What is the shoelace formula?

The shoelace formula (also called the surveyor's formula) computes polygon area from vertex coordinates. For a triangle with vertices (x_A, y_A), (x_B, y_B), (x_C, y_C) it is: Area = |x_A(y_B − y_C) + x_B(y_C − y_A) + x_C(y_A − y_B)| / 2.

Can I use negative coordinates?

Yes. The formula works with any real-number coordinates, including negative values. The absolute value in the formula ensures area is always non-negative regardless of vertex order.

What happens if the three points are collinear?

If all three points lie on the same straight line, the area is 0. The tool will display "0 — points are collinear" to flag this case explicitly.

Does the order of the vertices matter?

No. The absolute value in the shoelace formula means you get the same area regardless of whether you list the vertices clockwise or counterclockwise.

What units does the area use?

The area is in square units of whatever coordinate system you use. If your coordinates are in meters, the area is in square meters; if in feet, the area is in square feet.

How are side lengths calculated?

Each side length uses the Euclidean distance formula: d = √((x₂−x₁)² + (y₂−y₁)²).

Area of Triangle from Coordinates

Name: Area of Triangle from Coordinates
Availability: InStock
Author: Nham Vu

Enter the (x, y) coordinates of three vertices to instantly get triangle area, side lengths, and perimeter.

Vertex Coordinates

Vertex A

Vertex B

Vertex C

Enter coordinates on the left to see results

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Summary

Enter the (x, y) coordinates of three vertices to instantly get triangle area, side lengths, and perimeter.

How it works

Enter the x and y coordinates for each of the three vertices (A, B, C).
The tool applies the shoelace formula: Area = |x_A(y_B - y_C) + x_B(y_C - y_A) + x_C(y_A - y_B)| / 2.
Side lengths are computed with the distance formula between each pair of vertices.
Perimeter is the sum of all three side lengths.
Results update immediately as you type — no button click needed.

Use cases

Solve coordinate geometry problems in school or college courses.
Find the area of a triangular region on a map or grid.
Verify hand-calculated answers to analytic geometry exercises.
Calculate land area from surveyed corner points on a 2D plane.
Check that three given points are collinear (area = 0).
Compute triangle dimensions for game development or graphics programming.
Quickly derive perimeter and side lengths alongside area.
Explore how area changes as you shift one vertex.

Frequently Asked Questions

Last updated: 2026-07-04 · Reviewed by Nham Vu