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Rhombus Circumradius Calculator

Calculates the circumscribed circle of a rhombus from its two diagonals.

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Result

Circumradius (R)

3.6828

Working

Side = √(d₁²+d₂²)/2 = 5; R = √2·side³ / (2·Area) = 3.6828

Notes

  • · Side = √(d₁²+d₂²)/2, Area = d₁·d₂/2, and R = √2 × side³ / (2 × Area).

Rhombus Circumradius Calculator — How It Works

Rhombus 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 Rhombus Circumradius Calculator calculates this for a rhombus from two diagonals. Try the Rhombus Circumradius Calculator — instant results, no sign-up.

The formula

R = √2 × side³ / (2 × Area), where side = √(d₁²+d₂²)/2 and Area = d₁·d₂/2

Example

For a rhombus with two diagonals = 6 and 8:

R ≈ 3.6828

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

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