Trapezoid Circumradius Calculator — How It Works
Trapezoid Circumradius Calculator circumradius geometry calculator
Trapezoid 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 Trapezoid Circumradius Calculator calculates this for a isosceles trapezoid from the two parallel sides and the height. Try the Trapezoid Circumradius Calculator — instant results, no sign-up.
The formula
R = leg × (a+b) × √(ab+leg²) / (4 × Area), where leg = √(h² + ((a−b)/2)²)Example
For a isosceles trapezoid with the two parallel sides and the height = 10, 6, and 4:
R ≈ 5A 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 Trapezoid Circumradius Calculator runs entirely in your browser, no sign-up required.