Classifying Triangles Calculator

A classifying triangles calculator is an online geometry math tool that takes three measurements of a triangle and returns its full category. The triangle is the simplest polygon, so its complete classification needs only two pieces: a name by sides (scalene, isosceles, or equilateral) and a name by angles (acute, right, or obtuse). The calculator draws a labeled diagram with vertices A, B, C and side lengths a, b, c, which is helpful for students checking homework and teachers preparing worksheets.

Compare each pair of sides by measuring their lengths. An equilateral triangle has all three side lengths equal, an isosceles triangle has exactly two sides equal, and a scalene triangle has all three sides different. In geometry problems where measurements are rounded, the equality tolerance setting in the calculator decides how close two values must be to count as equal, which keeps the final solution stable.

Look at the largest of the three interior angles at vertices A, B, and C. An acute triangle has every angle measure below 90 degrees, a right triangle has exactly one angle of 90 degrees, and an obtuse triangle has one angle greater than 90 degrees. When you start with three side lengths instead of angle measurements, the law of cosines formula recovers each angle so you can still apply this same rule.

Yes — the 45-45-90 right isosceles triangle is the classic example. It has two equal legs and a 90 degree angle between them, so the shape is right by angles and isosceles by sides. In geometry, this combined classification is simply written "right isosceles". An equilateral triangle, on the other hand, is always acute because all three interior angles equal 60 degrees.

The triangle inequality is a foundational geometry rule stating that the sum of any two side lengths must be strictly greater than the third side. If a + b is not greater than c, or any other pair fails the formula, the three lengths cannot close into a triangle shape — they collapse to a straight line instead. The calculator will warn that the inputs are invalid in that case.

No. An equilateral triangle has all three side lengths equal, which forces the three interior angles at vertices A, B, and C to be equal as well. Since the angles must sum to 180 degrees, each one measures exactly 60 degrees. That makes every equilateral triangle acute, so a right equilateral or obtuse equilateral shape simply cannot exist in flat plane geometry.

The area is computed with Heron's formula, a classic geometry result. The calculator first finds the semi-perimeter s = (a + b + c) / 2, then applies area = √(s(s - a)(s - b)(s - c)) to produce the final solution. Because the formula uses only side lengths, the same approach works for any acute, right, or obtuse triangle — which is why many students learn Heron's method before vertex-coordinate area formulas.

Two angles determine the third angle because every flat triangle has a 180 degree angle sum. That fixes the triangle shape, and one known side fixes the scale. The calculator then uses the law of sines to calculate the other two side lengths, so an AAS or ASA entry can return a real perimeter, area, diagram, and classification instead of only a side-ratio estimate.

Two triangles that share the same three angles are similar in geometry — they have the same shape but can scale to any size. That is why the AAA input method returns normalized side lengths with a = 1, while the side ratios b/a and c/a stay accurate. Add at least one real measurement of a side to pin down the actual size; without it, a worksheet question asking "what is the length of side b?" has no unique numeric answer, which is a distinction many students miss at first.