The following diagrams depict a list of centroids. A centroid of an object X in n-dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X. For an object of uniform composition (mass, density, etc.) the centroid of a body is also its centre of mass.

Shape Figure Area

Triangular area

Quarter-circular area

Semicircular area

Quarter-elliptical area

Semielliptical area

Semiparabolic area The area between the curve and the

axis, from to

Parabolic area The area between the curve and the line

Parabolic spandrel The area between the curve and the

axis, from to

General spandrel The area between the curve and the

axis, from to

Circular sector

The area between the curve (in polar coordinates) and the pole, from to

Circular segment

Quarter-circular arc

The points on the circle and in the first quadrant

Semicircular arc

The points on the circle and above the axis

Arc of circle

The points on the curve (in polar coordinates) , from to