Hole Radius of Torus given Radius and Total Surface Area Calculator

Formula Used:

\[ \text{Hole Radius of Torus} = \text{Radius of Torus} - \left( \frac{\text{Total Surface Area of Torus}}{4 \times \pi^2 \times \text{Radius of Torus}} \right) \] \[ r_{\text{Hole}} = r - \left( \frac{TSA}{4 \times \pi^2 \times r} \right) \]

Hole Radius of Torus:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 inner radius of the toroidal shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{\text{Hole}} = r - \left( \frac{TSA}{4 \times \pi^2 \times r} \right) \]

Where:

\( r_{\text{Hole}} \) — Hole Radius of Torus (m)
\( r \) — Radius of Torus (m)
\( TSA \) — Total Surface Area of Torus (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the hole radius by subtracting the ratio of total surface area to the product of 4, π squared, and the radius from the radius itself.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius is essential in geometry and engineering applications involving toroidal shapes, such as in the design of rings, donuts, and certain mechanical components.

4. Using the Calculator

Tips: Enter the radius of the torus in meters and the total surface area in square meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a three-dimensional shape resembling a donut or ring, formed by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: How is the hole radius different from the radius of torus?
A: The radius of torus is the distance from the center of the torus to the center of the tube, while the hole radius is the distance from the center to the inner edge of the tube.

Q3: What are typical applications of torus geometry?
A: Torus geometry is used in various fields including architecture, engineering, physics (particularly in magnetic confinement fusion devices like tokamaks), and mathematics.

Q4: Can this formula be used for any torus?
A: This formula applies to standard circular tori where the cross-section is circular and the torus is symmetric.

Q5: What units should I use for the inputs?
A: The calculator uses meters for length and square meters for area, but you can use any consistent unit system as long as you maintain consistency.