Polygon Area Calculator (by Coordinates)
Result
Polygon Area Calculator (by Coordinates) Polygon Area Calculator (by Coordinates) is a mathematics calculator that helps you calculate the area of a geometric shape from its dimensions. The formula used is: Area = |x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|/2 (Shoela — free online calculator.
Formula
- Polygon area by coordinates calculator. This page states the geometric relationship used by the calculator and provides a worked example.
- The main inputs are x₁, y₁, x₂, y₂, x₃, y₃. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Polygon Area Calculator (by Coordinates)
- x₁: 0
- y₁: 0
- x₂: 4
- y₂: 0
- x₃: 4
- y₃: 3
For (0,0),(4,0),(4,3),(0,3), area=12.
Sample result: Calculating…
Frequently asked questions
What does the Polygon Area Calculator (by Coordinates) calculate?
Enter polygon vertices in boundary order for the shoelace formula.
Which values should I enter?
Enter x₁, y₁, x₂, y₂, x₃, y₃ using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: Triangle shoelace area=|Σ(xᵢyᵢ₊₁−xᵢ₊₁yᵢ)|/2; perimeter=sum of distances.
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.