I do this all the time, because I always have a ruler, and rarely have a compass...
Mark the center of the circle.
Divide the diameter in half.
So, for example, let's say I want a 6 1/2" circle. Half of that is 3 1/4".
Hold ruler so the radius dimension (3 1/4") is on the center mark.
Now, mark both zero and 6 1/2".
Rotate the ruler a bit, and do it again. And again. And again. It makes no difference how many times you do it, or how evenly spaced your marks are.
Connect the dots.
Or you could use a string to tie a pencil to a nail. Place nail in center of circle and rotate pencil around. Be sure to place string near point of pencil.
Yeah, the only problem with the string is it's a little harder to get an exact dimension. Gotta tie the knots just right.
I've used a thin strip of metal in a bind, furnace tin or flashing. Punch hole at center and another at radius, use scribe or marker to outline the circumference.
Plumber's tape works well as a semi-rigid, accurate dimensional medium instead of the string. It's also got regular holes in it for your pencil.
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