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Parallelogram Circumradius Calculator

Calculates the circumscribed circle of a parallelogram from two sides and the included angle.

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Result

Circumradius (R)

5.4467

Working

R = √(a²+b²) / (2·sinθ) = √(25+64) / (2·sin60°) = 5.4467

Notes

  • · R = √(a²+b²) / (2 × sinθ), where θ is the angle between sides a and b.

Parallelogram Circumradius Calculator — How It Works

Parallelogram 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 Parallelogram Circumradius Calculator calculates this for a parallelogram from two sides and the included angle. Try the Parallelogram Circumradius Calculator — instant results, no sign-up.

The formula

R = √(a²+b²) / (2 × sinθ)

Example

For a parallelogram with two sides and the included angle = 5, 8, and 60°:

R ≈ 5.4467

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

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