Law of Sines Calculator

The law of sines states that each side of a triangle divided by the sine of its opposite angle gives the same value. That common ratio, a over sin A equals b over sin B equals c over sin C, ties every side and angle together so one missing part can be found from the rest.

It always needs a matched pair, a known angle A and the side a opposite it, plus exactly one more value. Add angle B to find its opposite side b, or add side b to find its opposite angle B. From that pair and one extra the whole triangle is solved.

Angle C is whatever is left after A and B, so C equals 180 minus A minus B. Side c comes from the common ratio, side a divided by sin A, multiplied by the sine of angle C. That is why every result depends on the first angle-side pair being correct.

Finding an angle from a side uses the inverse sine, which has two possible answers between 0 and 180 degrees, known as the ambiguous case. This tool reports the acute solution because it is the common one. If your triangle is obtuse at B, the true angle is 180 minus the value shown.

If the side opposite the unknown angle is too long, the sine ratio needed exceeds one, which is impossible, so no triangle exists and the calculator shows an error. It also errors when angles A and B add up to 180 degrees or more, since that leaves no room for angle C.

You enter and read angles in degrees. Internally each angle is converted to radians by multiplying by pi over 180 before the sine is taken, then results are converted back to degrees, so you never handle radians yourself.

Yes. Enter the angle opposite your known side as angle A with that side as a, then enter the other known angle as angle B. Angle C follows automatically, and both remaining sides are computed from the ratio.

The law of sines needs an angle paired with its opposite side. If you only know three sides, or two sides with the angle between them, that pairing is missing and you should start with the law of cosines, then switch back here for the remaining parts.

Every angle and side is rounded to four decimal places to keep the display clean while hiding floating point noise. That is far more precision than most drawing or construction work requires.