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 found in physics, engineering, and architecture.

2. How Does the Calculator Work?

The calculator uses the torus volume formula:

Where:

• \( R \) — Major radius (distance from center of tube to center of torus)
• \( r \) — Minor radius (radius of the tube)
• \( V \) — Volume of the torus

Explanation: The formula accounts for the circular cross-section being rotated around the central axis, with the major radius determining the size of the "hole" in the middle.

3. Importance of Torus Volume Calculation

Details: Calculating torus volume is important in various engineering applications, including pipe design, architectural structures, and in physics for modeling magnetic fields in tokamaks.

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 cubic units of whatever length unit you used.

5. Frequently Asked Questions (FAQ)

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

Q2: Can this formula be used for partial toruses?
A: No, this formula calculates the volume of a complete torus. Partial toruses require more complex calculations.

Q3: What if my torus isn't perfectly circular?
A: This formula assumes perfect circular symmetry. For non-circular tori, numerical methods may be needed.

Q4: How does this relate to surface area?
A: The surface area of a torus is given by \( A = 4\pi^2 R r \), which is different from the volume formula.

Q5: What are real-world examples of tori?
A: Common examples include inner tubes, doughnuts, lifebuoys, and the shape of some nuclear fusion reactors.