Power Calculators

📍 Triangle Area from Coordinates Calculator

Calculate the area of a triangle from the x and y coordinates of its three vertices using the coordinate or shoelace formula.

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Fill in the details and click Calculate to see your results.


Also available in our Android app, with charts and full breakdown tables.

📘 About the Coordinate Triangle Area

Enter the x and y coordinates of all three vertices.

The formula works regardless of the triangle's orientation on the coordinate plane.

If the three points are collinear, the area is zero and they do not form a non-degenerate triangle.

🧮 Formula

Coordinate area formula
A = |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|/2

Where

  • A = triangle area
  • (x1,y1), (x2,y2), (x3,y3) = three vertices
Coordinates may be positive, negative or zero.

✏️ Worked example

Points (0,0), (6,0), (0,4)

You enter
Point A - x10
Point A - y10
Point B - x26
Point B - y20
Point C - x30
Point C - y34
You get
Triangle Area12
Non-Collinear Triangle1

The triangle has an area of 12 square units.

Try this example →

🧭 How to use this calculator

What you enter

  • Point A - x1
  • Point A - y1
  • Point B - x2
  • Point B - y2
  • Point C - x3
  • Point C - y3

What you get

  • Triangle Area
  • Non-Collinear Triangle

💡 Coordinate geometry

  • The determinant may be positive or negative depending on vertex order, so its absolute value is used for area.
  • The result is in square coordinate units.
  • Collinear points have zero area.

❓ Frequently asked questions

What is the coordinate formula for triangle area?

Take one half of the absolute value of x1(y2-y3)+x2(y3-y1)+x3(y1-y2).

Can coordinates be negative?

Yes. Negative x or y coordinates are valid Cartesian coordinates.

What if the points are collinear?

The calculated area is zero, so the points do not form a non-degenerate triangle.

Does the order of the three points matter?

No. Reordering the vertices changes only the sign of the determinant, and the absolute value gives the same area.