1. What is a Torus?

A torus is a doughnut-shaped surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. It's commonly seen in objects like inner tubes, rings, and some types of piping.

2. How Does the Calculator Work?

The calculator uses the torus surface area formula:

Where:

• \( R \) — Major radius (distance from center of tube to center of torus)
• \( r \) — Minor radius (radius of the tube)
• \( A \) — Surface area of the torus

Explanation: The formula calculates the surface area by multiplying the circumference of the torus (2πR) by the circumference of the tube (2πr), resulting in 4π²Rr.

3. Importance of Torus Calculations

Details: Calculating torus surface area is important in engineering, architecture, and manufacturing where toroidal shapes are used in components like pipes, gaskets, and structural elements.

4. Using the Calculator

Tips: Enter both radii in consistent units (e.g., meters, inches). Both values must be positive numbers. The result will be in square units of whatever unit you used for input.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between major and minor radius?
A: The major radius (R) is the distance from the center of the torus to the center of the tube. The minor radius (r) is the radius of the tube itself.

Q2: Can this calculate the volume of a torus?
A: No, this calculator only computes surface area. The volume formula is V = 2π²Rr².

Q3: What are real-world applications of torus calculations?
A: Used in designing pipes, tires, nuclear fusion reactors (tokamaks), and various mechanical components.

Q4: Does this work for elliptical or non-circular tori?
A: No, this formula is specifically for circular tori where both the tube and path are perfect circles.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric tori. Real-world objects may have slight variations.