JS function to calculate the active are of an HTML5 video (i.e. the are of the element that is showing the video).

video-dimensions.js

function videoDimensions(video) {
  // Ratio of the video's intrisic dimensions
  var videoRatio = video.videoWidth / video.videoHeight;
  // The width and height of the video element
  var width = video.offsetWidth, height = video.offsetHeight;
  // The ratio of the element's width to its height
  var elementRatio = width/height;
  // If the video element is short and wide
  if(elementRatio > videoRatio) width = height * videoRatio;
  // It must be tall and thin, or exactly equal to the original ratio
  else height = width / videoRatio;
  return {
    width: width,
    height: height
  };
}