Rounding over sharp edges is a staple of woodworking, and most woodworkers rely on a set of router bits in a variety of radii. Using a router for this job is practical if you have many, many linear feet of stock that needs an identical roundover, but it’s often faster to do it with a hand plane.
The process is very simple.
First, mark out the depth of your round-over using anything circular with the right radius. Once you get the hang of it, you can skip the layout stage, but the first few times it’s nice to have guidelines.
Use a hand plane to cut a 45 degree chamfer, and cut almost all the way down to your radiused layout lines on the end. It is easier to plane a neat chamfer with a long plane, such as a jointer.
Next, plane down each corner of the chamfer, which should be about 22.5 degrees.
After that, you can take one light pass over each of the four remaining corners, or you can just start sanding it all smooth. You can get very even roundovers like this.
If you are rounding over multiple edges, always do the end-grain first. You will blow-out the wood fibers on the exit-side of the board. But no matter.
As you round over the long-grain, you will plane off all the splinters. These edges are now ready for sanding, or scraping in hardwood. The whole process takes just minutes.
I usually don’t bother to lay out a radius on each side. I just count plane strokes. The original 45 degree chamfer took 20 strokes. The next bevels took five strokes each. Then I made one pass on each of the four remaining corners. So long as I take the same number of strokes on each side, the roundovers will be identical.
Thanks to Paul Sellers for showing me (and a lot of other guys) how to do this.