Quadrilateral Area Calculator (from Coordinates)
Find the area of any quadrilateral from the coordinates of its four corners using the shoelace formula. Enter the (x, y) points for vertices A, B, C and D in order around the shape, and the calculator returns the enclosed area. It works for squares, rectangles, parallelograms, trapezoids and irregular quadrilaterals alike.
Formula
Area = ½ × |x₁y₂ − x₂y₁ + x₂y₃ − x₃y₂ + x₃y₄ − x₄y₃ + x₄y₁ − x₁y₄|
- This is the shoelace (Gauss) formula applied to four vertices. Enter the corners in order — clockwise or counter-clockwise — as you travel around the boundary.
- Listing the points out of order (zig-zagging across the shape) produces a self-intersecting path and an incorrect area, so keep them sequential.
- The sign of the un-absolute sum gives the winding direction: positive for counter-clockwise, negative for clockwise.
- The area is in the square of the coordinate unit, and a zero result means the four points are collinear or otherwise enclose no region.
Example: rectangle A(0,0), B(6,0), C(6,4), D(0,4)
Inputs
- A — x₁: 0
- A — y₁: 0
- B — x₂: 6
- B — y₂: 0
- C — x₃: 6
- C — y₃: 4
- D — x₄: 0
- D — y₄: 4
These four points form a 6 × 4 rectangle, and the shoelace formula returns ½ × |0 + 24 + 0 + 0| = 24 square units, exactly 6 × 4.
Frequently asked questions
How does this find a quadrilateral's area?
It uses the shoelace formula, which cross-multiplies the coordinates of consecutive corners, sums them, halves the total and takes the absolute value.
Does the order of the corners matter?
Yes. Enter the four vertices in the order they appear around the shape. Out-of-order points create a crossed path and give a wrong area.
Will it work for irregular quadrilaterals?
Yes — as long as the shape is a simple (non-self-intersecting) quadrilateral, the formula handles any four-cornered figure, including irregular ones.
What does an area of zero mean?
It means the four points are collinear or otherwise fail to enclose a region, so there is no area to report.
What units does the answer use?
The area is in the square of the unit you use for the coordinates. Coordinates in metres yield an area in square metres.