Set width according to height [duplicate]

Answer 1

Edit: Missed that you wanted to set the width depending of the height, this does the opposite :(

---

To support all ratios you can use padding-bottom. Percentages in padding-bottom are always relative to the width of the element:

/* the wrapper has a width */
.wrapper {
  position: relative;
  width: 25%;
  margin-bottom: 10px;
}
/* these elements set the height (using padding-bottom) */
.square {
  padding-bottom: 100%;
  position: relative;
}
.widescreen {
  padding-bottom: 56.25%; /* 9/16 = 0.5625 */
}

/* 
 * This is the content. 
 * Needs position:absolute to not add to the width of the parent 
 */
.content {
  /* fill parent */
  position: absolute;  
  top: 0; bottom: 0;
  left: 0; right: 0;
  
  /* visual */
  padding: 10px;
  background: orange;
  color: white;
}

<div class="wrapper">
  <div class="square">
    <div class="content">square</div>
  </div>
</div>

<div class="wrapper">
  <div class="widescreen">
    <div class="content">16:9 ratio</div>
  </div>
</div>

The only downside is, that you need a bunch of wrapper elements.

Answer 2

There are two techiques I am aware of to keep the aspect ratio of an element according to it's height :

When height is relative to the viewport :

You can use vh units :

div {
  width: 75vh;
  height: 75vh;
  background:darkorange;
}

<div></div>

---

For a height based on the height of a parent element :

You can use a dummy image that has the aspect ratio you want. Example with a 1:1 aspect ratio you can use a 1*1 transparent .png image or as commented by @vlgalik a 1*1 base64 encoded gif :

html,body{
    height:100%;
    margin:0;
    padding:0;
}
#wrap{
    height:75%;
}
#el{
    display:inline-block;
    height:100%;
    background:darkorange;
}
#el img{
    display:block;
    height:100%;
    width:auto;
}

<div id="wrap">
    <div id="el">
        <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7">
    </div>
</div>

Note that this last demo doesn't update on window resize. But the aspect ratio is kept on page load

UPDATE :
As reported in the comments setting display:inline-flex: on #el seems to solve the updating on window resize problem.