# Thread: Calculate center of a triangle (XL 2003)

1. ## Calculate center of a triangle (XL 2003)

This is more of a geometry question, but I'm not sure where to ask. I'm trying to calculate the coordinates in Excel for the center of a triangle, the orthocenter I believe.

Is there a formula already in Excel to return the x, y coordinates of the center when given the x, y coordinates of the three vertices?

2. ## Re: Calculate center of a triangle (XL 2003)

It depends on what exactly you mean by the "center" of the triangle. There are several points that could be called the center:
<UL><LI>The intersection of the medians, i.e. the lines from a vertex to the midpoint of the opposite side. This intersection is called the centroid, and it is also the triangle's center of gravity: if you cut a triangle out of a material of uniform density and rest the triangle on a pin at the centroid, it'll be in balance.
<LI>The intersection of the altitudes, i.e. the lines from a vertex perpendicular to the opposite side. This is called the orthocenter.
<LI>The intersection of the angle bisectors.
<LI>The center of the circle passing through the three vertices, the circumcenter.[/list]See Triangle - wikipedia entry.

The centroid is the easiest to calculate: the x-coordinate is the average of the x-coordinates of the vertices and the y-coordinate is the average of the y-coordinates of the vertices.
So with the vertices in A1:B1, A2:B2 and A3:B3, the centroid is given by =AVERAGE(A1:A3) and =AVERAGE(B1:B3)

3. ## Re: Calculate center of a triangle (XL 2003)

Here is a spreadsheet to get the "OrthoCenter"

Steve

4. ## Re: Calculate center of a triangle (XL 2003)

Thanks all - these will get me started!

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