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Torus Radius Formula:
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The radius of a torus is calculated using the formula that relates the overall breadth of the torus and the radius of its circular cross-section. This geometric relationship helps determine the distance from the center of the torus to the center of its circular cross-section.
The calculator uses the torus radius formula:
Where:
Explanation: The formula calculates the main radius of the torus by subtracting the circular section radius from half of the total breadth of the torus.
Details: Accurate calculation of torus radius is essential in geometry, engineering, and architectural design where toroidal shapes are used. It helps in determining volume, surface area, and other geometric properties of torus-shaped objects.
Tips: Enter the breadth of the torus and the radius of the circular section in meters. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is a torus?
A: A torus is a three-dimensional geometric shape that resembles 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 main parameters of a torus?
A: The main parameters are the major radius (distance from center to tube center) and minor radius (radius of the tube).
Q3: Can this formula be used for all torus shapes?
A: Yes, this formula applies to all standard torus shapes where the circular cross-section is consistent throughout.
Q4: What units should be used for input values?
A: The calculator uses meters as the default unit, but any consistent unit system can be used as long as all inputs are in the same units.
Q5: What if the calculated radius is negative?
A: A negative result indicates that the circular section radius is larger than half the breadth, which is geometrically impossible for a standard torus. Please verify your input values.