Maths & numbers

Triangle centres from coordinates

Plot the centroid, incentre, circumcentre, orthocentre and nine-point centre.

Triangle centres from coordinates
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Use exact X,Y headings, without repeating the first point unless closing a polygon.

Up to 25 MB per file, 50,000 data rows, 200 columns and 2 million data cells. Fully blank rows and columns are ignored before row, column and cell limits are checked. Individual tools may have smaller result or chart limits.

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A clear answer. Here’s how.

Requires exactly three non-collinear two-dimensional vertices. Uses side-length barycentric weights for the incentre, perpendicular-bisector equations for the circumcentre, the vector identity H=A+B+C−2O for the orthocentre, and (O+H)/2 for the nine-point centre. Reports area, inradius and circumradius. Degenerate or extremely narrow triangles are rejected at a scale-relative tolerance.

See a worked example

Worked example

A fixed demonstration, separate from the values you enter above.

Point CSV
X,Y
0,0
4,0
0,3

Example result

Example result
CentreXY
Centroid1.333333333331
Incentre11
Circumcentre21.5
Orthocentre00
Nine-point centre10.75

Triangle area 6; inradius 1; circumradius 2.5. All coordinates use the input unit.

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