Free Classifying Triangles Calculator

Classifying Triangles by Sides and Angles

Welcome to the Classifying Triangles Calculator, a free triangle type finder online that helps you name any triangle based on its lengths or angles. Whether you need triangle classification by sides or triangle classification by angles, this tool provides instant and accurate identification. By entering a few measurements, you can quickly identify triangle type and learn more about its properties.

Triangle Classification by Sides

When you classify a triangle by its sides, you count how many sides share the same length:

• Equilateral triangle: All three sides are equal. Accordingly, each interior angle is also equal, measuring $60^{\circ}$.
• Isosceles triangle: Exactly two sides have the same length, while the third side differs. The angles opposite the equal sides are also equal.
• Scalene triangle: No side lengths are equal. All three sides and all three angles are different.

Triangle Classification by Angles

Look at the angle sizes to place the triangle into one of these three groups:

• Acute triangle: Every interior angle is less than $90^{\circ}$. The triangle is entirely "sharp‑angled".
• Obtuse triangle: One angle exceeds $90^{\circ}$, creating a "blunt" corner.
• Right triangle: One angle measures exactly $90^{\circ}$, forming a right angle. The side opposite this angle is the hypotenuse.

Remember, the sum of the three angles in any triangle is always $180^{\circ}$, a fact that the calculator uses to validate your input.

Combined Naming (Sides + Angles)

A more descriptive name can be created by combining the side and angle classifications. The table below lists every possible combination:

Combined Name	Side Property	Angle Property
Equilateral	All sides equal	All angles equal (each $60^{\circ}$)
Acute Scalene	All sides different	All angles less than $90^{\circ}$
Obtuse Scalene	All sides different	One angle greater than $90^{\circ}$
Right Scalene	All sides different	One angle exactly $90^{\circ}$
Acute Isosceles	Two sides equal	All angles less than $90^{\circ}$, two equal
Obtuse Isosceles	Two sides equal	One angle greater than $90^{\circ}$, two equal
Right Isosceles	Two sides equal	One angle exactly $90^{\circ}$, the other two equal

For instance, a triangle with two equal sides and a $90^{\circ}$ angle is a Right Isosceles triangle — a common shape in geometry.

How to Use the Triangle Type Identifier

To get the triangle classification, provide any one of these data sets:

• Three side lengths
• One angle and two sides
• Two angles

Once you submit the values, the calculator will:

• Show the triangle's name (by sides, by angles, and the combined form)
• Calculate any missing parameters (such as the third angle or the other sides)
• Display a sketch of the triangle

As a concrete example, entering side lengths $3$, $4$, and $5$ returns Right Scalene and computes the angles as approximately $36.87^{\circ}$, $53.13^{\circ}$, and $90^{\circ}$. Similarly, inputting two angles automatically determines the third angle and completes the classification.

Note that if you supply the three sides, the tool can work out the angles using the law of cosines. The opposite, however, is not possible — angle measures alone cannot give you the side lengths; a scale (at least one side) is required.

Why Use This Tool?

Manually checking side equalities and angle thresholds can be tedious, particularly with decimal values or mixed units. This triangle classification calculator automates the process, delivering error‑free results in seconds. Whether you're completing homework, preparing a lesson, or verifying measurements for a project, knowing the exact triangle type helps you apply the correct formulas and avoid mistakes.

We hope this guide has clarified the two main methods of triangle classification. Feel free to experiment with different inputs to see the wide variety of triangle names that exist!