How this calculator works
Both endpoints of the arc and the angle vertex lie on the circle. Moving the vertex along the opposite arc leaves the inscribed angle unchanged. A minor intercepted arc produces an acute angle; a major arc produces an obtuse angle. The arc-case table illustrates both possibilities at the entered radius.
Formula
Inscribed angle α = θ/2; intercepted arc s = rθ = 2rα; r = s/(2α). Arc equations use radians.
Worked example
A 120° intercepted arc on a circle of radius 3 m has length 2π m and gives an inscribed angle of 60°. A semicircle gives a 90° inscribed angle.
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Frequently asked questions
Which of the two arcs do I enter?
Use the arc between the endpoints that avoids the angle vertex. Choosing the other arc gives the supplementary inscribed angle.
Can the central angle exceed 180°?
Yes. A reflex central angle describes a major intercepted arc and gives an obtuse inscribed angle.
Why is the full circle excluded?
At 360° the endpoints coincide. Three distinct points can no longer define the intended inscribed angle.