Law of Cosines Calculator
Two parts: in A, give two sides and the angle between them to find the third side; in B, give all three sides to find any angle.
A. Missing Side — c = √(a² + b² − 2ab cos C)
B. Missing Angle — cos C = (a² + b² − c²) / (2ab)
How to use
- Pick Part A to find a missing side, or Part B to find a missing angle.
- In Part A, enter two sides and the angle between them, in degrees.
- In Part B, enter all three side lengths to solve for angle C.
- Read the answer plus the step-by-step breakdown showing the substitution.
Note: Cosine rule: c² = a² + b² − 2ab cos C. It works on any triangle, not only right triangles.
Tips
- Angles must be in degrees — entering radians is the most common mistake.
- Part A needs the angle between the two known sides (the included angle), not just any angle.
- The cosine rule works on any triangle, including obtuse ones — that is when it beats Pythagoras.