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Coordinate Geometry Area Calculator

Work out coordinate geometry area instantly with clear inputs, formula shown and shareable results.

About Coordinate Geometry Area Calculator

The area of a triangle from coordinates is half the absolute value of the determinant x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂). The sign of that determinant reveals whether the vertices were listed clockwise or counter-clockwise.

Formula

Coordinate area

A = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

Worked example

With the default values below, Coordinate Geometry Area Calculator returns Area of 19.5000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Vertex A (x, y)
1, 1
Vertex B (x, y)
7, 2
Vertex C (x, y)
4, 8

Results

Area
19.5000
Perimeter
20.4067
Signed determinant (2 × area)
39.0000
Vertex orientation
Counter-clockwise

Step by step

  1. 1Values used
  2. 2Coordinate area
  3. 3Area= 19.5000
  4. 4Perimeter= 20.4067
  5. 5Signed determinant (2 × area)= 39.0000
  6. 6Vertex orientation= Counter-clockwise

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does a zero determinant mean?

The three points lie on one straight line, so they enclose no area.

Does the point order matter?

Not for the area, because of the absolute value, but it flips the sign of the determinant and hence the reported orientation.

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