Circumscribed Circle Calculator

Circumscribed Circle Calculator

Find the circumcircle of a triangle from its three side lengths.

Last updated: June 2026 | By Patchworkr Team

Triangle Side Lengths
Circumradius
-
Enter three valid side lengths
Circle Area
-
Circumference
-
Triangle Area
-

Enter a real number.

Formulas

Heron’s Formula
A = √[s(s-a)(s-b)(s-c)]
Circumradius
R = abc / (4A)

How to Use

Enter the three side lengths of a valid triangle. The calculator checks positivity and triangle inequality before computing the circumcircle.

  1. Enter side lengths a, b, and c.
  2. Verify the sides can form a triangle.
  3. Read the circumradius, circumference, and circle area from the result card.

Example

For a 3-4-5 triangle, Heron’s formula gives area 6, so the circumradius is 2.5.

The associated circumcircle has circumference 15.707963 and area 19.634954.

Notes

The calculator rejects impossible triangles instead of returning NaN or a negative circumradius.

Side lengths are treated as real numbers, so blank strings and malformed tokens are rejected before any geometry is performed.

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