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Coordinate Triangle Area — result sheet
Calculate a triangle's area and orientation from the Cartesian coordinates of its three vertices.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Signed double area = x1(y2-y3) + x2(y3-y1) + x3(y1-y2); area = absolute value of signed double area / 2.
The coordinate determinant gives twice the signed triangle area. Its absolute value gives geometric area, while its sign records whether the vertices are listed counterclockwise or clockwise.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Point 1 x — minimum -1000000; maximum 1000000
- Point 1 y — minimum -1000000; maximum 1000000
- Point 2 x — minimum -1000000; maximum 1000000
- Point 2 y — minimum -1000000; maximum 1000000
- Point 3 x — minimum -1000000; maximum 1000000
- Point 3 y — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Point 1 x | 0 |
| Point 1 y | 0 |
| Point 2 x | 4 |
| Point 2 y | 0 |
| Point 3 x | 0 |
| Point 3 y | 3 |
Triangle area 6 square units; orientation counterclockwise.
Assumptions and limits
- Coordinates are Cartesian points in a common linear unit.
- The three vertices are non-collinear and are considered in the entered order.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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