HTML - how can I show tooltip ONLY when ellipsis is activated

Here's a way that does it using the built-in ellipsis setting, and adds the title attribute on-demand (with jQuery) building on Martin Smith's comment:

$('.mightOverflow').bind('mouseenter', function(){
    var $this = $(this);

    if(this.offsetWidth < this.scrollWidth && !$this.attr('title')){
        $this.attr('title', $this.text());
    }
});

Here's a pure CSS solution. No need for jQuery. It won't show a tooltip, instead it'll just expand the content to its full length on mouseover.

Works great if you have content that gets replaced. Then you don't have to run a jQuery function every time.

.might-overflow {
    text-overflow: ellipsis;
    overflow : hidden;
    white-space: nowrap;
}

.might-overflow:hover {
    text-overflow: clip;
    white-space: normal;
    word-break: break-all;
}

Here are two other pure CSS solutions:

  1. Show the truncated text in place:

.overflow {
  overflow: hidden;
  -ms-text-overflow: ellipsis;
  text-overflow: ellipsis;
  white-space: nowrap;
}

.overflow:hover {
  overflow: visible;
}

.overflow:hover span {
  position: relative;
  background-color: white;

  box-shadow: 0 0 4px 0 black;
  border-radius: 1px;
}
<div>
  <span class="overflow" style="float: left; width: 50px">
    <span>Long text that might overflow.</span>
  </span>
  Lorem ipsum dolor sit amet, consectetur adipisicing elit. Ad recusandae perspiciatis accusantium quas aut explicabo ab. Doloremque quam eos, alias dolore, iusto pariatur earum, ullam, quidem dolores deleniti perspiciatis omnis.
</div>
  1. Show an arbitrary "tooltip":

.wrap {
  position: relative;
}

.overflow {
  white-space: nowrap; 
  overflow: hidden;
  text-overflow: ellipsis;
  
  pointer-events:none;
}

.overflow:after {
  content:"";
  display: block;
  position: absolute;
  top: 0;
  right: 0;
  width: 20px;
  height: 15px;
  z-index: 1;
  border: 1px solid red; /* for visualization only */
  pointer-events:initial;

}

.overflow:hover:after{
  cursor: pointer;
}

.tooltip {
  /* visibility: hidden; */
  display: none;
  position: absolute;
  top: 10;
  left: 0;
  background-color: #fff;
  padding: 10px;
  -webkit-box-shadow: 0 0 50px 0 rgba(0,0,0,0.3);
  opacity: 0;
  transition: opacity 0.5s ease;
}


.overflow:hover + .tooltip {
  /*visibility: visible; */
  display: initial;
  transition: opacity 0.5s ease;
  opacity: 1;
}
<div>
  <span class="wrap">
    <span class="overflow" style="float: left; width: 50px">Long text that might overflow</span>
    <span class='tooltip'>Long text that might overflow.</span>
  </span>
  Lorem ipsum dolor sit amet, consectetur adipisicing elit. Ad recusandae perspiciatis accusantium quas aut explicabo ab. Doloremque quam eos, alias dolore, iusto pariatur earum, ullam, quidem dolores deleniti perspiciatis omnis.
</div>

uosɐſ's answer is fundamentally correct, but you probably don't want to do it in the mouseenter event. That's going to cause it to do the calculation to determine if it's needed, each time you mouse over the element. Unless the size of the element is changing, there's no reason to do that.

It would be better to just call this code immediately after the element is added to the DOM:

var $ele = $('#mightOverflow');
var ele = $ele.eq(0);
if (ele.offsetWidth < ele.scrollWidth)
    $ele.attr('title', $ele.text());

Or, if you don't know when exactly it's added, then call that code after the page is finished loading.

if you have more than a single element that you need to do this with, then you can give them all the same class (such as "mightOverflow"), and use this code to update them all:

$('.mightOverflow').each(function() {
    var $ele = $(this);
    if (this.offsetWidth < this.scrollWidth)
        $ele.attr('title', $ele.text());
});