Torus Radius Calculator

Torus Minor Radius Formula:

\[ r = \sqrt{\frac{V}{2 \pi^2 R}} \]

Minor Radius (r):

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1. What is the Torus Radius Formula?

The torus radius formula calculates the minor radius (r) of a torus given its volume (V) and major radius (R). A torus is a doughnut-shaped surface of revolution generated by revolving a circle in 3D space.

2. How Does the Calculator Work?

The calculator uses the torus minor radius formula:

\[ r = \sqrt{\frac{V}{2 \pi^2 R}} \]

Where:

\( V \) — Volume of the torus
\( R \) — Major radius (distance from center of tube to center of torus)
\( r \) — Minor radius (radius of the tube)
\( \pi \) — Mathematical constant Pi (~3.14159)

Explanation: The formula derives from the volume formula of a torus solved for the minor radius.

3. Importance of Torus Calculations

Details: Torus calculations are important in various fields including physics, engineering, and architecture where toroidal shapes are used.

4. Using the Calculator

Tips: Enter volume in cubic units and major radius in linear units. Both values must be positive numbers.

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 tube to the center of the torus, while the minor radius (r) is the radius of the tube itself.

Q2: What are typical applications of torus calculations?
A: Used in designing donut-shaped objects, tokamak reactors in nuclear fusion, some types of pipes, and various architectural elements.

Q3: Can this formula be used for partial tori?
A: No, this formula applies only to complete, circular tori. Partial tori require more complex calculations.

Q4: What units should I use?
A: Use consistent units - if volume is in m³, radius should be in m, and the result will be in m.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for an ideal torus geometry.