Calculator Inputs
Formula Used
The calculator uses the determinant, also called the shoelace method, for coordinates. This method works directly from three plotted points and avoids needing base and height first.
Extra outputs use these supporting formulas:
- Distance between points: √[(x2 - x1)² + (y2 - y1)²]
- Perimeter: AB + BC + CA
- Centroid: ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3)
- Inradius: Area / semiperimeter
- Circumradius: (AB × BC × CA) / (4 × Area)
How to Use This Calculator
- Enter the x and y values for points A, B, and C.
- Choose a custom unit label, such as square meters or square units.
- Select your preferred decimal precision for output formatting.
- Enable the step display if you want the determinant breakdown.
- Press the calculate button to show the result above the form.
- Review area, side lengths, centroid, perimeter, classification, and the graph.
- Use the CSV button for data export or the PDF button for a printable summary.
Example Data Table
| Point A | Point B | Point C | Area | Perimeter | Centroid | Type |
|---|---|---|---|---|---|---|
| (1, 2) | (6, 3) | (4, 8) | 13.5000 | 17.1924 | (3.6667, 4.3333) | Scalene, Acute |
| (0, 0) | (5, 0) | (0, 4) | 10.0000 | 15.4031 | (1.6667, 1.3333) | Scalene, Right |
| (-2, 1) | (3, 5) | (6, -1) | 21.0000 | 18.9190 | (2.3333, 1.6667) | Scalene, Acute |
FAQs
1. What does this calculator measure?
It computes the area enclosed by three coordinate points. It also reports side lengths, centroid, perimeter, orientation, triangle type, and several supporting geometric checks.
2. Which formula is used for the area?
The tool uses the determinant or shoelace formula. It is reliable for coordinate geometry because it works directly from plotted points without first finding a separate base and height.
3. What if the result is zero?
A zero area means the three points are collinear or overlapping in a way that does not form a real triangle. The calculator labels that case as degenerate.
4. Why is signed area shown too?
Signed area preserves vertex order information. A positive sign indicates counterclockwise order, while a negative sign indicates clockwise order. The displayed area always uses the absolute value.
5. Can I use negative coordinates?
Yes. The formula works with positive, negative, and decimal coordinates. Negative values are common in analytic geometry, surveying layouts, and graph-based design problems.
6. What is the centroid?
The centroid is the average of the three x values and the three y values. It marks the balancing point of the triangle and is useful in many geometry problems.
7. Why are CSV and PDF exports helpful?
CSV is useful for records, spreadsheets, and repeated comparisons. PDF is better for sharing, printing, assignments, reports, and project documentation with a consistent layout.
8. Does the graph change with my values?
Yes. After calculation, the chart plots your three points, connects them in order, shades the triangle, and marks the centroid for a fast visual check.