Bretschneider Quadrilateral Area Calculator

About this calculator

Bretschneider's formula generalizes Heron's triangle-area formula to any quadrilateral — convex or not, cyclic or not — using only its four side lengths and the sum of two opposite angles. For sides a, b, c, d and opposite angles A and C, the area is Area = √[(s−a)(s−b)(s−c)(s−d) − abcd·cos²((A+C)/2)], where s is the semiperimeter (a+b+c+d)/2.

When A + C = 180° (a cyclic quadrilateral, meaning it can be inscribed in a circle), the cosine term vanishes and the formula reduces exactly to Brahmagupta's formula.

Surveyors, CAD/CAM engineers, and geometry students use Bretschneider's version for the general case — an irregular plot of land or a four-sided panel — where the shape isn't cyclic and the simpler formula doesn't apply.