1. What is the Radius of Toroid Formula?

The formula calculates the radius of a toroid given its volume and cross-sectional area. A toroid is a doughnut-shaped solid generated by revolving a circle around an axis external to the circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of Toroid (m)
• \( V \) — Volume of Toroid (m³)
• \( A_{\text{Cross Section}} \) — Cross Sectional Area of Toroid (m²)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives from the geometric relationship between a toroid's volume, cross-sectional area, and its major radius.

3. Importance of Toroid Radius Calculation

Details: Calculating the radius of a toroid is essential in various engineering and physics applications, particularly in electromagnetism where toroidal coils are used in transformers and inductors.

4. Using the Calculator

Tips: Enter volume in cubic meters (m³) and cross-sectional area in square meters (m²). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a toroid?
A: A toroid is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What units should I use for input values?
A: The calculator expects volume in cubic meters and area in square meters for consistent results.

Q3: Can this formula be used for any toroid shape?
A: This formula applies specifically to toroids with circular cross-sections. For other cross-sectional shapes, different formulas may be required.

Q4: What if I have the minor radius instead of cross-sectional area?
A: If you have the minor radius (r_minor), the cross-sectional area would be π×(r_minor)² for a circular cross-section.

Q5: Are there practical applications of this calculation?
A: Yes, this calculation is particularly useful in electrical engineering for designing toroidal transformers and inductors where the radius affects magnetic properties.