Nephroid Area Calculator
Nephroidepicycloidarea12πa²whereaisrollingradius and fixed radius2a.
Description
Nephroid area depends on the curve's radius convention.
Nephroid area depends on the curve's radius convention.1
This tool calculates enclosed area using rolling-circle radius a and fixed-circle radius 2a.
When to use Nephroid Area Calculator
This tool calculates enclosed area using rolling-circle radius a and fixed-circle radius 2a.
How to use Nephroid Area Calculator and how it works
- Prepare rolling circle radius, using the input definitions and matching units below.
- Enter the required fields and run Nephroid 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 |
|---|---|---|---|
| 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 12*pi*a^2 in squared length units under fixed-circle radius 2a. No other radius convention or numerical area integration is used.
area=12*pi*a^2 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": {
"rollingCircleRadius": 1
},
"output": {
"result": {
"value": 37.69911184307752
}
}
}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 Perimeter Calculator for a complementary operation: A nephroid is an epicycloid whose convention here uses a fixed-circle radius twice the rolling-circle radius.
Use Lemniscate Perimeter Approximation for a complementary operation: The Bernoulli lemniscate perimeter depends on an explicit polar scale convention.
References
-
Nephroid Area Calculator — tool.io
Similar or alternative tools
- Nephroid Perimeter Calculator
A nephroid is an epicycloid whose convention here uses a fixed-circle radius twice the rolling-circle radius.
- Lemniscate Perimeter Approximation
The Bernoulli lemniscate perimeter depends on an explicit polar scale convention.