Classify any triangle by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Enter 3 sides or 3 angles to see full properties and classification.
Triangles are the simplest polygons, yet they come in a rich variety of types depending on their side lengths and angles. Classifying a triangle is a foundational geometry skill taught from middle school through college. This calculator lets you classify any triangle two ways simultaneously: by its sides (equilateral, isosceles, or scalene) and by its angles (acute, right, or obtuse).
When you enter three side lengths, the calculator uses the law of cosines to derive all three interior angles, then checks the classification criteria automatically. Alternatively, you can enter three angles (which must sum to 180°) to classify the triangle and see proportional side lengths. Beyond just labeling the triangle, the tool computes area via Heron's formula, perimeter, inradius, circumradius, and all three altitudes.
Visual bars show side and angle proportions at a glance, while a decision table walks through each classification test so students can see exactly which criteria their triangle meets. A collapsible reference table summarizes all six triangle types with their properties. Whether you're a student learning geometry, a teacher preparing examples, or an engineer verifying a structural triangle, this calculator provides instant, thorough classification.
This classifying triangles calculator reduces manual rework when you need quick checks for assignments, exam prep, and design calculations. You can enter Input Mode and immediately see dependent measurements, validity checks, and geometry relationships in one place. That makes it easier to catch input mistakes early and confirm your final answer before moving to the next step.
By sides: Equilateral (a=b=c), Isosceles (exactly two equal), Scalene (all different). By angles: Acute (all < 90°), Right (one = 90°), Obtuse (one > 90°). Angle from sides: cos A = (b²+c²−a²) / (2bc). Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.
Result: For inputmode=5, the tool returns the solved classifying triangles outputs shown in the result cards.
This example uses a realistic input set from the calculator workflow. After entry, the calculator applies the built-in classifying triangles formulas and reports derived values, checks, and classifications automatically.
This page is tailored to classifying triangles, with outputs tied directly to the form fields (Input Mode). Instead of a one-line formula dump, it consolidates validation, derived metrics, and interpretation so you can solve and verify in one pass.
Use this tool for homework checks, worksheet generation, tutoring walkthroughs, and quick engineering geometry estimates. Presets and visual output blocks make it easier to compare scenarios and understand how each input affects the final result.
Keep units consistent, match each value to the correct field, and watch validity indicators before using the final numbers. If your case looks off, change one input at a time and use the output details to identify the mismatch quickly.
By sides — equilateral (all equal), isosceles (two equal), or scalene (all different). By angles — acute (all less than 90°), right (one equals 90°), or obtuse (one greater than 90°).
Yes. For example, a triangle with sides 2, 2, 3.5 has two equal sides (isosceles) and its largest angle exceeds 90° (obtuse).
Sort the sides so a ≤ b ≤ c. If a² + b² > c², all angles are less than 90° and the triangle is acute.
For triangles, they are the same — if all sides are equal, all angles are 60°, and vice versa. This equivalence does not hold for polygons with more sides.
In Euclidean geometry, the interior angles of any triangle always sum to exactly 180°. This is a consequence of the parallel postulate.
Yes — a 45-45-90 triangle is both. It has two equal legs and a right angle between them.