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Torus Surface Area — result sheet
Calculate the surface area of an ordinary ring torus from its major and minor radii.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: S=4*pi^2*R*r for an ordinary ring torus with R>r>0; R is major and r is minor radius.
The ring-torus surface area follows from rotating a circular tube of radius r around a circle of radius R. The ordinary non-self-intersecting ring case requires the major radius to exceed the minor radius.
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 center of its tube.; minimum 1.0E-6; maximum 1000000
- Minor radius r — length units; Radius of the circular tube rotated around the major circle.; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Major radius R | 5 |
| Minor radius r | 2 |
S=4pi^2(5)(2)=40pi^2, approximately 394.784176 square units.
Assumptions and limits
- The shape is a smooth ordinary ring torus generated by rotating a circle of radius r around an external coplanar axis at distance R.
- R and r are compatible positive length units and satisfy R > r, excluding horn and spindle torus cases.
- The result is ideal geometric surface area and does not include thickness, roughness, seams, openings, coating, or material properties.
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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