Law of Cosines

Find side c from a, b, C.

Solve side c from a, b, and included angle C via c² = a² + b² − 2ab cos(C). Degrees or radians per your inputs.

What Law of Cosines does

Solve side c from a, b, and included angle C via c² = a² + b² − 2ab cos(C). Degrees or radians per your inputs.

The interactive controls for Law of Cosines load after this article so crawlers still read the instructions. Path /calculate/law-of-cosines is the canonical address. Work happens on this device; Tool-You does not take a copy of the file or pasted text for Law of Cosines.

How to use Law of Cosines

  1. Confirm you need Law of Cosines, not Law of Sines (Find sides from a, A, B.). Address: /calculate/law-of-cosines.
  2. Enter the numbers or dates Law of Cosines uses. Find side c from a, b, C.
  3. Read the result as Law of Cosines defines it — not as Triangle Solver (Solve SSS / SAS / ASA triangles.). Solve side c from a, b, and included angle C via c² = a² + b² − 2ab cos(C). Degrees or radians per your inputs.
  4. Law of Cosines is an estimate in the browser, not professional advice. Runs locally in the browser. Invalid input disables or fails visibly. Not medical/legal advice where noted.
  5. Need a different formula? Try Triangle Solver (Solve SSS / SAS / ASA triangles.) instead of stretching Law of Cosines.

When not to use Law of Cosines

Skip Law of Cosines when a neighbor tool matches better — start with Law of Sines or Triangle Solver — or when the description already warns the job will fail. In the tool’s own words: Solve side c from a, b, and included angle C via c² = a² + b² − 2ab cos(C). Degrees or radians per your inputs.

Questions about Law of Cosines

What does Law of Cosines do that other Calculate pages on this site do not?
Solve side c from a, b, and included angle C via c² = a² + b² − 2ab cos(C). Degrees or radians per your inputs. Short version: Find side c from a, b, C.
Does Law of Cosines upload my file or text to Tool-You servers?
No. Law of Cosines runs in this browser tab. Files stay on the device. Limit note: Runs locally in the browser. Invalid input disables or fails visibly. Not medical/legal advice where noted.
Should I use Law of Sines instead of Law of Cosines?
Use Law of Cosines when you need Find side c from a, b, C. Use Law of Sines when you need Find sides from a, A, B. They share a category (Calculate) but not the same job.
What are the limits of Law of Cosines?
Runs locally in the browser. Invalid input disables or fails visibly. Not medical/legal advice where noted. Also: Solve side c from a, b, and included angle C via c² = a² + b² − 2ab cos(C). Degrees or radians per your inputs.