Welcome to Calcugo's classifying triangles calculator, which can help you name a chosen triangle. Triangles have two types of names. With our calculator, you'll learn how to classify triangles by their sides. Then, you'll also find out how to name them based on the sizes of their angles. Give it three side lengths (or three angles) and it instantly tells you both names — for example, a right scalene triangle.
How to classify a triangle by its sides?
To classify a triangle by its sides, you need to check how many sides have equal lengths:
- Equilateral triangle – has three equal sides (and three equal angles);
- Isosceles triangle – has two equal sides; and
- Scalene triangle – has no equal sides.
How to classify a triangle by its angles?
There are three types of triangles based on their angles:
- If all of the triangle angles are less than 90°, then it's an acute triangle;
- If one of the angles measures more than 90°, it's an obtuse triangle; and
- If one of the angles is exactly 90°, then it's a right triangle.
When you enter three side lengths, the calculator finds each interior angle with the law of cosines, so it can name the triangle by its angles too. When you enter the angles directly, it checks that they add up to 180° and names the triangle by its sides from how many angles are equal.
What are the two ways triangles are named?
Now you know that triangles can be classified by their sides or angles. A triangle can be equilateral, isosceles, or scalene, but also acute, obtuse, or right. When you try using our classifying triangles calculator, you'll also find out that you can mix these names to give a more detailed description:
| Name | Sides | Angles |
|---|---|---|
| Equilateral | all equal | all equal to 60° |
| Acute scalene | all different | all less than 90° |
| Obtuse scalene | all different | one larger than 90° |
| Right scalene | all different | one equal to 90° |
| Acute isosceles | two equal | all less than 90° and two equal |
| Obtuse isosceles | two equal | one larger than 90° and the other two equal |
| Right isosceles | two equal | one equal to 90° and the other two equal |
🔎 An equilateral triangle is a special case: because its three sides are equal, its three angles are automatically equal to 60°, so it is always acute. That's why we simply call it "equilateral" rather than "acute equilateral".
How to use the classifying triangles calculator?
Using the calculator takes only a few seconds:
- Choose whether you want to classify by sides or by angles.
- For the sides mode, pick your unit system (metric or US/imperial), then enter the three side lengths a, b, and c. For the angles mode, enter the three angles α, β, and γ in degrees (they must add up to 180°).
- Read the combined name (e.g., "Right scalene"), along with the classification by sides and by angles. In the sides mode you also get the perimeter, the area (via Heron's formula), and all three interior angles.
FAQs
- What are the two ways to classify a triangle?
- By its sides (equilateral, isosceles, or scalene) and by its angles (acute, right, or obtuse). Combining both gives a full description such as "obtuse isosceles".
- Can a triangle be both isosceles and right?
- Yes. A right isosceles triangle has one 90° angle and two equal 45° angles, with the two legs equal in length — the classic 45-45-90 triangle.
- Is an equilateral triangle acute?
- Always. Its three angles are each 60°, which is less than 90°, so an equilateral triangle is a special acute triangle. We name it simply "equilateral".
- Do 3, 4, and 5 make a special triangle?
- Yes. Because 3² + 4² = 5², the largest angle is exactly 90°, and since all three sides differ, it is a right scalene triangle.
- What if my three angles don't add up to 180°?
- Then they cannot form a valid triangle. The sum of the interior angles of any triangle in the plane is always exactly 180°, so the calculator will ask you to correct the values.