What is the incenter of a triangle?

The incenter is the point where the three angle bisectors of a triangle meet. It is equidistant from all three sides and serves as the center of the inscribed circle (incircle).

What is the inradius?

The inradius (r) is the radius of the largest circle that fits inside the triangle, touching all three sides. It equals the triangle area divided by its semi-perimeter.

What if the three points are collinear?

Collinear points form a degenerate triangle with zero area, making the inradius zero. The calculator will display an error in that case.

Does the incenter always lie inside the triangle?

Yes. Unlike the circumcenter or orthocenter, the incenter always lies strictly inside the triangle regardless of whether the triangle is acute, right, or obtuse.

How is the incenter different from the centroid?

The centroid is the average of the three vertices (equal weights) and is the center of mass. The incenter is a weighted average where each vertex is weighted by the length of the opposite side.

Triangle Incenter Calculator

Name: Triangle Incenter Calculator
Availability: InStock
Author: Nham Vu

Enter the coordinates of three vertices to find the triangle incenter and the radius of its inscribed circle.

Vertex Coordinates

Vertex A

Vertex B

Vertex C

Results

Enter vertex coordinates and click Calculate.

Summary

Enter the coordinates of three vertices to find the triangle incenter and the radius of its inscribed circle.

How it works

Enter the x and y coordinates of all three vertices (A, B, C).
The calculator computes the side lengths a, b, and c opposite each vertex.
The incenter is the weighted average of the vertices by opposite side length: I = (a·A + b·B + c·C) / (a+b+c).
The inradius r = Area / s, where s is the semi-perimeter and Area is computed via the cross product formula.
Results display the incenter coordinates and the inradius rounded to 6 decimal places.

Use cases

Determine where to place the center of an inscribed circle in a triangular region.
Verify hand calculations for geometry homework or exams.
Find the incenter in computer graphics or game development for triangle meshes.
Compute the inradius for structural or architectural designs involving triangular panels.
Cross-check results from a triangle circumcenter or centroid calculator.

Frequently Asked Questions

Last updated: 2026-07-04 · Reviewed by Nham Vu