mathematics calculator
Triangle Area From Coordinates Calculator
Calculate a triangle's area from three Cartesian coordinate pairs using a determinant.
Triangle Area From Coordinates
Triangle area
Enter the x and y coordinates of three vertices.
Vertex order may be clockwise or counter-clockwise; collinear points are rejected.
Formula version 1.0.0
How to use this calculator
- Enter the x and y coordinates of all three vertices.
- Use one coordinate unit and reference frame.
- Select Calculate.
- Read the positive area and check that the points are not collinear.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
(x₁,y₁) | First vertex | coordinate length |
(x₂,y₂) | Second vertex | coordinate length |
(x₃,y₃) | Third vertex | coordinate length |
A | Triangle area | square coordinate length |
Checked examples
Right triangle
Inputs: (0,0), (4,0), (0,3)
Calculation: A=|0(0−3)+4(3−0)+0(0−0)|÷2
Result: 6 square units
The determinant matches one-half base times height.
Check: triangle-coordinates-core.test.ts
Translated triangle
Inputs: (10,−2), (14,−2), (10,1)
Calculation: Apply the same determinant after translation
Result: 6 square units
Moving every point equally does not change area.
Check: triangle-coordinates-core.test.ts
Assumptions, rounding, and limits
- Coordinates are finite and share one Cartesian system.
- Axes use compatible scales.
- The points are not collinear.
- The calculation is planar and orientation-independent.
Frequently asked questions
Does vertex order matter?
No. Reversing orientation changes determinant sign, but absolute area is unchanged.
Why are collinear points rejected?
They form a line with zero area rather than a triangle.
Can coordinates be negative?
Yes. Any finite Cartesian coordinates are accepted.
Sources and review
- OpenStax: The Cross Product — Area from vector products
- Wolfram MathWorld: Triangle Area — Coordinate determinant formula
- Formula version
- triangle.coordinates-area@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Planar Cartesian coordinates with compatible axis scales.
- Next review
- On material formula/source change, or by 2028-10-25.
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