When it really matters how close you are to dead center on a circle, this tool (see drawing) can help you to get spot on. To make it, dado a couple of 1x3s to fashion a 90° half-lap joint. Then glue and screw the pieces together. Now pick one edge of the longer arm as your scribing edge, and drive two 16d nails through the short arm. The distance of the nails, A and B, should be equidistant from the scribing edge.
To use this center-finding tool, set the nails against the circumference of your circular object, and scribe a line down the long arm. Now rotate the tool a quarter-turn or so, and repeat the process. Where the two scribed lines cross is dead center.
You can build one of these gizmos in any size that you need. The two nails should be no less than a quarter of the diameter apart, nor wider apart than three-quarters of the diameter. I use one all the time for finding the centers of Sonotubes. Although I can’t draw a line across thin air, I can stretch a piece of string into two knife cuts on opposite sides of the tube located by the center-finder’s arm.
—T. H. Richards, Mont Tremblant, None
Edited and Illustrated by Charles Miller
From Fine Homebuilding #112
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Brilliant. It is based on the mathematics for finding the radius of a circle, and thus the center, by drawing and measuring a chord. Simple Pythagoras arithmetic learned in the 8th grade. The sum of the squares of the sides is equal to the square of the hypotenuse.
You can also do it with your square- see https://www.youtube.com/watch?v=4mVYceMvhls