How do I calculate the length of material needed for a curve?

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.

What is the difference between arc length and chord length?

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.

How do I bend wood to a specific radius?

Steam bending works for radii greater than about 25x the timber thickness. Lamination (gluing thin strips around a form) works for tighter radii. Kerfing (saw cuts on the back face) allows even tighter bends. The arc calculator helps you design the form or jig.

What is the sagitta and why does it matter?

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.

WoodCalcs

Arc Calculator — Length, Rise & Chord for Curves

Calculate arc lengths, rise, chord, and radius for curved woodworking pieces.

Radius

Central Angle

How We Calculate This

This calculator computes arc geometry from a radius and central angle.

Key formulas

Arc length = R x theta (theta in radians)

Chord = 2R x sin(theta/2)

Sagitta = R x (1 - cos(theta/2))

Sector area = 0.5 x R² x theta

Where theta = central angle in radians = degrees x pi / 180.

Frequently Asked Questions

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Last updated: February 2026

All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.