A river that rose in the Iron Hills, far to the north and east of the known parts of Middle-earth. Its winding course took it southwards for more than two hundred miles, until its waters emptied into the Celduin (the River Running) and were carried on southwards to the Sea of Rhûn.

The river's name, Carnen, is a direct Elvish equivalent of its Mannish name, the Redwater. Both are very likely a reference to its source in the Iron Hills, since rivers whose sources lie among iron deposits have water with a very distinctive red-orange colour.