Triangle Area Calculator
Calculate triangle area, perimeter, angles, altitudes, circumradius, inradius, and classification. Supports base-height, Heron's formula, and SAS methods with unit selection and a complete 15-prop..
Classifying Triangles Calculator
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.
Planning notes, formulas, and examples
About the Classifying Triangles Calculator
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, it gives instant, thorough classification.
When This Page Helps
Use this when you need to identify a triangle by both side type and angle type without manually checking every rule one by one. It is useful in coursework and drafting because the classification, angle totals, and side relationships all come from the same triangle data.
How to Use the Inputs
- Select whether you want to enter 3 sides or 3 angles.
- Enter the values or click a preset for common triangle types.
- For angle input, ensure the three angles sum to 180°.
- View the classification banner showing the triangle type by sides and angles.
- Explore computed properties: area, perimeter, inradius, circumradius, and altitudes.
- Check the decision table to see which classification tests pass.
Formula used
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.Example Calculation
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.
Tips & Best Practices
- A triangle is equilateral if and only if all three angles are 60°.
- To check for a right triangle from sides, verify a² + b² = c² (where c is the longest side).
- An isosceles right triangle always has angles 45°-45°-90°.
- The triangle inequality states a + b > c for all side pairings — inputs that violate this are rejected.
- Obtuse triangles have the circumcenter outside the triangle.
When To Use This Calculator
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. Use it when you need a repeatable calculation in the math / geometry category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.
How To Check The Result
Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.
Practical Notes
Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.
Sources & Methodology
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Frequently Asked Questions
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.
More in this topic
Law of Cosines Calculator — Solve Any Triangle
Solve any triangle using the law of cosines. Find unknown sides or angles, compute area, perimeter, circumradius, inradius, and classify the triangle type.
Circumscribed Circle Calculator
Calculate the circumscribed circle (circumcircle) of a triangle or regular polygon. Find the circumradius, circle area, area ratios, and perimeter comparisons in one view.