Mollweide's Formula Checker

About this calculator

Mollweide's formula is an identity that relates all six parts of a triangle — its three sides and three angles — in a single equation: (a−b)/c = sin((A−B)/2) / cos(C/2). Because it involves every side and angle at once, unlike the Law of Sines or Law of Cosines which use only a subset, it's especially useful as an independent check: if a triangle's sides and angles are correct, this identity must hold exactly.

Trigonometry students and teachers use Mollweide's formula to verify that a solved triangle (from the Law of Sines or Law of Cosines) is internally consistent, catching arithmetic or angle-ambiguity errors that a single-relationship check might miss. Surveyors and navigators solving oblique triangles have historically used it the same way, as a cross-check before trusting a triangulation result.