Hole Radius of Torus Calculator

Formula Used:

\[ \text{Hole Radius of Torus} = \text{Radius of Torus} - \text{Radius of Circular Section of Torus} \] \[ r_{\text{Hole}} = r - r_{\text{Circular Section}} \]

Hole Radius of Torus:

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1. What is the Hole Radius of Torus?

The Hole Radius of Torus is the shortest line connecting the center of the Torus to the nearest point on the circumference of the circular cross-section of the Torus. It represents the distance from the center of the torus to the inner edge of its circular cross-section.

2. How Does the Calculator Work?

The calculator uses the simple formula:

\[ r_{\text{Hole}} = r - r_{\text{Circular Section}} \]

Where:

\( r_{\text{Hole}} \) — Hole Radius of Torus (m)
\( r \) — Radius of Torus (m)
\( r_{\text{Circular Section}} \) — Radius of Circular Section of Torus (m)

Explanation: The hole radius is simply the difference between the overall torus radius and the radius of its circular cross-section.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius is essential in geometry and engineering applications involving toroidal shapes, such as designing donut-shaped objects, toroidal transformers, or architectural elements with torus geometry.

4. Using the Calculator

Tips: Enter both radius values in meters. Ensure that the Radius of Circular Section is smaller than the Radius of Torus to get a valid positive hole radius. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a three-dimensional geometric shape that resembles a donut or an inner tube. It's a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: Can the hole radius be negative?
A: No, the hole radius cannot be negative. If the circular section radius is larger than the torus radius, it would indicate an invalid geometric configuration.

Q3: What are the units for these measurements?
A: The calculator uses meters, but the same formula applies to any consistent unit system (cm, mm, inches, etc.).

Q4: How is this different from the major and minor radius?
A: The Radius of Torus is the major radius (distance from center to tube center), while the Radius of Circular Section is the minor radius (tube radius). The hole radius is the distance from the center to the inner edge of the tube.

Q5: Where is this calculation used in real life?
A: This calculation is used in manufacturing (donut-shaped products), architecture (torus-shaped structures), physics (toroidal magnetic fields), and engineering (toroidal pressure vessels).