Triangle Calculator

A triangle is fully determined by three well-chosen values, and this triangle calculator covers all five classic cases: three sides (SSS), two sides with the included angle (SAS), two angles with the included side (ASA), two angles with a non-included side (AAS), and the ambiguous two sides with a non-included angle (SSA). Pick the case, type the three known values, and the calculator returns every side, every angle in degrees, the area, the perimeter and all three heights — together with an SVG diagram drawn to the exact shape of your triangle, vertices and sides labeled.

The working is never hidden. Sides found with the law of cosines show the c² = a² + b² − 2ab·cos C substitution, angles recovered from three sides show their cosine value, sides from the law of sines show the a / sin A = c / sin C proportion, and the area line states whether Heron's formula (for SSS) or ½·a·b·sin C was used. Input is validated first: the triangle inequality for SSS, and the rule that two angles must sum to less than 180° for ASA and AAS.

The SSA case gets special care because it is genuinely ambiguous: the same two sides and non-included angle can produce two different triangles, exactly one, or none at all. This calculator reports the situation honestly — when sin B comes out above 1 you get a clear no-solution message, and when both an acute and an obtuse angle B fit, both complete triangles are computed and drawn side by side.

For the special case of a 90° corner — finding a hypotenuse or a missing leg from a² + b² = c² with exact radical answers like 5√2 — the dedicated Pythagorean theorem calculator on this site is the sharper tool. Everything runs locally in your browser: nothing is uploaded, there is no registration, and you can solve as many triangles as you like on desktop and mobile alike.