Finding and marking the exact center of a small metal rod or dowel is more difficult than finding the center of a larger circle. I recently wanted to mark the center of a 1" long x 3/8" diameter brass rod, then drill a 1/8" concentric hole the entire length. Yes, just a brass rod with a hole down the center. A professional machinist with a metal working lathe might have no problem with this, but for the average garage shop guy (me) it was no easy task. I learned a few tricks and made a jig that made the job easier and the results better.
With apologies to my friends in metric countries (everybody except U.S.), my example is in Imperial units. Everything applies to S.I. components and drill bits.
Step 1: Find the center of the rod - Method # 1
Method # 1 (not necessarily the best).
The classic method of finding the center of a round object is to use a center finder head attached to a standard metal rule, such as used in a combination square. You hold the round item in the V-notch and scribe a fine line. That line is a diameter of the circle. Rotate the piece, and scribe another line. Where the two lines intersect is the center. Easy and accurate for large circles (say over 1" diameter), not so easy for a 3/8" rod. Forget about using a pencil; use a sharp knife point, like an Exacto knife. Even with a sharp knife, the line can be a bit off center.
Step 2: Find the center of the rod - Method # 2
Use a Forstner or brad point drill bit the same size as the rod. The point at the center will be reliably dead center. Place the rod and drill bit on a hard flat surface, and with the point of the bit scribe a couple of lines on the rod end. Where the lines intersect will be the center.