Check if an element's content is overflowing?

The element may be overflown vertically, horizontally or both. This function will return you a boolean value if the DOM element is overflown:

function isOverflown(element) {
  return element.scrollHeight > element.clientHeight || element.scrollWidth > element.clientWidth;
}

function isOverflown(element) {
  return element.scrollHeight > element.clientHeight || element.scrollWidth > element.clientWidth;
}

var els = document.getElementsByClassName('demos');
for (var i = 0; i < els.length; i++) {
  var el = els[i];
  el.style.borderColor = (isOverflown(el) ? 'red' : 'green');
  console.log("Element #" + i + " is " + (isOverflown(el) ? '' : 'not ') + "overflown.");
}

.demos {
  white-space: nowrap;
  overflow: hidden;
  width: 120px;
  border: 3px solid black;
}

<div class='demos'>This is some text inside the div which we are testing</div>
<div class='demos'>This is text.</div>

ES6 example:

const isOverflown = ({ clientWidth, clientHeight, scrollWidth, scrollHeight }) => {
    return scrollHeight > clientHeight || scrollWidth > clientWidth;
}

If you want to show only an identifier for more content, then you can do this with pure CSS. I use pure scrolling shadows for this. The trick is the use of background-attachment: local;. Your css looks like this:

.scrollbox {
  overflow: auto;
  width: 200px;
  max-height: 200px;
  margin: 50px auto;

  background:
    /* Shadow covers */
    linear-gradient(white 30%, rgba(255,255,255,0)),
    linear-gradient(rgba(255,255,255,0), white 70%) 0 100%,
    
    /* Shadows */
    radial-gradient(50% 0, farthest-side, rgba(0,0,0,.2), rgba(0,0,0,0)),
    radial-gradient(50% 100%,farthest-side, rgba(0,0,0,.2), rgba(0,0,0,0)) 0 100%;
  background:
    /* Shadow covers */
    linear-gradient(white 30%, rgba(255,255,255,0)),
    linear-gradient(rgba(255,255,255,0), white 70%) 0 100%,
    
    /* Shadows */
    radial-gradient(farthest-side at 50% 0, rgba(0,0,0,.2), rgba(0,0,0,0)),
    radial-gradient(farthest-side at 50% 100%, rgba(0,0,0,.2), rgba(0,0,0,0)) 0 100%;
  background-repeat: no-repeat;
  background-color: white;
  background-size: 100% 40px, 100% 40px, 100% 14px, 100% 14px;
  
  /* Opera doesn't support this in the shorthand */
  background-attachment: local, local, scroll, scroll;
}

<div class="scrollbox">
  <ul>
    <li>Not enough content to scroll</li>
    <li>2</li>
    <li>3</li>
    <li>4</li>
    <li>5</li>
  </ul>
</div>


<div class="scrollbox">
  <ul>
    <li>Ah! Scroll below!</li>
    <li>2</li>
    <li>3</li>
    <li>4</li>
    <li>5</li>
    <li>6</li>
    <li>7</li>
    <li>8</li>
    <li>9</li>
    <li>10</li>
    <li>1</li>
    <li>2</li>
    <li>3</li>
    <li>4</li>
    <li>5</li>
    <li>6</li>
    <li>7</li>
    <li>8</li>
    <li>The end!</li>
    <li>No shadow there.</li>
  </ul>
</div>

The code and the example you can find on http://dabblet.com/gist/2462915

And an explanation you can find here: http://lea.verou.me/2012/04/background-attachment-local/.

Comparing element.scrollHeight to element.clientHeight should do the task.

Below are the images from MDN explaining Element.scrollHeight and Element.clientHeight.

Scroll Height

Client Height

I made a multipart codepen demonstrating the above answers ( e.g. using overflow hidden and height) but also how you would expand / collapse overflowed items

Example 1: https://codepen.io/Kagerjay/pen/rraKLB ( Real simple example, no javascript, just to clip overflowed items)

Example 2: https://codepen.io/Kagerjay/pen/LBErJL (Single event handler show more / showless on overflowed items)

Example 3: https://codepen.io/Kagerjay/pen/MBYBoJ (Multi event handler on many show more/ show less on overflowed items)

I have attached example 3 below as well, I use Jade/Pug so it might be a tad verbose. I suggest checking out the codepens I've made its simpler to grasp.

// Overflow boolean checker
function isOverflown(element){
  return element.scrollHeight > element.clientHeight || element.scrollWidth > element.clientWidth;
}

// Jquery Toggle Text Plugin
$.fn.toggleText = function(t1, t2){
  if (this.text() == t1) this.text(t2);
  else                   this.text(t1);
  return this;
};

// Toggle Overflow
function toggleOverflow(e){
  e.target.parentElement.classList.toggle("grid-parent--showall");
  $(e.target).toggleText("Show More", "Show LESS");
}

// Where stuff happens
var parents = document.querySelectorAll(".grid-parent");

parents.forEach(parent => {
  if(isOverflown(parent)){
    parent.lastElementChild.classList.add("btn-show");
    parent.lastElementChild.addEventListener('click', toggleOverflow);
  }
})

body {
  background-color: #EEF0ED;
  margin-bottom: 300px;
}

.grid-parent {
  margin: 20px;
  width: 250px;
  background-color: lightgrey;
  display: flex;
  flex-wrap: wrap;
  overflow: hidden;
  max-height: 100px;
  position: relative;
}
.grid-parent--showall {
  max-height: none;
}

.grid-item {
  background-color: blue;
  width: 50px;
  height: 50px;
  box-sizing: border-box;
  border: 1px solid red;
}
.grid-item:nth-of-type(even) {
  background-color: lightblue;
}

.btn-expand {
  display: none;
  z-index: 3;
  position: absolute;
  right: 0px;
  bottom: 0px;
  padding: 3px;
  background-color: red;
  color: white;
}

.btn-show {
  display: block;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<section>
  <p>Any grid-parent over 10 child items has a "SHOW MORE" button to expand</p>
  <p>Click "SHOW MORE" to see the results</p>
</section>
<radio></radio>
<div class="wrapper">
  <h3>5 child elements</h3>
  <div class="grid-parent">
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="btn-expand">Show More</div>
  </div>
  <h3>8 child elements</h3>
  <div class="grid-parent">
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="btn-expand">Show More</div>
  </div>
  <h3>10 child elements</h3>
  <div class="grid-parent">
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="btn-expand">Show More</div>
  </div>
  <h3>13 child elements</h3>
  <div class="grid-parent">
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="btn-expand">Show More</div>
  </div>
  <h3>16 child elements</h3>
  <div class="grid-parent">
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="btn-expand">Show More</div>
  </div>
  <h3>19 child elements</h3>
  <div class="grid-parent">
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="grid-item"></div>
    <div class="btn-expand">Show More</div>
  </div>
</div>

Check if an element's content is overflowing?

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