Law of Cosines Calculator
Solve triangles with two sides and an angle.
Enter your values
Enter the side a you are working with.
Enter the side b you are working with.
Enter the included angle c in degrees.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Solve triangles with two sides and an angle. |
|---|---|
| Category | Math |
| Inputs needed | Side a, Side b, Included angle C |
| Main output | Side c |
| Formula | c² = a² + b² − 2ab cos C |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Side a
- Enter the side a you are working with.
- Side b
- Enter the side b you are working with.
- Included angle C(degrees)
- Enter the included angle c in degrees.
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.
What do I need to enter into the Law of Cosines Calculator?
Just 3 values: side a, side b, included angle c. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Law of Cosines Calculator work out the answer?
The law of cosines generalises Pythagoras: c² = a² + b² − 2ab·cos C. It applies the formula c² = a² + b² − 2ab cos C and shows the working so you can check each step by hand.
Is the Law of Cosines Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.