JSFiddle - React, Tailwind, and code Playground

HTML

<div id="el"></div>

CSS

#el {
    background-image: url(http://content1.promiflash.de/article-images/w500/grumpy-cat-und-eine-blume.jpg);
    background-position: center;
    width: 300px;
    height: 250px;
    margin-bottom: 10px;
}

JavaScript

function bgSize($el, cb){
    $('<img />')
        .load(function(){ cb(this.width, this.height); })
        .attr('src', $el.css('background-image').match(/^url\("?(.+?)"?\)$/)[1]);
}

bgSize($('#el'), function(width, height){
    $('body').append('width : ' + width + ' height : ' + height);
});