Law of Cosines Calculator
Solve triangles using the law of cosines.
This Law of Cosines Calculator allows you to calculate or convert values instantly. It is free, fast, and easy to use.
- Free Online Tool
- Instant Results
- Mobile Friendly
- No Installation
- Secure & Private
Understanding This Calculator
Law of Cosines Formula
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
c² = a² + b² - 2ab × cos(C)
Example 1
Side a = 5, Side b = 8, Angle C = 60°
- c² = 5² + 8² - 2(5)(8)cos(60°)
- c² = 25 + 64 - 80(0.5)
- c² = 89 - 40 = 49
- c = √49 = 7
Example 2
Side a = 10, Side b = 10, Angle C = 90° (Right Triangle)
- c² = 10² + 10² - 2(100)cos(90°)
- c² = 100 + 100 - 0 (since cos 90° is 0)
- c = √200 ≈ 14.14
How to Use
- Enter two sides of the triangle.
- Enter the angle between them.
- Get the third side and other angles.
Frequently Asked Questions
How do I use the Law of Cosines Calculator?
Enter your values in the input fields, and the result will appear instantly.
Is this calculator free to use?
Yes, this calculator is 100% free and does not require any registration or subscription.
Is it mobile-friendly?
Absolutely! Our tool is optimized for all devices, including mobile phones, tablets, and desktop computers.