Coordinate Triangle Area Calculator
Enter the (x, y) coordinates of three corners and get the exact area of the triangle — using the shoelace formula, which works no matter what order you list the points.
Just the six numbers
Enter the x and y of each of the three vertices and the calculator returns the enclosed area at once — no need to measure side lengths or angles.
Any order works
The formula takes the absolute value, so listing the corners clockwise or counter-clockwise gives the same positive area.
What does this calculate?
Area straight from the corner points
This triangle area coordinates calculator finds the area of a triangle when all you know is where its three corners sit on the plane. Give it the (x, y) coordinates of each vertex and it returns the area of the region they enclose, measured in square coordinate units. It uses the shoelace formula (also called the surveyor's formula or Gauss's area formula), a result of coordinate geometry that turns six numbers directly into an area without ever needing the side lengths, the base, or the height. It is the tool behind land-survey area, computer-graphics polygon fills, and any geometry problem where points are easier to read off than distances.
Enter the x and y of all three corners to get the exact area of the triangle instantly — in any vertex order.
The shoelace formula takes half of the absolute value of a sum built from the three coordinate pairs. Each x is multiplied by the difference of the other two y values.
area = ½ × |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|The sum inside the bars is twice the signed area. If the corners are listed counter-clockwise the sign is positive, and if clockwise it is negative — but the absolute value strips the sign away, so you always get a non-negative area regardless of the order you typed the points in.
Take the right triangle with corners at (0, 0), (4, 0), and (0, 3).
Plug the coordinates into the formula
x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2) becomes 0(0 − 3) + 4(3 − 0) + 0(0 − 0).
Evaluate the sum
That is 0 + 12 + 0 = 12 — this is twice the signed area.
Take half of the absolute value
½ × |12| = 6 — the area of the triangle in square units, which matches the base-times-height check (½ × 4 × 3 = 6).
The number you get is the area enclosed by the three points, expressed in square coordinate units — if your coordinates are in metres, the area is in square metres. Two features of the formula are worth understanding. First, the absolute value means the result never goes negative and never depends on the order in which you enter the corners: clockwise or counter-clockwise, vertex 1 first or vertex 3 first, the answer is identical. Second, if the three points happen to lie on a single straight line, they enclose no region at all, and the formula correctly returns an area of exactly zero — a handy way to test whether three points are collinear. For every other arrangement the result is the true area, exact to the precision of the numbers you enter, with no rounding baked into the method itself.
The formula is exact, but a couple of points are worth keeping in mind.
Plane coordinates and consistent units
This calculator works with three points on a flat (2D) plane and assumes both coordinates of every point use the same unit. A zero result is not an error — it means the three points are collinear and enclose no area. For points in 3D space, or for the area from side lengths instead of coordinates, use Heron's formula instead.