Calculate chord length from a central angle, arc length, or sagitta with the geometry checks built in.
Last updated: June 2026 | By Patchworkr Team
Live results update as you type
Radius needs a real number.
A chord is a straight line segment that connects two points on a circle.
The longest chord is the diameter. That gives a built-in limit: chord length cannot exceed 2r.
This calculator checks that limit before it computes a value.
For a radius of 10 and a central angle of 60 deg, the chord length is 2 * 10 * sin(30 deg) = 10.
The chord is shorter than the arc, which is exactly what the geometry predicts.
Can sagitta be larger than the radius?
No. That would describe a circle segment that is not possible in this model.
Can the angle be zero?
Yes. A zero angle gives a zero-length chord as a degenerate boundary case.
Why do you use radians internally?
The sine function in the chord formula expects radians, so degrees are converted before calculation.
What if the chord is the diameter?
Then the angle is 180 deg and the chord length is exactly 2r.
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