Coordinate Geometry Calculator

Area, perimeter, centroid and orientation of any polygon from its vertex coordinates using the shoelace formula.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Coordinate Geometry Calculator

Computes the area, perimeter and centroid of any simple polygon from the coordinates of its vertices, using the shoelace (surveyor’s) formula. Triangles, quadrilaterals and irregular plots of land are all handled the same way.

Limitations

The polygon must be simple (its edges must not cross). For self-intersecting outlines the formula returns a signed sum of regions, not the visible area.

How to use it

Enter the vertices in order around the polygon, one “x, y” pair per line.
Press Calculate.
Check the diagram to confirm the shape is the one you meant.

Example

(0,0), (4,0), (4,3), (0,3)

→ Area 12, perimeter 14, centroid (2, 1.5)

Formulas used

A = \frac{1}{2}\left|\sum_{i=1}^{n} (x_i y_{i+1} - x_{i+1} y_i)\right|

Shoelace formula; the vertex after the last one is the first.

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About the Coordinate Geometry Calculator

Limitations

How to use it

Formulas used

Related tools

About the Coordinate Geometry Calculator

Limitations

How to use it

Formulas used