Nephroid Perimeter Calculator
Nephroidepicycloidperimeter24awhereaisrollingradius.
Description
A nephroid is an epicycloid whose convention here uses a fixed-circle radius twice the rolling-circle radius.
A nephroid is an epicycloid whose convention here uses a fixed-circle radius twice the rolling-circle radius.1
This tool calculates perimeter using that rolling-radius scale.
When to use Nephroid Perimeter Calculator
This tool calculates perimeter using that rolling-radius scale.
How to use Nephroid Perimeter Calculator and how it works
- Prepare rolling circle radius, using the input definitions and matching units below.
- Enter the required fields and run Nephroid Perimeter 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 |
|---|---|---|---|
| rollingCircleRadius | Positive rolling-circle radius a; fixed-circle radius is 2a. | number | Required; strictly positive; finite; other constraints below |
Require positive rolling-circle radius a. Return 24*a in the same length unit under the nephroid fixed-radius 2a convention. No arc sampling or alternative radius convention is inferred.
perimeter=24*a 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 length in the supplied radius, side or curve-scale unit. | number |
{
"input": {
"rollingCircleRadius": 1
},
"output": {
"result": {
"value": 24
}
}
}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 Nephroid Area Calculator for a complementary operation: Nephroid area depends on the curve's radius convention.
Use Lemniscate Perimeter Approximation for a complementary operation: The Bernoulli lemniscate perimeter depends on an explicit polar scale convention.
References
-
Nephroid Perimeter Calculator — tool.io
Similar or alternative tools
- Nephroid Area Calculator
Nephroid area depends on the curve's radius convention.
- Lemniscate Perimeter Approximation
The Bernoulli lemniscate perimeter depends on an explicit polar scale convention.