Horizontally center an absolute positioned element inside a 100% width DIV

Use the element width:

#logo {
    background:red;
    height:50px;
    position:absolute;
    width:50px;
    left:50%;
    margin-left:-25px;
}

If you would like to not use calculations you can do this:

#logo {
  background:red;
  width:50px;
  height:50px;
  position:absolute;
  left: 0;
  right: 0;
  margin: 0 auto;
}