Classifying Triangles Calculator
The classifying triangles calculator can help you determine the name of a triangle based on the lengths of its sides or the sizes of its angles.
The right-angle test
| Two shorter sides squared | 50 |
| Longest side squared | 36 |
| Verdict | sum is larger — acute |
Working
| Semi-perimeter s | 8 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 12 |
| Height on side a | 2 × area ÷ a = 4.8 |
| Inradius | area ÷ s = 1.5 |
| Circumradius | abc ÷ 4·area = 3.125 |
| Angle sum | 180° (always 180°) |
The formula
compare the sides, then test a² + b² against c²
Two independent classifications
Every triangle gets one label for its sides — equilateral (all three equal), isosceles (exactly two) or scalene (none) — and one for its largest angle: acute, right or obtuse. The two are largely independent, so a triangle can be an obtuse isosceles or a right scalene. The only impossible combinations involve equilateral, which is always acute.
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.