Triangle Circumcircle Calculator

Enter the three sides a, b, c of a triangle to find the circumscribed circle radius, diameter, area, plus the triangle area and angles, with a diagram.

Input

Enter the three side lengths a, b, c of a triangle to compute the circumcircle radius, diameter and area along with the triangle area and its angles.

Side a

Side b

Side c

Result

Circumradius R

4.131182

Triangle area

20.333163

Circumcircle diameter

8.262364

Circumcircle circumference

25.956984

Circumcircle area

53.616515

Angles (degrees)

A 46.567463° / B 57.910049° / C 75.522488°

The length unit is shared across all sides, so areas use that unit squared. Angles are shown in degrees.

How it works

The triangle area uses Heron formula S＝√(s(s−a)(s−b)(s−c)) with s＝(a＋b＋c)÷2.
The circumradius is R＝abc÷(4×S), where S is the triangle area.
The circumcircle diameter is 2R, the circumference is 2πR, and the circle area is πR squared.
Each angle comes from the law of cosines. For example, the angle A opposite side a is cos A＝(b²＋c²−a²)÷(2bc).
All three sides must be positive and satisfy the triangle inequality: any two sides must sum to more than the third.
The length unit is shared across the three sides, so areas are expressed in that unit squared.

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