Arc Calculator — Length, Rise & Chord for Curves

The arc length is the actual length of material along the curve. It is calculated as: Arc length = Radius x Angle (in radians). For a quarter circle (90 degrees), the arc is about 1.57 times the radius. Always add extra length for clamping and waste.

The chord is the straight-line distance between the two endpoints of the arc. The arc length is the actual curved distance along the arc. The arc is always longer than the chord. Use chord length for measuring the opening; use arc length for material requirements.

Unsteamed (cold) bending is limited to radii of roughly 20-30x the timber thickness. Steam bending lets you go much tighter — typically down to a thickness-to-radius ratio of about 1:10 (radius around 10x thickness), or as tight as 1:5 with straight-grained ash or oak and a compression strap. For radii tighter than steam allows, use lamination (thin strips glued around a form); kerfing (saw cuts on the back face) allows the tightest bends. The arc calculator helps you design the form or jig.

The sagitta is the maximum height of the arc above the chord (straight line between endpoints). It tells you how much rise your curved piece has. This is essential for determining the width of blank material needed - you need at least the sagitta plus material thickness.