Torus Calculator

Torus Volume and Surface Area Calculator

Calculate the volume and surface area of a torus (donut shape). Perfect for engineering, architectural design, and mathematical applications.

A torus is a three-dimensional shape formed by rotating a circle around an axis. This calculator helps you determine its volume and surface area based on the major and minor radii.

Formula

Volume = 2π²Rr²
Surface Area = 4π²Rr

Where:

  • R:major radius (distance from center to tube center)
  • r:minor radius (radius of the tube)

Understanding the Torus

A torus is created by rotating a circle around an axis that lies in the same plane as the circle. The major radius (R) must be greater than the minor radius (r) to create a proper torus.

Applications

Tori appear in architecture, engineering (like O-rings and bearings), magnetic fields in fusion reactors, and even in molecular structures.

Frequently Asked Questions

What determines a torus's shape?

The shape of a torus is determined by its major radius (R) and minor radius (r). The ratio R/r affects how "fat" or "thin" the torus appears.

Where are tori used in real life?

Tori are found in many practical applications: O-rings, tire inner tubes, pool floats, and architectural features like curved arches and domes.