Law of Cosines Calculator
Solve triangles with two sides and an angle.
Enter your values
ⓘ Live results
Results
- Side c
- 6.66634
- Angle A
- 46.237°
- Angle B
- 96.763°
- Area
- 26.47986
- Perimeter
- 25.66634
Quick answer
The law of cosines generalises Pythagoras: c² = a² + b² − 2ab·cos C.
c² = a² + b² − 2ab cos C
How to use the Law of Cosines Calculator
- 1Enter the two known sides.
- 2Enter the angle between them in degrees.
- 3Read the missing side and angles.
Worked example
Using the values the calculator loads with:
Inputs
- Side a8
- Side b11
- Included angle C37 degrees
Results
- Side c6.66634
- Angle A46.237°
- Angle B96.763°
- Area26.47986
- Perimeter25.66634
Frequently asked questions
When do I use cosine vs sine rule?
Cosine rule for two sides and the included angle, or three sides; sine rule otherwise.
Does it work for right triangles?
Yes — with C = 90° it reduces to Pythagoras.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.