Its the same depth as the radiator. Check out this bench that AT reader, ShannonC, stumbled upon at a neighborhood antiques/design store.
It's located in her very narrow hallway and establishes a bit of a landing strip when she comes in the door. We love how it fits so perfectly right next to the radiator. And since it's no deeper than the radiator, it doesn't feel like it's intruding on the hallway space at all. She's pleased with her find, too:
...it's perfect for our super-narrow hallway! We've always wanted a place to sit and take off our shoes, but with a hallway that's less than 3.5 feet wide, we never thought it would be possible. We're very happy with it!