Conical Radius Fretboard Formula

by Elaine Hartstein

Originally published in American Lutherie #34, 1993 and Big Red Book of American Lutherie Volume Three, 2004



As a follow-up to Tim Earls’ article “In Search of the Perfect Cone” in American Lutherie #30, I’ve come up with a formula for finding the hypothetically-ideal radius for the fingerboard at any distance from the nut. Since a set of nonparallel strings cannot lie flat on a cylindrical fretboard, we wish to discover the geometry of the cone described by the strings. As Tim Olsen suggested, the outside strings (as opposed to the edges of the fingerboard) should define the cone. The cone defined by the fingerboard edge would give results with a smaller radius.