The relationship
Formula
c = 2r sin(θ÷2) · h = r(1 − cos(θ÷2)) · A = ½r²(θ − sin θ)
For a radius of 10 cm and an angle of 60°: chord = 10 cm, sagitta ≈ 1.3397 cm, and minor segment area ≈ 9.0586 cm².
Arches & cut lines
Circle Chord & Segment Calculator
Turn a radius plus angle, chord, or sagitta into the full geometry of a minor circular segment. Useful for arches, layouts, fabrication and curve checks.
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INPUT
Define the minor segment
Use an angle, chord or sagitta with the radius.
RESULT
Calculated instantly
Chord length10 cm
Sagitta1.3397 cm
Central angle60°
Arc length10.472 cm
Minor segment area9.0586 cm²
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Straight answers
Common questions
What is a chord compared with an arc?
A chord is a straight line between two points on a circle. The arc is the curved part of the circumference between those points.
Can I calculate chord length without an angle?
Yes. A radius plus a valid sagitta is enough to derive the angle and chord length.
What is the difference between minor and major segments?
The minor segment uses the shorter arc and is at most a semicircle. The major segment is the remaining larger part of the circle.