignore document type declaration.
            if (sibling.nodeType == Node.DOCUMENT_TYPE_NODE)
                continue;

            if (sibling.nodeName == element.nodeName)
                ++index;
        }

        for (var sibling = element.nextSibling; 
            sibling && !hasFollowingSiblings;
            sibling = sibling.nextSibling)
        {
            if (sibling.nodeName == element.nodeName)
                hasFollowingSiblings = true;
        }

        var tagName = (element.prefix ? element.prefix + ":" : "") 
                          + element.localName;
        var pathIndex = (index || hasFollowingSiblings ? "[" 
                   + (index + 1) + "]" : "");
        paths.splice(0, 0, tagName + pathIndex);
    }

    return paths.length ? "https://stackoverflow.com/" + paths.join("https://stackoverflow.com/") : null;
};