Get the Size of a CSS Background Image Using JavaScript?

Yes, and I'd do it like this...

window.onload = function () {
  var imageSrc = document
    .getElementById('hello')
    .style.backgroundImage.replace(/url\((['"])?(.*?)\1\)/gi, '$2')
    .split(',')[0];

  // I just broke it up on newlines for readability

  var image = new Image();
  image.src = imageSrc;

  image.onload = function () {
    var width = image.width,
      height = image.height;
    alert('width =' + width + ', height = ' + height);
  };
};

Some notes...

• We need to remove the url() part that JavaScript returns to get the proper image source. We need to split on , in case the element has multiple background images.
• We make a new Image object and set its src to the new image.
• We can then read the width & height.

jQuery would probably a lot less of a headache to get going.

Can't comment under answers, so here is jQuery version including background-size (posted because this question is first one in google search and may be useful to someone else than me):

function getBackgroundSize(selector, callback) {
  var img = new Image(),
      // here we will place image's width and height
      width, height,
      // here we get the size of the background and split it to array
      backgroundSize = $(selector).css('background-size').split(' ');

  // checking if width was set to pixel value
  if (/px/.test(backgroundSize[0])) width = parseInt(backgroundSize[0]);
  // checking if width was set to percent value
  if (/%/.test(backgroundSize[0])) width = $(selector).parent().width() * (parseInt(backgroundSize[0]) / 100);
  // checking if height was set to pixel value
  if (/px/.test(backgroundSize[1])) height = parseInt(backgroundSize[1]);
  // checking if height was set to percent value
  if (/%/.test(backgroundSize[1])) height = $(selector).parent().height() * (parseInt(backgroundSize[0]) / 100);

  img.onload = function () {
    // check if width was set earlier, if not then set it now
    if (typeof width == 'undefined') width = this.width;
    // do the same with height
    if (typeof height == 'undefined') height = this.height;
    // call the callback
    callback({ width: width, height: height });
  }
  // extract image source from css using one, simple regex
  // src should be set AFTER onload handler
  img.src = $(selector).css('background-image').replace(/url\(['"]*(.*?)['"]*\)/g, '$1');
}

or as jQuery plugin:

(function ($) {
// for better performance, define regexes once, before the code
var pxRegex = /px/, percentRegex = /%/, urlRegex = /url\(['"]*(.*?)['"]*\)/g;
$.fn.getBackgroundSize = function (callback) {
  var img = new Image(), width, height, backgroundSize = this.css('background-size').split(' ');

  if (pxRegex.test(backgroundSize[0])) width = parseInt(backgroundSize[0]);
  if (percentRegex.test(backgroundSize[0])) width = this.parent().width() * (parseInt(backgroundSize[0]) / 100);
  if (pxRegex.test(backgroundSize[1])) height = parseInt(backgroundSize[1]);
  if (percentRegex.test(backgroundSize[1])) height = this.parent().height() * (parseInt(backgroundSize[0]) / 100);
  // additional performance boost, if width and height was set just call the callback and return
  if ((typeof width != 'undefined') && (typeof height != 'undefined')) {
    callback({ width: width, height: height });
    return this;
  }
  img.onload = function () {
    if (typeof width == 'undefined') width = this.width;
    if (typeof height == 'undefined') height = this.height;
    callback({ width: width, height: height });
  }
  img.src = this.css('background-image').replace(urlRegex, '$1');
  return this;
}
})(jQuery);