Curved Run Calculator
Curved run — segment & miter calculator
Fitting straight track around an arch. Measure the curve's rise and full span; this gives the radius, how many segments to cut, and the one miter angle that repeats at every joint. On a circular arc, equal chords all bend the same amount — so it's a single saw setting for the whole curve.
Measure the arch
X is the height at the center; W is the full width across the opening (springline to springline). The tool halves it internally — half-span = 30".
Nudge the count until the piece length lands nearest your target. Equal pieces close the arc exactly with one repeating miter.
The curve, segmented
Cut each piece
bend 7.9°/jointEvery full piece is an identical shallow keystone — miter both ends the same and flip alternate pieces end-for-end so the bevels nest. The miter is small enough that it never exceeds a saw's range, so no flipping trick needed here.
Where the curve meets straight track
The arc leaves the springline at 43.6° above horizontal. To butt the end pieces into a straight horizontal run, miter that joint at 19.8° on each side (curve end-piece and the straight track).
R = (Y² + X²) / 2X · joint bend β · miter β/2
