Law of Cosines Calculator
Find Side (SAS)
Find side c given sides a, b and included angle C
Find Angle (SSS)
Find all angles given three sides
Formula
c² = a² + b² - 2ab·cos(C) | cos(A) = (b²+c²-a²)/(2bc) | Heron's: Area = √(s(s-a)(s-b)(s-c))
Frequently Asked Questions
What is the Law of Cosines?
The Law of Cosines states: c² = a² + b² - 2ab·cos(C), where C is the angle between sides a and b. It generalizes the Pythagorean theorem (when C = 90°, cos(90°) = 0, giving c² = a² + b²).
When do I use Law of Cosines vs Law of Sines?
Use Law of Cosines for SSS (three sides) or SAS (two sides + included angle). Use Law of Sines for ASA (two angles + included side), AAS (two angles + non-included side), or SSA (ambiguous case).
You may also need
+
Law of Sines Calculator
Free law of sines calculator. Solve triangles using the sine rule to find unknown sides and angles including the ambiguous case (SSA).
Math+
Trigonometry Calculator
Free trigonometry calculator. Calculate sin, cos, tan, sec, csc, cot for any angle in degrees or radians with exact values shown.
Math+
Pythagorean Theorem Calculator
Free Pythagorean theorem calculator. Find the missing side of a right triangle. Calculate hypotenuse or leg length from two known sides.
Math