Circumradius Triangle Calculator
Trianglecircumradiusabc/(4Δ),strictnondegeneratesides.
Description
A triangle's circumradius relates its three side lengths to its area.
A triangle's circumradius relates its three side lengths to its area.1
This tool evaluates that geometric relation for a nondegenerate triangle without computing a circumcenter.
When to use Circumradius Triangle Calculator
Use this tool to evaluate that geometric relation for a nondegenerate triangle without computing a circumcenter.
How to use Circumradius Triangle Calculator and how it works
- Prepare sideA, sideB, sideC, with the units, conventions and assumptions below.
- Enter the required fields and run Circumradius Triangle 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 |
|---|---|---|---|
| sideA | Positive triangle side a in the same length unit as sides b and c. | number | Required; strictly positive; finite; other constraints below |
| sideB | Positive triangle side b in the same length unit as sides a and c. | number | Required; strictly positive; finite; other constraints below |
| sideC | Positive triangle side c in the same length unit as sides a and b. | number | Required; strictly positive; finite; other constraints below |
Require three strictly positive sides satisfying every strict triangle inequality. Calculate Heron's positive area and then a*b*c/(4*area), returning the circumradius in the side-length unit. Degenerate or impossible triangles are errors.
s=(a+b+c)/2; area=sqrt(s*(s-a)*(s-b)*(s-c)); radius=a*b*c/(4*area) 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 | Circumradius in the input side-length unit. | number |
{
"input": {
"sideA": 3,
"sideB": 4,
"sideC": 5
},
"output": {
"result": {
"value": 2.5
}
}
}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 Deltoid Area Calculator for a complementary operation: A deltoid's area depends on whether its scale means the rolling-circle radius or an outer radius.
Use Cardioid Perimeter Calculator for a complementary operation: A cardioid perimeter depends on the polar coefficient in r=a times one plus cos theta.
References
-
Circumradius Triangle Calculator — tool.io
Similar or alternative tools
- Deltoid Area Calculator
A deltoid's area depends on whether its scale means the rolling-circle radius or an outer radius.
- Cardioid Perimeter Calculator
A cardioid perimeter depends on the polar coefficient in r=a times one plus cos theta.