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.