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Square Circumradius Calculator — How It Works

Square Circumradius Calculator circumradius geometry calculator

Square 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 Square Circumradius Calculator calculates this for a square from side length. Try the Square Circumradius Calculator — instant results, no sign-up.

The formula

R = side × √2 / 2

Example

For a square with side length = 4:

R ≈ 2.8284

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