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Sector Circumradius Calculator — How It Works

Sector Circumradius Calculator circumradius geometry calculator

Sector Circumradius Calculator — How It Works

The circumradius (R) is the radius of the circle that passes through all the key points of a shape — its circumscribed circle. The Sector Circumradius Calculator calculates this for a circular sector from the radius (and angle, for reference). Try the Sector Circumradius Calculator — instant results, no sign-up.

The formula

R = radius (a sector lies on its own circle, regardless of its angle)

Example

For a circular sector with the radius (and angle, for reference) = 5 and 90°:

R ≈ 5

A note on “circumradius” for this shape

For shapes that aren’t always cyclic (have a circle through every vertex) in their general form — like a rhombus, parallelogram, or trapezoid — this calculator applies the standard circumradius formula for the cyclic case (e.g. assuming a rectangle for parallelograms, or an isosceles trapezoid). For squares, regular polygons, semicircles, and sectors, the circumradius is well-defined for every such shape.

FAQ

Is this free?

Yes — the Sector Circumradius Calculator runs entirely in your browser, no sign-up required.