List of centroids


The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of. For an object of uniform composition, the centroid of a body is also its center of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines.

2-D Centroids

For each two-dimensional shape below, the area and the centroid coordinates are given:
ShapeFigureArea
rectangle area
General triangular area
Isosceles-triangular area
Right-triangular area
Circular area
Quarter-circular area
Semicircular area
Circular sector
Circular segment
Quarter-circular arcThe points on the circle and in the first quadrant
Semicircular arcThe points on the circle and above the axis
Arc of circleThe points on the curve , from to
elliptical area
Quarter-elliptical area
Semielliptical area
Parabolic areaThe area between the curve and the line
Semiparabolic area
The area between the curve and the axis, from to
Parabolic spandrelThe area between the curve and the axis, from to
General spandrelThe area between the curve and the axis, from to

3-D Centroids

For each three-dimensional body below, the volume and the centroid coordinates, are given:
ShapeFigureVolume
Cuboida, b = the sides of the cuboid's base
c = the third side of the cuboid
Right-rectangular pyramida, b = the sides of the base
h = the distance is from base to the apex
General triangular prismb = the base side of the prism's triangular base,
h = the height of the prism's triangular base
L = the length of the prism		see above
for general
triangular base
Isoscele triangular prismb = the base side of the prism's triangular base,
h = the height of the prism's triangular base
L = the length of the prism
Right-triangular prismb = the base side of the prism's triangular base,
h = the perpendicular side of the prism's triangular base
L = the length of the prism
Right circular cylinderr = the radius of the cylinder
h = the height of the cylinder
Right circular solid coner = the radius of the cone's base
h = the distance is from base to the apex
Solid spherer = the radius of the sphere
Solid hemispherer = the radius of the hemisphere
Solid semi-ellipsoid of revolution around z-axea = the radius of the base circle
h = the height of the semi-ellipsoid from the base cicle's center to the edge
Solid paraboloid of revolution around z-axea = the radius of the base circle
h = the height of the paboloid from the base cicle's center to the edge
Solid ellipsoida, b, c = the principal semi-axes of the ellipsoid
Solid semi-ellipsoid around z-axea, b = the principal semi-axes of the base ellipse
c = the principal z-semi-axe from the center of base ellipse
Solid paraboloid around z-axea, b = the principal semi-axes of the base ellipse
c = the principal z-semi-axe from the center of base ellipse