Skip to content

Trapezoid Circumradius Calculator

Calculates the circumscribed circle of an isosceles trapezoid from its parallel sides and height.

0 views

Result

Circumradius (R)

5

Working

Leg = √(h² + ((a−b)/2)²) = 4.4721; R = leg·(a+b)·√(ab+leg²) / (4·Area) = 5

Notes

  • · Leg = √(h² + ((a−b)/2)²), Area = (a+b)/2 × h, and R = leg × (a+b) × √(ab+leg²) / (4 × Area).

Trapezoid Circumradius Calculator — How It Works

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 ≈ 5

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

Read on the blog →