A toroid is specified by the radius of revolution
R measured from the center of the section rotated. For symmetrical sections volume and surface of the body may be computed (with circumference
C and area
A of the section):
Square toroid The volume (V) and surface area (S) of a toroid are given by the following equations, where A is the area of the square section of side, and R is the radius of revolution. :V = 2 \pi R A :S = 2 \pi R C
Circular toroid The volume (V) and surface area (S) of a toroid are given by the following equations, where r is the radius of the circular section, and R is the radius of the overall shape. :V = 2 \pi^2 r^2 R :S = 4 \pi^2 r R
Pappus's centroid theorem generalizes the formulas here to arbitrary surfaces of revolution. == See also ==