Law of Cosines Calculator
Find the third side of a triangle using the law of cosines
About this calculator
The Law of Cosines Calculator helps you find the missing side length of any triangle when you know two sides and the included angle between them. This powerful mathematical tool extends beyond right triangles, making it essential for geometry students, engineers, surveyors, and professionals in construction and navigation. Unlike the Pythagorean theorem which only works for right triangles, the law of cosines applies to all triangle types - acute, obtuse, and right triangles - making it incredibly versatile for real-world applications and academic problem-solving.
How to use
Enter the lengths of two known sides of your triangle in the designated input fields. Then input the measure of the angle between these two sides in degrees. Click calculate to instantly find the length of the third side using the law of cosines formula: c² = a² + b² - 2ab cos(C).
Frequently asked questions
What is the law of cosines formula?
The law of cosines formula is c² = a² + b² - 2ab cos(C), where c is the unknown side, a and b are known sides, and C is the included angle.
Can I use this for right triangles?
Yes, the law of cosines works for all triangles. For right triangles, it simplifies to the Pythagorean theorem when the angle is 90 degrees.
What units should I use for angles?
Enter angles in degrees. The calculator will automatically convert to radians for the cosine calculation and provide results in the same length units you input.