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Regular Pentagon Circumradius Calculator

Calculates the circumscribed circle of a regular pentagon from its side length.

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Result

Circumradius (R)

4.2533

Working

R = side / (2·sin36°) = 5 / 1.1756 = 4.2533

Notes

  • · R = side / (2 × sin36°).

Regular Pentagon Circumradius Calculator — How It Works

Regular Pentagon 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 Regular Pentagon Circumradius Calculator calculates this for a regular pentagon from side length. Try the Regular Pentagon Circumradius Calculator — instant results, no sign-up.

The formula

R = side / (2 × sin36°)

Example

For a regular pentagon with side length = 5:

R ≈ 4.2533

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 Regular Pentagon Circumradius Calculator runs entirely in your browser, no sign-up required.

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