Brahmagupta Area Calculator

Brahmagupta area√Π(s−a) only for independently established convex CYCLIC quadrilateral; sidevectorscannotproveconcyclicity, not generic Bretschneiderquadrilateral.

Description

Brahmagupta's area formula applies to an independently established convex cyclic quadrilateral.

Brahmagupta's area formula applies to an independently established convex cyclic quadrilateral.^[1]

This tool calculates area from four side lengths without using those lengths to certify concyclicity.

When to use Brahmagupta Area Calculator

Use this tool to calculate area from four side lengths without using those lengths to certify concyclicity.

How to use Brahmagupta Area Calculator and how it works

Prepare actualCyclicQuadrilateralSides, with the units, conventions and assumptions below.
Enter the required fields and run Brahmagupta Area Calculator.
Read result.cyclicQuadrilateralArea 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
actualCyclicQuadrilateralSides	Exactly four positive side lengths in one length unit; cyclicity must be independently established.	array of number	Required; other constraints below

Require four strictly positive sides and require each side to be less than their semiperimeter s. Compute sqrt((s-a)*(s-b)*(s-c)*(s-d)). The returned area assumes a convex cyclic quadrilateral; the input validation does not establish cyclicity, and the same sides can enclose other areas in noncyclic configurations.

s=(a+b+c+d)/2; area=sqrt((s-a)*(s-b)*(s-c)*(s-d))

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.cyclicQuadrilateralArea	Conditional cyclic quadrilateral area in squared side-length units.	number

json

{
  "input": {
    "actualCyclicQuadrilateralSides": [
      2,
      2,
      2,
      2
    ]
  },
  "output": {
    "result": {
      "cyclicQuadrilateralArea": 4
    }
  }
}

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

Brahmagupta Area 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.