What is the law of cosines?

It generalises the Pythagorean theorem to any triangle: c² = a² + b² − 2ab·cos(C). It lets you find a side from two sides and the included angle, or an angle from three known sides.

When should I use SSS versus SAS?

Use SSS (three sides) when you know all three side lengths and need the angles. Use SAS (side-angle-side) when you know two sides and the angle between them and need the third side.

Does it work for right and obtuse triangles?

Yes. The law of cosines works for any triangle. For a right angle the cosine term vanishes and it reduces to the Pythagorean theorem.

Law of Cosines Calculator

Solve any triangle from three sides or two sides and an angle.

Solve any triangle with the cosine rule

The law of cosines — c² = a² + b² − 2ab·cos(C) — solves triangles that the simpler right-angle rules cannot. Pick SSS to recover all three angles from three sides, or SAS to find the missing side from two sides and the angle between them.

The tool also reports the area and perimeter. Sides a, b and c sit opposite angles A, B and C. All math happens locally in your browser.