Triangle Type Calculator
Classify by sides and angles
Enter Three Sides
Triangle Diagram
Triangle Classification
Triangles can be classified in two main ways: by the lengths of their sides, and by the measures of their angles.
Classification by Sides
- Equilateral: All three sides are equal (a = b = c). All angles are 60°.
- Isosceles: Two sides are equal. The angles opposite the equal sides are also equal.
- Scalene: All three sides have different lengths. All three angles are different.
Classification by Angles
- Acute: All three angles are less than 90°.
- Right: One angle is exactly 90°. The side opposite the right angle is the hypotenuse.
- Obtuse: One angle is greater than 90° (and the other two are acute).
Combined Classifications
A triangle can have both classifications. Examples:
- Acute Scalene: All angles < 90°, all sides different
- Right Isosceles: One 90° angle, two equal sides (45-45-90 triangle)
- Obtuse Isosceles: One angle > 90°, two equal sides
Frequently Asked Questions
How do I classify a triangle?
Compare the side lengths to classify by sides, then calculate or measure the angles to classify by angles.
Can a triangle be both isosceles and right?
Yes, a 45-45-90 triangle is both isosceles (two equal sides) and right (one 90° angle).
Is an equilateral triangle also isosceles?
Technically yes, since an equilateral triangle has two (actually three) equal sides. However, we typically classify it as equilateral.
Can a triangle be obtuse and equilateral?
No, equilateral triangles always have all angles equal to 60°, so they are always acute.
How do I know if a triangle is obtuse?
Calculate all angles. If the largest angle is greater than 90°, the triangle is obtuse. Or check if a² + b² < c² (where c is the longest side).
What's the most common triangle type?
Scalene triangles are most common in general cases since they require no special relationships between sides or angles.