Chord Length Calculator
Calculate chord length, sagitta, and arc properties from radius and angle. Features a dynamic SVG diagram for construction and machining visualization.
About
Precise calculation of chord lengths is a frequent requirement in mechanical engineering, architectural drafting, and CNC machining. Errors in these dimensions often lead to material waste or structural misalignment. This tool solves for the chord length given the radius and the subtended angle, or inversely calculates the angle required to span a specific chord.
The logic relies on fundamental trigonometric relationships within a circle segment. Beyond the chord itself, the calculator derives the sagitta (the height of the arc) and the arc length, parameters necessary for bending operations and layout work.
Formulas
The primary calculation uses the law of sines applied to the isosceles triangle formed by the radius vectors and the chord. For a circle of radius r and central angle θ:
When the chord length c and radius r are known, the angle θ is derived using the inverse sine function:
Reference Data
| Variable | Symbol | Formula / Relationship | Context |
|---|---|---|---|
| Chord Length | c | 2r sin(θ2) | Straight line distance between two points on the curve. |
| Sagitta | s | r ( 1 − cos(θ2) ) | Height of the arc segment (bulge). |
| Arc Length | L | r × θ (rad) | Distance along the curved path. |
| Radius | r | c2 sin(θ/2) | Distance from center to edge. |
| Apothem | a | r cos(θ2) | Distance from center to the midpoint of the chord. |