Triangle Area from Coordinates Calculator
Find a triangle's area from its three vertices with the shoelace formula.
What is Area from Coordinates?
The shoelace formula gives a triangle's area from its three vertices alone — no base, no height and no trig. It is the coordinate-plane counterpart of Heron's formula, and it is what you use when the sides are not given but the corners are.
How it works
The engine evaluates ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|, which is the signed area of the polygon the three points trace, then takes the absolute value so the answer does not depend on the order the vertices are entered in. The side lengths come from the distance formula and the centroid from averaging the vertices, so the whole triangle is solved from the same input.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.