About the Coordinate Triangle Area Calculator
Area of a triangle from the coordinates of its three vertices using the shoelace formula — also tells you if the points are collinear.
Also known as: area of triangle with coordinates, shoelace formula, triangle area from vertices, collinear points.
How to use this calculator
- Enter x₁, y₁, x₂, y₂ and the other fields.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Open “Step-by-step” to see how the answer was worked out.
- Use Copy result or Share to save the answer or send a link with your inputs.
Coordinate Triangle Area formula
A = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
Worked example
Using the values pre-filled in the calculator above:
- x₁ = 0
- y₁ = 0
- x₂ = 4
- y₂ = 0
- x₃ = 1
- y₃ = 3
the calculator returns:
- Area: 6
- Collinear?: No
- Centroid: (1.666667, 1)
Working
½ |0(0 − 3) + 4(3 − 0) + 1(0 − 0)| = ½ × 12 = 6