Law of Cosines Side Calculator

About this calculator

The law of cosines extends the Pythagorean theorem to non-right triangles: c² = a² + b² − 2ab·cos(C), where C is the angle between the two known sides a and b. When C happens to be 90°, cos(C) = 0 and the formula collapses back to a² + b² = c², which is why it's often introduced as the "generalized Pythagorean theorem."

Surveyors use it to compute an unknown boundary length from two measured sides and the angle between them, navigators use it for dead-reckoning triangles, and structural engineers use it to size a diagonal brace when the two connecting members and their included angle are already fixed by the design.