The circle as base element.

General case

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Segments in the general case

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The radius of the circle  

Perimeters in the general case

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Perimeter of base circle 

Areas in the general case

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Area of the base circle  

Centroids in the general case

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Centroid positions are measured from the lower left point of the surrounding square.
Centroid positions of the base circle:  

Normalised case

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In the normalised case the area of the base circle is set to 1.
So  

Segments in the normalised case

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Segment of the base circle  

Perimeters in the normalised case

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Perimeter of base circle 

Areas in the normalised case

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Area of the base circle is by definition  

Centroids in the normalised case

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Centroid positions of the base circle: