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Ring Torus Volume — result sheet
Calculate the volume of a non-self-intersecting ring torus from its major radius and smaller tube radius.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: V = 2 pi^2 R r^2 for a ring torus with major radius R greater than minor radius r.
The torus volume is the area of the circular tube multiplied by the distance traveled by its centroid around the axis, giving 2 pi^2 R r^2.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Major radius R — length units; Distance from the torus center to the centerline of its tube.; minimum 1.0E-6; maximum 1000000000
- Minor radius r — length units; Radius of the circular tube around the torus centerline.; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Major radius R | 5 |
| Minor radius r | 2 |
V = 2 pi^2 x 5 x 2^2 = 40 pi^2, approximately 394.784 cubic length units.
Assumptions and limits
- The torus is an ordinary ring torus with a circular tube and major radius strictly greater than minor radius.
- Both radii use the same length unit, so the result is in cubic length units.
- The solid is ideal and uniform; wall thickness, holes, material, and manufacturing tolerances are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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