Enter major radius (R) and minor radius (r), then click Calculate.

A toroid (commonly called a torus) is a three-dimensional shape resembling a doughnut or an inner tube. It is generated by revolving a circle of radius r (minor radius) around an axis coplanar with the circle at a distance R (major radius) from the center of the circle. The volume of a torus is calculated using the formula V = 2π²Rr², where R is the distance from the center of the tube to the center of the torus, and r is the radius of the tube. The surface area is A = 4π²Rr. This shape appears in many real-world applications: magnetic confinement fusion reactors (tokamaks), ring magnets, doughnuts, tires, and in topology and geometry studies. The formula is derived using the Pappus's centroid theorem or by integration in cylindrical coordinates. Understanding torus geometry is essential for mechanical engineering, physics, and advanced mathematics.

1. Enter the Major Radius (R) – distance from the center of the torus to the center of the tube.
2. Enter the Minor Radius (r) – radius of the tube cross-section.
3. Note: For a standard torus, R must be greater than r.
4. Click Calculate to compute the volume and surface area.
5. The result shows volume, surface area, cross-section area, and circumferences.
6. Click Reset to restore default example values.