Law of Sines/Cosines Calculator
Solve any triangle from three sides (SSS), two sides and the included angle (SAS), or two angles and a side (AAS), using the laws of sines and cosines.
Inputs explained
- Known values — Which combination of sides and angles you already know.
- Side a — A known side length. Always required.
- Side b — Second side (SSS and SAS modes).
- Side c — Third side (SSS mode). The three sides must satisfy the triangle inequality.
- Included angle C (between a and b) — The angle between sides a and b (SAS mode).
- Angle A (opposite side a) — Angle opposite side a (AAS mode).
- Angle B (opposite side b) — Angle opposite side b (AAS mode). A + B must be less than 180°.
How to use it
- Fill in the fields above — each input has a hint describing exactly what to enter
- Press Calculate to get your result instantly, right on this page
- Copy the result, save the tool to favorites, or share and embed it anywhere
Understanding the result
Example: With a = 5, b = 7, and included angle C = 60°, the law of cosines gives c ≈ 6.245.
Frequently asked questions
When does this calculator use the law of cosines instead of the law of sines? The law of cosines is used when you know all three sides (SSS) or two sides and the included angle (SAS), because the law of sines alone can't solve those cases directly.
Why might there be two possible answers for an angle in some AAS cases? When solving with two angles and a side, ambiguous cases can occasionally arise from the law of sines, but supplying two angles plus a side generally fixes the triangle uniquely since the third angle is determined by the angle sum of 180°.
Is the Law of Sines/Cosines Calculator free to use? Yes — it is completely free, with no sign-up, no download and no usage limits. You can use it as often as you need.
Is my data private? Yes. The calculation runs entirely in your browser — the values you enter are never sent to our servers, stored or shared with anyone.
What information do I need? Just the following: Known values, Side a, Side b, Side c, Included angle C (between a and b), Angle A (opposite side a), Angle B (opposite side b). Each field includes a hint explaining exactly what to enter.
Can I use it on my phone? Yes — the tool is fully responsive and works on any device, and the same calculator is available in the EasyWorkCalcs mobile app.
Privacy
Everything you enter into the Law of Sines/Cosines Calculator is processed entirely in your browser. Nothing is uploaded, stored or shared — your data stays on your device.