How to make a floated div 100% height of its parent?

Here is the HTML:

<div id="outer">
    <div id="inner"></div>
    Test
</div>

And here is the CSS:

#inner {
  float: left;
  height: 100%;
}

Upon inspection with the Chrome developer tools, the inner div is getting a height of 0px.

How can I force it to be 100% of the height of the parent div?