Triangle Circumradius Calculator

How it is calculated

Enter the three side lengths in any one unit. The tool first computes the semi-perimeter s = (a + b + c) ÷ 2, then the area with Heron's formula Area = √(s(s − a)(s − b)(s − c)), and finally R = a × b × c ÷ (4 × Area). R is shown with four decimals in the same length unit as the sides, and the area with two decimals in squared units (the output is labelled generic 'units'). All sides must be above zero and must satisfy the triangle inequality: each pair of sides must add up to strictly more than the third. If one side equals the sum of the other two the triangle is flat, and the tool returns no result.

Common mistakes

• Entering sides that do not form a triangle, such as 3, 4 and 7, where 3 + 4 equals 7; the tool returns no result for these.
• Mixing units between sides, for example one side in metres and another in centimetres.
• Confusing the circumradius with the inradius; the circumscribed circle passes through the three vertices and is always at least as large as the inscribed circle.
• Expecting the circumcentre to lie inside the triangle; in an obtuse triangle it lies outside, though R is still correct.
• Entering sides rounded too coarsely for a thin triangle; when the triangle is nearly flat the area is tiny and R changes a lot with small errors in the sides.