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, or in other words, has the same density at all points, 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.
For each two-dimensional shape below, the area and the centroid coordinates are given:
Shape | Figure | Area | ||
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rectangle area | ![]() |
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General triangular area | ![]() |
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Isosceles-triangular area | ![]() |
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Right-triangular area | ![]() |
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Circular area | ![]() |
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Quarter-circular area[2] | ![]() |
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Semicircular area[3] | ![]() |
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Circular sector | ![]() |
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Circular segment | ![]() |
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Annular sector | ![]() |
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Quarter-circular arc | The points on the circle |
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Semicircular arc | The points on the circle |
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Arcofcircle | The points on the curve (in polar coordinates) |
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elliptical area | ![]() |
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Quarter-elliptical area | ![]() |
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Semielliptical area | ![]() |
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Parabolic area | The area between the curve |
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Semiparabolic area
The area between the curve |
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Parabolic spandrel | The area between the curve |
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General spandrel | The area between the curve |
For each three-dimensional body below, the volume and the centroid coordinates are given:
Shape | Figure | Volume | |||
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Cuboid | a, b = the sides of the cuboid's base c = the third side of the cuboid |
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Right-rectangular pyramid | a, b = the sides of the base h = the distance is from base to the apex |
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General triangular prism | b = 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 |
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Isosceles triangular prism | b = the base side of the prism's triangular base, h = the height of the prism's triangular base L = the length of the prism |
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Right-triangular prism | b = 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 |
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Right circular cylinder | r = the radius of the cylinder h = the height of the cylinder |
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Right circular solid cone | r = the radius of the cone's base h = the distance is from base to the apex |
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Solid sphere | r = the radius of the sphere | ||||
Solid hemisphere | r = the radius of the hemisphere | ||||
Solid semi-ellipsoid of revolution around z-axis | a = the radius of the base circle h = the height of the semi-ellipsoid from the base cicle's center to the edge |
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Solid paraboloid of revolution around z-axis | a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge |
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Solid ellipsoid | a, b, c = the principal semi-axes of the ellipsoid | ||||
Solid semi-ellipsoid around z-axis | a, b = the principal semi-axes of the base ellipse c = the principal z-semi-axe from the center of base ellipse |
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Solid paraboloid around z-axis | a, b = the principal semi-axes of the base ellipse c = the principal z-semi-axe from the center of base ellipse |