Carpentry and Woodworking - handrail advice

Hi,
I just installed a handrail in a cellar stairway, but I'm going to have to butt up another 18" piece to it. The rail is a 10-footer, which was all they had.
I'm figuring on a three-inch dia. piece of hardwood stock which would butt up to the rail almost exactly, but how to butt 'em up for safety has me wondering.
The piece will run from the top end of the handrail to be attached flush to a wall facing it (90degrees) at an upward angle.:thinker:

Is this 18" piece going to be a return, or an extension of the rail you have? I can't tell from the description you give. You can't join two pieces using a solid block behind them, as that would negate the hand holding capability. I would have shopped further and gotten a full 12' piece to do the job in singularity. You won't ever get more strength from that shorter piece.

you might use a center finder and drill a hole for a dowel to pin them together. if so use a piece of all thread and epoxy or gorilla glue to hold them together. make sure it extendes atleast 3 in into each one.

are you going to cowboy up or just lay there and bleed?

Cut a thin slice of the rail to use as a template. Drill both ends to accept either dowels (I used 2, 3/8" dowel or a double ended lag (can't remember the name). Glue everything together. This is the method used to connect curved sections to a straight rail and it's pretty strong.

Many thanks, guys.
I'll set up with the glue and dowels; should work fine.
The doityourslef.com guys always come through, usually over in the automotive side for me.
Best regards
Jim in Quincy MA