Law of sines calculator
Choose where the known side sits, opposite angle A or between the two angles, then enter both angles and its length.
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How to use it
- Enter known side, angle a, angle b and known side length.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
C = 180° - A - B, then a / sin A = b / sin B = c / sin C = 2R, where R is the circumradius. Area = ½ × a × b × sin C.
Example
Inputs: Known side = Side a, opposite angle A (AAS), Angle A = 30 °, Angle B = 45 °, Known side length = 10. Result: Side b: 14.1421; Side a: 10; Side c: 19.3185.
Limits and caveats
- For two sides and a non-included angle (SSA), use the SSA triangle calculator, since that case can have two answers.
- Angles are in degrees.
Questions about this tool
When do I use the law of sines?
When you know two angles and any side, or two sides and an angle opposite one of them.
What is the difference between ASA and AAS?
In ASA the known side lies between the two angles, in AAS it is opposite one of them. Both give exactly one triangle.
How is the law of sines linked to the circumcircle?
The ratio a / sin A equals the diameter of the circle through all three vertices, which is 2R.