A Crosscut Saw Guide Priced in Squareness: Freehand Error, the Fence-and-Slot Bound, and the Gap It Leaves at the Board Edge

A crosscut that is off square leaves a gap at one side of the joint, and the gap grows with the width of the board. This paper prices a common fence-and-slot saw guide in those terms. Freehand cut-angle error for a stated unpractised user is modelled as normally distributed with a standard deviation of 2.8 degrees: the mean absolute error is 2.234 degrees, the 90th-percentile absolute error is 4.606 degrees, and the probability of a gap exceeding 0.5 mm on a 200 mm board is 95.92 percent. A guide with a 90 mm slotted block (0.50 mm slot clearance) and a 150 mm fence (0.30 mm contact play) bounds the angle to 0.433 degrees in the worst case, made of a 0.318-degree slot contribution and a 0.115-degree fence contribution. The worst-case gap falls to 0.76 mm on a 100 mm board, 1.51 mm on a 200 mm board, and 2.27 mm on a 300 mm board — a 10.7-fold reduction against the freehand 90th percentile at 200 mm, but still above a 0.5 mm fitted-joint target at every width considered. The guide therefore converts an unusable cut into a cut that can be planed or sanded to fit; it does not, at these clearances, deliver a glue-ready square edge on wide boards, and claims that it does are contradicted by its own geometry. To reach a total bound of 0.3 degrees the slot clearance must fall to 0.291 mm, and slot wear to 1.2 mm clearance more than doubles the guided gap at 200 mm, to 3.07 mm.