How to use the circumradius and inradius calculator
Knowing the three side lengths of a triangle is enough to find both the radius of its circumcircle and the radius of its incircle. This calculator takes the three sides, works out the area with Heron’s formula and then reports the circumradius R, the inradius r and the type of triangle.
The formulas used are R = abc ÷ 4K and r = K ÷ s, where K is the Heron area and s is the semiperimeter. Dividing by a rounded area would magnify the error, so every step runs on unrounded values and rounding to six decimal places happens only when the numbers are printed.
The sides are checked for validity first. The longest side must be shorter than the sum of the other two; cases such as 1, 2 and 3 collapse to zero area, so no radius is defined and a message appears instead. Comparisons that would otherwise rely on exact equality use a tolerance of 1e-9 to stay safe against floating-point error.
The result also compares the square of the longest side with the sum of the other two squares to say whether the triangle is right, acute or obtuse, and it notes when two sides are equal. The last line prints the gap in Euler’s inequality R ≥ 2r, which holds for every triangle; for an equilateral triangle the gap is 0, confirming R = 2r.
Frequently Asked Questions
With sides a, b and c, Heron’s formula gives the area K, and then the circumradius is R = abc ÷ 4K while the inradius is r = K ÷ s, where s is the semiperimeter (half the perimeter).
If the longest side is longer than or equal to the sum of the other two, no triangle exists. For 1, 2 and 3 the sum 1+2 equals 3, so the shape collapses to a line with zero area and a message is shown instead.
Yes. Euler’s inequality holds for every triangle, with equality R = 2r only for an equilateral triangle. The calculator prints R − 2r so you can see the result checks out.