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
- Confirm you need Law of Cosines, not Law of Sines (Find sides from a, A, B.). Address: /calculate/law-of-cosines.
- Enter the numbers or dates Law of Cosines uses. Find side c from a, b, C.
- 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.
- 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.
- 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.