Make a div fill the height of the remaining screen space

I am working on a web application where I want the content to fill the height of the entire screen.

The page has a header, which contains a logo, and account information. This could be an arbitrary height. I want the content div to fill the rest of the page to the bottom.

I have a header div and a content div. At the moment I am using a table for the layout like so:

CSS and HTML

#page {
  height: 100%;
  width: 100%
}

#tdcontent {
  height: 100%;
}

#content {
  overflow: auto;  /* or overflow: hidden; */
}
<table id="page">
  <tr>
    <td id="tdheader">
      <div id="header">...</div>
    </td>
  </tr>
  <tr>
    <td id="tdcontent">
      <div id="content">...</div>
    </td>
  </tr>
</table>

The entire height of the page is filled, and no scrolling is required.

For anything inside the content div, setting top: 0; will put it right underneath the header. Sometimes the content will be a real table, with its height set to 100%. Putting header inside content will not allow this to work.

Is there a way to achieve the same effect without using the table?

Update:

Elements inside the content div will have heights set to percentages as well. So something at 100% inside the div will fill it to the bottom. As will two elements at 50%.

Update 2:

For instance, if the header takes up 20% of the screen’s height, a table specified at 50% inside #content would take up 40% of the screen space. So far, wrapping the entire thing in a table is the only thing that works.