Triangle incircle and circumcircle calculator
Useful for plane geometry problems and design work when you need a circle touching the sides of a triangle or passing through its corners.
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How to use it
- Enter side a, side b and side c.
- 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
Area S by Heron and s the semi-perimeter. Inradius r = S / s, and circumradius R = abc / (4S).
Example
Inputs: Side a = 3, Side b = 4, Side c = 5. Result: Inradius r: 1; Circumradius R: 2.5; Triangle area: 6.
Limits and caveats
- Use one length unit; both radii come out in that same unit.
Questions about this tool
Where is the centre of the incircle?
Where the three angle bisectors meet. The circle touches every side.
Where is the centre of the circumcircle?
Where the perpendicular bisectors of the sides meet. In a right triangle it sits at the midpoint of the hypotenuse.
Why is R half the hypotenuse in a right triangle?
A right angle stands on a diameter of its circumcircle, so the hypotenuse is a full diameter.