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Chord Length Calculator.

Calculate chord length from radius and central angle.

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Chord length: 5.646425

Chord length

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Use Cases

Engineering and Construction

Determine the straight-line distance across a circular arc, useful for designing arches, bridges, or curved structures.

Example: Find the chord length for a circular arch with radius 10 m and central angle 1.2 rad.

Geometry and Mathematics Education

Solve geometry problems involving circles, such as finding distances between points on a circle or verifying properties of chords.

Example: Calculate the chord length for a circle with radius 5 units and central angle 60° (convert to radians).

Frequently Asked Questions

What is a chord in a circle?
A chord is a straight line segment whose endpoints both lie on the circle. The chord length is the distance between these two points. It is determined by the radius and the central angle subtended by the chord.
How is chord length calculated?
The chord length is calculated using the formula: chord length = 2 * radius * sin(central angle / 2). The central angle must be in radians. This formula derives from the geometry of an isosceles triangle formed by the two radii and the chord.
What units should I use for the radius and angle?
The radius can be in any unit (e.g., meters, feet, inches). The central angle must be in radians. If you have the angle in degrees, convert it to radians first (multiply by π/180). The chord length will be in the same unit as the radius.

Tips & Common Mistakes

Tips

  • Ensure the central angle is in radians. If you have degrees, convert by multiplying by π/180 (e.g., 60° = π/3 rad).
  • The central angle must be between 0 and 2π (or 0 and 360°). For angles greater than 2π, reduce it to the equivalent angle within one full rotation.
  • For a full circle (central angle = 2π), the chord length equals the diameter (2 * radius). For a semicircle (π), the chord is the diameter as well.
  • Use consistent units for radius and chord length. The result will be in the same unit as the radius.

Common Mistakes to Avoid

  • Using degrees instead of radians without conversion. Always convert to radians before applying the formula.
  • Forgetting to divide the central angle by 2 in the formula. The sine function requires half the angle.
  • Entering a negative radius or angle. Radius must be positive, and angle should be non-negative (0 to 2π).

Last updated: August 13, 2026