Law of Cosines Calculator
Use the law of cosines to find the third side from two sides and the angle between them, or any angle from three sides.
About the Law of Cosines Calculator
The law of cosines extends Pythagoras to every triangle: the extra term −2ab·cos C corrects for C not being 90°. When C = 90°, cos C = 0 and it becomes a² + b² = c².
The formula
c² = a² + b² − 2ab·cos C
- Angle from sides
- cos C = (a² + b² − c²) ÷ 2ab
Worked example
a = 7, b = 9, C = 50°
- c² = 49 + 81 − 126 × cos 50° ≈ 49.008
- c ≈ 7.0006
Questions people ask
Does it work for obtuse triangles?
Yes. cos C is negative when C > 90°, which makes c longer, as it should.
Why is it called the cosine rule?
Same thing; “law of cosines” is US usage.