Triangle Calculator — Solve SSS, SAS, ASA, AAS and SSA

This triangle calculator solves any triangle from three known values, as long as one of them is a side: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA or AAS), or two sides and an angle that is not between them (SSA). It returns every missing side and angle plus the area, perimeter, all three heights, the inradius and circumradius, and whether the triangle is acute, right or obtuse.

How to use this tool

1. Label the triangle: side a is opposite angle A, side b opposite B and side c opposite C.
2. Enter exactly three values, including at least one side, and leave the rest empty.
3. Read the missing sides and angles, area, heights and type.
4. If two triangles fit your SSA values, both are listed in the table.

Formula

Law of cosines: c² = a² + b² − 2ab·cos C · Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C

SSS and SAS use the law of cosines; ASA, AAS and SSA use the law of sines with A + B + C = 180°. Area comes from Heron's formula, the height to side a is 2 × area ÷ a, the inradius is area ÷ (perimeter ÷ 2) and the circumradius is a ÷ (2 sin A). In the SSA case sin B = b·sin A ÷ a can give no triangle, one, or two (B and 180° − B).

Example

With sides a = 5, b = 7, c = 8, cos B = (5² + 8² − 7²) ÷ (2·5·8) = 0.5, so B = 60°; the other angles are A ≈ 38.21° and C ≈ 81.79°. The area is ½ × 5 × 8 × sin 60° ≈ 17.32, the perimeter 20, and the triangle is acute and scalene.