Triangle Calculator

SSS means you know all 3 sides — use the law of cosines to find each angle. SAS means you know 2 sides and the angle BETWEEN them — use law of cosines for the third side. ASA means you know 2 angles and the side BETWEEN them — the third angle is 180° minus the other two, then use law of sines for the missing sides.

For any triangle, the sum of any two sides must be greater than the third. If a = 1, b = 2, c = 10, no triangle exists — sides 1 and 2 together can't reach the endpoints of side 10. The calculator catches this and tells you the inputs are invalid.

Heights (altitudes) are perpendicular distances from each vertex to the opposite side — they're what's in the area formula. Medians connect each vertex to the MIDPOINT of the opposite side. Angle bisectors split each vertex angle exactly in half and meet the opposite side at a different point. All three are different cevians from the same vertex.

The inradius (r) is the radius of the largest circle that fits INSIDE the triangle, tangent to all three sides — r = area / semi-perimeter. The circumradius (R) is the radius of the unique circle that passes through all three VERTICES — R = (a × b × c) / (4 × area). Useful for engineering, geometric proofs, and inscribed/circumscribed problems.

By sides: equilateral (3 equal), isosceles (2 equal), scalene (0 equal). By angles: acute (all < 90°), right (one = 90°), obtuse (one > 90°). Every triangle has BOTH classifications — e.g. 'isosceles right triangle' or 'scalene obtuse triangle'. The calculator returns both with a one-line reason for each.

SSA is the ambiguous case — it can have zero, one, or two valid triangle solutions depending on the values. This calculator covers SSS, SAS, ASA, and right triangles, which all have unique solutions. For SSA, sketch the configuration first to see how many triangles exist.

JavaScript uses IEEE 754 double-precision floating-point, accurate to ~15 significant digits. For real geometry, surveying, engineering drawings — far more precise than measurement tools. In Customize mode you can pick the display precision (2 / 3 / 4 / 6 decimal places).