Home
Back
Volume Of Torus Formula:
| From: | To: |
The volume of a torus is calculated using the formula \( V = 2\pi^2 r^2 (R + r) \), where \( r \) is the radius of the circular cross-section and \( R \) is the hole radius (distance from the center of the torus to the center of the tube).
The calculator uses the torus volume formula:
Where:
Explanation: This formula calculates the volume of a torus by considering it as a surface of revolution, where a circle of radius \( r \) is rotated around an axis at a distance \( R \) from the center of the circle.
Details: Calculating the volume of a torus is important in various engineering and mathematical applications, including mechanical design, architecture, and geometric modeling. It helps in determining material requirements and spatial planning.
Tips: Enter the radius of the circular section and the hole radius in meters. Both values must be positive numbers. The calculator will compute the volume using the torus volume formula.
Q1: What is a torus?
A: A torus is a doughnut-shaped surface generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
Q2: What are the units for torus volume?
A: The volume is typically measured in cubic meters (m³) or other cubic units depending on the input dimensions.
Q3: Can the formula be used for any torus?
A: Yes, this formula applies to all tori as long as the circular cross-section remains constant throughout.
Q4: What if the hole radius is zero?
A: If the hole radius is zero, the torus becomes a sphere, but the formula would need to be adjusted as this represents a special case.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric tori. The accuracy depends on the precision of the input values.