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    <p>The center of gravity (also known as "center of mass" or "centroid" can be calculated with the following formula:</p> <pre><code>X = SUM[(Xi + Xi+1) * (Xi * Yi+1 - Xi+1 * Yi)] / 6 / A Y = SUM[(Yi + Yi+1) * (Xi * Yi+1 - Xi+1 * Yi)] / 6 / A </code></pre> <p>Extracted from <a href="http://en.wikipedia.org/wiki/Centroid" rel="noreferrer">Wikipedia</a>: The centroid of a non-self-intersecting closed polygon defined by n vertices (x0,y0), (x1,y1), ..., (xn−1,yn−1) is the point (Cx, Cy), where<br> <img src="https://i.stack.imgur.com/qUUMG.png" alt="X coordinate of the center"><br> <img src="https://i.stack.imgur.com/VJM7O.png" alt="Y coordinate of the center"><br> and where A is the polygon's signed area,<br> <img src="https://i.stack.imgur.com/STuAL.png" alt="Area formula"></p> <p>Example using VBasic:</p> <pre><code>' Find the polygon's centroid. Public Sub FindCentroid(ByRef X As Single, ByRef Y As _ Single) Dim pt As Integer Dim second_factor As Single Dim polygon_area As Single ' Add the first point at the end of the array. ReDim Preserve m_Points(1 To m_NumPoints + 1) m_Points(m_NumPoints + 1) = m_Points(1) ' Find the centroid. X = 0 Y = 0 For pt = 1 To m_NumPoints second_factor = _ m_Points(pt).X * m_Points(pt + 1).Y - _ m_Points(pt + 1).X * m_Points(pt).Y X = X + (m_Points(pt).X + m_Points(pt + 1).X) * _ second_factor Y = Y + (m_Points(pt).Y + m_Points(pt + 1).Y) * _ second_factor Next pt ' Divide by 6 times the polygon's area. polygon_area = PolygonArea X = X / 6 / polygon_area Y = Y / 6 / polygon_area ' If the values are negative, the polygon is ' oriented counterclockwise. Reverse the signs. If X &lt; 0 Then X = -X Y = -Y End If End Sub </code></pre> <p>For more info check this <a href="http://paulbourke.net/geometry/polyarea/" rel="noreferrer">website</a> or <a href="http://en.wikipedia.org/wiki/Centroid" rel="noreferrer">Wikipedia</a>.</p> <p>Hope it helps.</p> <p>Regards!</p>
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    1. COwho said Green formula was useless for computer science :)
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    2. CODude thanks for the reply but thats the website that I was looking at! The link is in the original post :) I need a formula that will work for self intersecting polygons!!!
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    3. CO@mixkat For a intersecting polygon you have to use the _integral formula_ as described in the wikipedia article. Or decompose the polygon into non-intersecting polygons and use the method described above.
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