Chord Length Calculator
Calculate chord length, arc length, sagitta, and sector area based on radius and central angle. Chord Length Calculator helps students, engineers, designers, and surveyors solve circular geometry problems accurately.
Highlights
- Calculate chord length from a circle’s radius and central angle.
- Find arc length, sagitta, sector area, and diameter in one place.
- Support angles in degrees or radians for flexible calculations.
- Choose from a wide range of metric and imperial units.
- Ideal for students, engineers, designers, and surveyors.
Table of Contents
How Chord Length Calculator Works?
The calculator models a circle using the entered radius r and central angle θ. The angle may be entered in degrees or radians, while the trigonometric formulas use the corresponding angular value. A chord is the straight line joining two points on the circle, whereas the arc is the curved path between those points.
Here, c is the chord length. The arc length is proportional to the central angle:
The sagitta is the perpendicular distance from the chord midpoint to the corresponding arc. It is calculated as:
The sector area is the region bounded by two radii and the arc:
Finally, the diameter is twice the radius:
For example, with a radius of 10 and a central angle of 90°, the calculator produces the following approximate results:
| Output | Result |
|---|---|
| Chord Length | 14.142 |
| Arc Length | 15.708 |
| Sagitta | 2.929 |
| Sector Area | 78.540 |
| Diameter | 20 |
Practical Use Cases
Students can use the calculator to check geometry exercises involving circles, central angles, chords, arcs, sector areas, and sagitta measurements.
Engineers can estimate curved-section dimensions for mechanical components, circular openings, tanks, pipelines, and structural layouts.
Designers can determine the straight-line span, curved perimeter distance, and enclosed sector area when creating circular features, arches, patterns, or product layouts.
Surveyors can calculate the chord and arc associated with a circular curve, helping describe curved boundaries and geometric alignment plans.
Fabricators and builders can use the sagitta and chord length to mark out circular arcs accurately when constructing panels, frames, roofs, or curved surfaces.
Accuracy and Limitations
The calculator applies standard circle-geometry formulas and supports radii from 0.000001 to 1,000,000,000 and central angles from 0.000001° or radian equivalent through 360°. Results are subject to normal floating-point rounding, especially for extremely small angles or very large radius values. The arc length, sagitta, and sector area correspond to the entered central angle, while the chord formula gives the straight-line distance between the endpoints; at a 360° angle, the endpoints coincide and the chord length is zero. The calculator assumes an ideal circle and does not account for measurement errors, distorted geometry, or manufacturing tolerances.
Quick Examples
Example #1: Quarter-Circle Chord
Calculate circular measurements for a 10 m radius with a 90-degree central angle.
Example #2: Small Circular Segment
Determine the chord and related geometry for a 25 cm radius and a 60-degree central angle.
Example #3: Radians-Based Chord
Calculate circular dimensions using a 2 m radius and a central angle expressed in radians.
