Finds the straight-line distance between two points on a circle’s circumference, given the radius and the central angle between them.
How it works
Twice the radius is multiplied by the sine of half the central angle to give the chord’s straight-line length.
What this does not include
This does not include the curved arc length between the same two points — that’s a different measurement along the circle’s edge rather than a straight line.
How to use this calculator
- Enter the circle’s radius and the central angle between the two points.
A worked example
A circle with radius 5 and a 60° central angle: chord length = 2r×sin(angle/2) = 5 — at exactly 60°, the chord length equals the radius, forming an equilateral triangle with the center.
Radius 10, 90° angle: chord length = 14.1421.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Distance from the circle’s center to its edge |
| Angle | Central angle subtending the chord, in degrees |
Edge cases worth knowing
A 60° central angle always produces a chord equal to the radius — a special case worth remembering, since it comes directly from the geometry of an equilateral triangle formed with the center.
A radius of zero collapses every chord to zero length regardless of angle, so the calculator declines to show a result.
Frequently asked questions
What’s a real-world example of a chord?
The straight edge cut across a circular pipe, or the string of a bow — any straight line connecting two points on a curve.
What happens at a 180° central angle?
The chord becomes the circle’s diameter — the longest possible chord.
Is the chord always shorter than the arc between the same points?
Yes — a straight line between two points is always the shortest path, while the arc curves around and is always longer (except at a 0° angle, where both are zero).
