Triangle inradius and circumradius calculator
Enter the three sides of a triangle to find the largest circle that fits inside it and the circle that passes through its corners.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter side a, side b, side c and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Inradius r = area ÷ s and circumradius R = (a × b × c) ÷ (4 × area), with the area from Heron's formula and s the semi-perimeter.
Example
Inputs: Side a = 13, Side b = 14, Side c = 15, Length unit = Centimeters (cm). Result: Inradius: 4 cm; Circumradius: 8.125 cm; Incircle area: 50.2655 cm².
Limits and caveats
- In an obtuse triangle the circumcenter lies outside the triangle; the radius is still correct.
- The unit choice only labels the results.
Questions about this tool
What is the incircle of a triangle?
The largest circle that touches all three sides from inside. Its center is where the angle bisectors meet.
What is the circumcircle of a triangle?
The circle through all three vertices. Its center is where the perpendicular bisectors of the sides meet.
What is the circumradius of a right triangle?
Exactly half the hypotenuse. The 3, 4, 5 triangle has a circumradius of 2.5.