Height equal to dynamic width (CSS fluid layout)

It is possible without any Javascript :)

The HTML:

<div class='box'>
    <div class='content'>Aspect ratio of 1:1</div>
</div> 

The CSS:

.box {
    position: relative;
    width:    50%; /* desired width */
}

.box:before {
    content:     "";
    display:     block;
    padding-top: 100%; /* initial ratio of 1:1*/
}

.content {
    position: absolute;
    top:      0;
    left:     0;
    bottom:   0;
    right:    0;
}

/* Other ratios - just apply the desired class to the "box" element */
.ratio2_1:before{
    padding-top: 50%;
}
.ratio1_2:before{
    padding-top: 200%;
}
.ratio4_3:before{
    padding-top: 75%;
}
.ratio16_9:before{
    padding-top: 56.25%;
}

Best method now : the aspect-ratio property (2022)

div {
  aspect-ratio : 1 / 1;
  width:50%;
  border:1px solid red;
}

<div>Aspect ratio : 1 / 1</div>

Other method : use vw units for a responsive height/width according to the viewport width.

vw : 1/100th of the width of the viewport. (Source MDN)

DEMO

HTML:

<div></div>

CSS for a 1:1 aspect ratio:

div{
    width:80vw;
    height:80vw; /* same as width */
}

Table to calculate height according to the desired aspect ratio and width of element.

   aspect ratio  |  multiply width by
    -----------------------------------
         1:1      |         1
         1:3      |         3
         4:3      |        0.75
        16:9      |       0.5625

This technique allows you to :

• insert any content inside the element without using position:absolute;
• no unecessary HTML markup (only one element)
• adapt the elements aspect ratio according to the height of the viewport using vh units
• you can make a responsive square or other aspect ratio that alway fits in viewport according to the height and width of the viewport (see this answer : Responsive square according to width and height of viewport or this demo)

These units are supported by IE9+ see canIuse for more info

[Update: Although I discovered this trick independently, I’ve since learned that Thierry Koblentz beat me to it. You can find his 2009 article on A List Apart. Credit where credit is due.]

I know this is an old question, but I encountered a similar problem that I did solve only with CSS. Here is my blog post that discusses the solution. Included in the post is a live example. Code is reposted below.

#container {
  display: inline-block;
  position: relative;
  width: 50%;
}

#dummy {
  margin-top: 75%;
  /* 4:3 aspect ratio */
}

#element {
  position: absolute;
  top: 0;
  bottom: 0;
  left: 0;
  right: 0;
  background-color: silver/* show me! */
}

<div id="container">
  <div id="dummy"></div>
  <div id="element">
    some text
  </div>
</div>

There is a way using CSS!

If you set your width depending on the parent container you can set the height to 0 and set padding-bottom to the percentage which will be calculated depending on the current width:

.some_element {
    position: relative;
    width: 20%;
    height: 0;
    padding-bottom: 20%;
}

This works well in all major browsers.

JSFiddle: https://jsfiddle.net/ayb9nzj3/