Calculators
Triangle Incenter Calculator
Find a triangle’s incenter and incircle radius from three Cartesian vertices, privately in your browser.
Find the center of a triangle’s inscribed circle.
Let a = |BC|, b = |CA|, and c = |AB|. The incenter is I = (aA + bB + cC)/(a+b+c), applied separately to each coordinate. The inradius is twice the triangle area divided by its perimeter. For A = (0, 0), B = (6, 0), C = (0, 9), the incenter is approximately (2.0916730868, 2.0916730868) and the inradius is 2.0916730868 units. This point is where the internal angle bisectors meet and is equidistant from the three sides. Use consistent units on a flat Cartesian plane, not latitude and longitude. Signed decimals and scientific notation are accepted; coordinate magnitudes must be zero or 1e-100 to 1e100. Repeated vertices and triangles whose doubled area is at most 1e-12 times the longest side squared are rejected. Browser floating-point arithmetic can lose small differences between large coordinates. Results display up to 12 significant digits. Inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is the incenter calculated?
Weight each vertex by the length of its opposite side and divide the weighted coordinate sums by the perimeter.
How is the inradius calculated?
Divide twice the triangle area by its perimeter. The radius uses the same length unit as the coordinates.
Is the incenter the same as the centroid?
The incenter is the intersection of internal angle bisectors. The centroid is the intersection of medians. They coincide for an equilateral triangle but generally differ.
Why are some vertices rejected?
Repeated and collinear vertices do not define a triangle with an incircle. Nearly collinear triangles are rejected to avoid unreliable floating-point results.
Are coordinates uploaded?
No. Calculations run locally in your browser.