How does the Circumscribed Circle work?

R = (a × b × c) / (4 × Area) Then: Where Area = √(s(s−a)(s−b)(s−c)) by Heron's formula Then: s = (a + b + c) / 2 (semi-perimeter) Then: For a right triangle: R = hypotenuse / 2.

Can you give an example of how to use the Circumscribed Circle?

Example: Input Triangle with sides 3, 4, 5 gives a result of R = (3×4×5)/(4×6) = 2.5.

Is the Circumscribed Circle free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Circumscribed Circle?

Our Circumscribed Circle uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Circumscribed Circle

Circumscribed Circle (Circumradius)

Side a

Side b

Side c

The circumscribed circle (circumcircle) of a triangle is the unique circle passing through all three vertices. The circumradius R is the radius of this circle.

Symbol	Name	Unit	Description
a, b, c	triangle side lengths	length	—
K	triangle area	length²	—
R	circumradius	length	—

Sides	Area	Circumradius R
3,4,5	6	2.50
5,5,6	12	3.13
6,6,6	15.59	3.46
5,12,13	30	6.50

References

›Circumscribed circle — Wolfram MathWorld

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Circumscribed Circle

Circumscribed Circle (Circumradius)

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Circumscribed Circle (Circumradius)