Torus Surface Area Calculator
Ring torus area4π²Rr, actualR>r>0, no spindle/horn overlap or volume.
Description
A ring torus has a major radius larger than its tube radius, giving a non-self-intersecting surface.
A ring torus has a major radius larger than its tube radius, giving a non-self-intersecting surface.1
This tool calculates its surface area from those radii in consistent length units.
When to use Torus Surface Area Calculator
This tool calculates its surface area from those radii in consistent length units.
How to use Torus Surface Area Calculator and how it works
- Prepare major radius, tube radius, using the input definitions and matching units below.
- Enter the required fields and run Torus Surface Area Calculator.
- Read result.value using the units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualMajorRadius | Actual Major Radius. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualTubeRadius | Actual Tube Radius. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Require positive major radius R and tube radius r in the same unit, with R>r. Return 4*pi^2*R*r in squared length units. Horn and spindle cases are rejected; no volume is calculated.
area=4*pi^2*R*r Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Geometric area in squared input length or lattice units under the stated convention. | number |
{
"input": {
"actualMajorRadius": 2,
"actualTubeRadius": 1
},
"output": {
"result": {
"value": 78.95683520871486
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Star Polygon Area Calculator for a complementary operation: A regular star polygon's algebraic area counts winding multiplicity and can differ from the area of its filled union.
Use Regular N-Gon Perimeter Calculator for a complementary operation: A regular polygon perimeter is its number of equal sides times their common length.
References
-
Torus Surface Area Calculator — tool.io
Similar or alternative tools
- Star Polygon Area Calculator
A regular star polygon's algebraic area counts winding multiplicity and can differ from the area of its filled union.
- Regular N-Gon Perimeter Calculator
A regular polygon perimeter is its number of equal sides times their common length.