Triangle solver
Give any three measurements; get every side, angle and the area back.
Side a
Side b
Side c
Angle A
Angle B
Angle C
Area
Heron's formula
Perimeter
Solved by the Law of cosines (SSS). This is a right triangle.
To scale
How it works
Three independent measurements fix a triangle completely — with one famous exception. Which three you have determines which law does the work.
Law of sines: a / sin A = b / sin B = c / sin C
Law of cosines: c² = a² + b² − 2ab·cos C
Heron's area: s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)) Which case is which
- SSS — three sides
- Law of cosines, rearranged to give each angle. Always exactly one triangle.
- SAS — two sides and the angle between them
- Law of cosines for the third side, then the law of sines. Always exactly one triangle.
- ASA / AAS — two angles and any side
- The third angle is 180° minus the other two; the law of sines gives the remaining sides.
- SSA — two sides and an angle not between them
- The ambiguous case: zero, one or two triangles can fit. This solver asks you to disambiguate rather than silently pick one.
The triangle inequality
Any two sides must add to more than the third. 3, 4 and 8 cannot form a triangle — the short sides cannot reach across. The solver checks this before doing anything else.
Right triangles
When one angle is 90°, the law of cosines collapses to a² + b² = c², because cos 90° = 0. Pythagoras is the special case, not a separate rule.