Last updated October 10, 2026 · Report an error
Every triangle can be classified two completely independent ways: by its sides (scalene: all three different lengths, isosceles: exactly two equal, equilateral: all three equal) and by its angles (acute: all three angles under 90°, right: exactly one angle equal to 90°, obtuse: exactly one angle over 90°). Because these two classification systems are independent, a full description of a triangle's shape actually needs both labels together — "isosceles right triangle" and "scalene obtuse triangle" are both perfectly valid, complete descriptions.
How it works
Enter three side lengths, three angles, or both. If you provide sides, the calculator first verifies they satisfy the triangle inequality (each pair of sides must sum to more than the third) before comparing the three lengths for equality to determine the side-classification. If angles are provided (or derivable from the sides via the Law of Cosines), it checks whether all three are under 90° (acute), one is exactly 90° (right), or one exceeds 90° (obtuse) — angles always sum to 180° in a valid triangle, which is used as a consistency check.
- Enter given information.
- Enter side a.
- Enter side b.
- Enter side c.
- Enter angle A.
- Enter angle B.
- Enter angle C.
- Click Calculate to see your results.
Examples
3-4-5 triangle
By sides: scalene (3, 4, and 5 are all different). By angles: right, since 3² + 4² = 9 + 16 = 25 = 5², satisfying the Pythagorean theorem.
Equilateral 5-5-5
By sides: equilateral (all three sides equal 5). By angles: acute, since an equilateral triangle always has three 60° angles, and 60° < 90°.
Isosceles 5-5-9
By sides: isosceles (two sides equal 5). By angles: obtuse — using the Law of Cosines on the angle opposite the side of length 9: cos(C) = (5²+5²−9²)/(2×5×5) = (50−81)/50 = −0.62, so C = arccos(−0.62) ≈ 128.3°, which is greater than 90°.
Who should use it
- Geometry homework requiring a full triangle classification.
- Verifying a constructed or measured triangle's type.
- Teaching the distinction between the two independent classification systems.
Industry applications
- Geometry education
- Engineering and drafting (verifying structural triangle shapes)
Advantages
- Classifies by both systems (sides and angles) in one step.
- Shows the underlying reasoning, not just a label.
Limitations
- Requires either valid angle measures or side lengths that satisfy the triangle inequality — invalid input can't be classified.
Common mistakes to avoid
- Assuming a triangle can only be classified one way — every triangle actually has both a side-classification and an angle-classification simultaneously.
- Assuming isosceles or scalene triangles are always a specific angle type — only equilateral triangles are guaranteed to always be acute.
- Forgetting to verify the triangle inequality first when given three raw side lengths, since not every three numbers actually form a valid triangle.
Best practices
- Always check the triangle inequality first when starting from raw side lengths, before attempting to classify the shape.
- Use the sum-of-squares shortcut (comparing the longest side squared to the sum of the other two squared) as a fast way to determine acute/right/obtuse from sides alone.
- State both classifications together (e.g., "isosceles right triangle") for a complete description.
Tips
- Need to first confirm three lengths actually form a valid triangle? Use the Triangle Inequality Theorem Calculator.