通常，您可以比较client[Height|Width]与scroll[Height|Width]以便检测到此情况…
…但是，当可见溢出时，这些值将相同。因此，检测程序必须考虑到这一点：

// Determines if the passed element is overflowing its bounds,
// either vertically or horizontally.
// Will temporarily modify the "overflow" style to detect this
// if necessary.
function checkOverflow(el)
{
   var curOverflow = el.style.overflow;

   if ( !curOverflow || curOverflow === "visible" )
      el.style.overflow = "hidden";

   var isOverflowing = el.clientWidth < el.scrollWidth 
      || el.clientHeight < el.scrollHeight;

   el.style.overflow = curOverflow;

   return isOverflowing;
}

在FF3，FF40.0.2，IE6，Chrome 0.2.149.30中进行了测试。