How do I find the angles from three sides?

By the law of cosines: cos A = (b²+c²−a²)/(2bc), then take the inverse cosine. Choose SSS and all three angles are computed.

Why can SSA have two solutions?

With two sides and a non-included angle the unknown angle can be acute or its obtuse supplement — the “ambiguous case”. The tool reports the alternative value of B when one exists.

How do I know three lengths form a triangle?

Each pair must sum to more than the third side; otherwise the tool says no triangle exists.

How is the circumradius calculated?

R = abc / (4·Area), and the inradius is r = Area / s with s the semi-perimeter. Both are shown.

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🔺Triangle Solver - Law of Sines and Law of Cosines Calculator

Give any three elements of a triangle (including at least one side) and the rest are solved for you: all three sides and angles, area, perimeter, the three heights, circumradius R and inradius r, plus whether the triangle is acute, right or obtuse.

Free · No sign-up · Runs in your browserLast updated: 2026-10-26

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How to use Triangle Solver

1Choose what you know: SSS, SAS, ASA, AAS or SSA
2Enter the three known values (angles in degrees)
3Read every side, angle and derived quantity

FAQ

How do I find the angles from three sides?: By the law of cosines: cos A = (b²+c²−a²)/(2bc), then take the inverse cosine. Choose SSS and all three angles are computed.
Why can SSA have two solutions?: With two sides and a non-included angle the unknown angle can be acute or its obtuse supplement — the “ambiguous case”. The tool reports the alternative value of B when one exists.
How do I know three lengths form a triangle?: Each pair must sum to more than the third side; otherwise the tool says no triangle exists.
How is the circumradius calculated?: R = abc / (4·Area), and the inradius is r = Area / s with s the semi-perimeter. Both are shown.