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Triangle Centroid Calculator — result sheet
Find the centroid of a triangle from the coordinates of its three vertices and report its area.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Gx = (x₁+x₂+x₃)/3; Gy = (y₁+y₂+y₃)/3; area = |x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|/2.
The centroid is the arithmetic mean of the three vertex coordinates. The same coordinates also provide the triangle’s signed-area magnitude, which helps reveal a collinear or nearly collinear input.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vertex 1 x — minimum -1000000000; maximum 1000000000
- Vertex 1 y — minimum -1000000000; maximum 1000000000
- Vertex 2 x — minimum -1000000000; maximum 1000000000
- Vertex 2 y — minimum -1000000000; maximum 1000000000
- Vertex 3 x — minimum -1000000000; maximum 1000000000
- Vertex 3 y — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Vertex 1 x | 0 |
| Vertex 1 y | 0 |
| Vertex 2 x | 6 |
| Vertex 2 y | 0 |
| Vertex 3 x | 0 |
| Vertex 3 y | 3 |
Centroid: (2, 1); area: 9 square units.
Assumptions and limits
- The vertices are expressed in one Cartesian coordinate system and use one consistent unit.
- The centroid formula applies to a triangle; a zero area means the three points are collinear.
- Coordinates may be negative and are not interpreted as latitude/longitude on a curved Earth.
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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