Calculate arc height for single or compound radius fretboards. Supports 7.25", 9.5", 12", 16" and custom radii.
Pick one of the preset radii — 7.25", 9.5", 10", 12", 16" or 20" — or type any custom value in inches. Then enter the fretboard width in millimeters; the calculator starts at 42 mm, and accepts boards from 20 mm to 100 mm wide.
The tool treats the board surface as a chord across a circle of the chosen radius and solves the arc height: h = R − √(R² − (W/2)²). Width is converted from millimeters to inches internally, and the resulting crown is reported in both inches and millimeters.
Crown height falls as radius grows: the same 42 mm board rises 1.20 mm at 7.25", 0.92 mm at 9.5", 0.72 mm at 12" and only 0.54 mm at 16". When half the board width reaches or exceeds the radius, the geometry has no real solution and no result is returned.
The playing surface is shaped like a slice of a cylinder, and the radius states how large that cylinder is, in inches. A small figure such as 7.25" means a strongly curved surface, while larger values like 16" or 20" approach a nearly flat board.
Using h = R − √(R² − (W/2)²), a 42 mm wide board on a 9.5" radius rises 0.0360" (0.92 mm) at its center line. For comparison, the same board crowns 1.20 mm at 7.25" and just 0.54 mm at 16".
A board whose curvature flattens progressively from nut to heel. The calculator's compound function interpolates linearly — radius at fret n = nut radius + (heel radius − nut radius) × n ÷ total frets — so a 7.25"-to-12" board passes through every intermediate radius evenly along its length.
If half the board width equals or exceeds the radius, the board would be wider than the circle that defines it, and the square root in the arc-height formula has no real solution. The tool rejects that geometry rather than reporting a meaningless number.
Radius is entered in inches, matching how the presets from 7.25" to 20" are labeled, while board width is entered in millimeters and divided by 25.4 internally. The computed arc height is reported both in inches (four decimals) and in millimeters (two decimals).