Triangle Centers Calculator
Calculate a triangle’s centroid, incenter, circumcenter and orthocenter from its vertices. Compare radii and locate the centers on equal-scale axes.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
The centroid averages vertex coordinates. The incenter uses opposite-side lengths as weights. Solve equal-distance equations for the circumcenter. The orthocenter followsH=A+B+C−2O.
G=(A+B+C)/3; I=(aA+bB+cC)/(a+b+c); H=A+B+C−2O
Worked example
ForA=(0,0), B=(6,0), C=(0,8), centroid=(2,8/3), incenter=(2,2), circumcenter=(3,4), and orthocenter=(0,0). Circumradius=5 and inradius=2.
Assumptions and input details
Coordinate inputs accept fractions or decimals up to six places, with magnitude≤1e6 and reduced denominator≤1e6. All coordinates share one abstract coordinate unit. Classification can be exact while displayed coordinates and diagrams are approximate. Vertices must be noncollinear. Triangles with area/max-side²<1e−10 are rejected as numerically too flat. G,I,O,H label the four centers; coincident or visually close markers share a label. O andH may lie outside an obtuse triangle.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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