Total Surface Area Of Torus Given Radius And Hole Radius Calculator

Total Surface Area of Torus Formula:

\[ TSA = 4\pi^2 r (r - r_{Hole}) \]

Total Surface Area of Torus (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Total Surface Area of Torus?

The Total Surface Area of a Torus is the complete area covering both the outer and inner surfaces of the toroidal shape. A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

2. How Does the Calculator Work?

The calculator uses the torus surface area formula:

\[ TSA = 4\pi^2 r (r - r_{Hole}) \]

Where:

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

Explanation: The formula calculates the surface area by considering the major radius (distance from center to tube center) and minor radius (tube radius) of the torus.

3. Importance of Torus Surface Area Calculation

Details: Calculating the surface area of a torus is important in various engineering applications, architectural design, manufacturing processes, and mathematical modeling where toroidal shapes are used.

4. Using the Calculator

Tips: Enter the radius of torus and hole radius in meters. Both values must be positive numbers, and the hole radius must be smaller than the torus radius for a valid torus shape.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a doughnut-shaped surface generated by rotating a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What's the difference between radius and hole radius?
A: The radius is the distance from the center of the torus to the center of the tube, while the hole radius is the radius of the circular cross-section of the tube.

Q3: Can the hole radius be zero?
A: Mathematically yes, but practically a torus with zero hole radius would be a sphere. The formula remains valid.

Q4: What are real-world applications of torus calculations?
A: Torus calculations are used in designing tires, doughnuts, life preservers, nuclear fusion reactors (tokamaks), and various mechanical components.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect torus shape. The accuracy depends on the precision of input values and the implementation of the mathematical constant π.