Centroid
Of An Area 


The
centroid of an area is similar to the center of mass of a body.
Calculating the centroid involves only the geometrical shape of the area.
The center of gravity will equal the centroid if the body is homogenous
i.e. constant density. Integration formulas for calculating the Centroid
are: 



When
calculating the centroid of a complex shape. Divide the shape up into a
combination of known shapes. Then use the the following formula: 



The
centroid location of many common shapes is known. The Properties of Areas
page includes the Centroid Location, Area, Area Moments of Inertia, Area
Polar Moments of Inertia, & Area Radius of Gyration for many common
shapes. 
Center
of Mass 





The Center of Mass
(center of gravity) of a solid is similar to the Centroid of Solid.
However, calculating the centroid involves only the geometrical shape of
the solid. The center of
gravity will equal to the centroid if the body is homogenous i.e. constant
density. Integration formulas
for calculating the Center of Mass are:




Composite
Solids 





When calculating the
centroid of a complex shape. Divide the shape up into a combination of
known shapes. Then use the the following formula:


Centroid
of Solids 





The centroid of a
solid is similar to the center of mass. However, calculating the centroid
involves only the geometrical shape of the solid. The center of
gravity will equal the centroid if the body is homogenous i.e. constant
density. Integration formulas
for calculating the Centroid are:
