1. What is the Radius of Torus Formula?

The formula calculates the radius of a torus given its total surface area and the radius of its circular cross-section. This geometric relationship helps determine the overall size of a torus based on its surface properties.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of Torus (m)
• \( TSA \) — Total Surface Area of Torus (m²)
• \( \pi \) — Archimedes' constant (≈3.14159)
• \( r_{\text{Circular Section}} \) — Radius of Circular Section of Torus (m)

Explanation: The formula derives from the geometric relationship between the torus's total surface area and its cross-sectional properties.

3. Importance of Torus Radius Calculation

Details: Calculating the radius of a torus is essential in various engineering and mathematical applications, including mechanical design, architecture, and 3D modeling where toroidal shapes are used.

4. Using the Calculator

Tips: Enter total surface area in square meters and radius of circular section in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: What are the units for the inputs and outputs?
A: The calculator uses meters for length measurements and square meters for area measurements. Ensure consistent units for accurate results.

Q3: Can this formula be used for partial torus surfaces?
A: No, this formula specifically calculates the radius for a complete torus with known total surface area.

Q4: What if I have the volume instead of surface area?
A: A different formula would be needed as this calculator specifically uses surface area to calculate the radius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of a perfect torus, assuming precise input values.