Deltoid Area Calculator
Deltoid hypocycloid area2πa²wherea ROLLING circle radius, not full circumradius3a.
Description
A deltoid's area depends on whether its scale means the rolling-circle radius or an outer radius.
A deltoid's area depends on whether its scale means the rolling-circle radius or an outer radius.1
This tool calculates area using the rolling-circle radius convention.
When to use Deltoid Area Calculator
Use this tool to calculate area using the rolling-circle radius convention.
How to use Deltoid Area Calculator and how it works
- Prepare rollingCircleRadius, with the units, conventions and assumptions below.
- Enter the required fields and run Deltoid Area Calculator.
- Read result.value using the output definitions 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 for the standard deltoid, in the chosen length unit. | number | Required; strictly positive; finite; other constraints below |
Require a strictly positive rolling radius in a chosen length unit. Compute 2*pi*r^2 and return area in that unit squared. The radius is the rolling-circle radius, not the enclosing radius or the distance to a cusp.
area=2*pi*rollingRadius^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 units. | number |
{
"input": {
"rollingCircleRadius": 1
},
"output": {
"result": {
"value": 6.283185307179586
}
}
}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 Cardioid Perimeter Calculator for a complementary operation: A cardioid perimeter depends on the polar coefficient in r=a times one plus cos theta.
Use Cardioid Area Calculator for a complementary operation: A cardioid area depends on its stated polar scale convention.
References
-
Deltoid Area Calculator — tool.io
Similar or alternative tools
- Cardioid Perimeter Calculator
A cardioid perimeter depends on the polar coefficient in r=a times one plus cos theta.
- Cardioid Area Calculator
A cardioid area depends on its stated polar scale convention.