Triangle Area from Coordinates Calculator

About this calculator

When a triangle is defined by three vertex coordinates rather than a base and height, its area can be computed directly with the shoelace formula, also called the surveyor's formula: half the absolute value of the sum of cross-multiplied coordinate pairs, taken in order around the triangle. This avoids the extra step of first computing side lengths or a perpendicular height, working purely from (x, y) positions.

Surveyors use exactly this formula, hence its alternate name, to compute the area of a plot of land from GPS or theodolite-measured boundary coordinates, computer graphics and game engines use it to determine triangle winding order and area for rendering and collision detection, and GIS software uses the same underlying method, generalized to more vertices, for polygon area calculations on maps.

Enter the (x, y) coordinates of a triangle's three vertices and this calculator returns its area.