Classifying Triangles Calculator

Background.

Three lengths settle a triangle completely. Once the sides are known every angle is fixed, so both of the ways geometry names triangles, by how many sides are equal and by the size of the largest angle, can be read straight off the side lengths without a protractor.

The side test is a matter of matching: three equal sides make an equilateral triangle, exactly two an isosceles one, and none a scalene one. The angle test is where some arithmetic comes in. The largest angle always sits opposite the longest side, so it is the only angle worth checking. Square the two shorter sides and add them, then compare the total with the square of the longest. Equal means the angle is exactly 90° and the triangle is right-angled, the converse of Pythagoras' theorem. More means the largest angle is under 90°, so every angle is, and the triangle is acute. Less means the largest angle is over 90° and the triangle is obtuse.

Builders use the right-angle case every day. Mark 3 units along one wall and 4 along the other; when the diagonal between the marks measures exactly 5, the corner is square. Scaled to 0.9 m, 1.2 m and 1.5 m, the same check sets out a floor slab.

Before any of that, the three lengths must form a triangle at all. The two shorter sides together have to be longer than the longest; if they only equal it, the shape collapses into a straight line, and the page refuses it.

All the comparisons are exact. That suits whole numbers and terminating decimals, but it has a consequence for shapes whose sides involve square roots, explained in the questions below.

What is classifying triangles calculator?

Classifying a triangle means naming it in two independent ways. By its sides it is equilateral (all three equal), isosceles (exactly two equal) or scalene (all different). By its angles it is acute (every angle under 90°), right (one angle of exactly 90°) or obtuse (one angle over 90°). The full name puts the two together, as in 'isosceles obtuse triangle'. Not every pairing is possible: an equilateral triangle has three angles of 60°, so it is always acute.

How to use this calculator.

1. 01Enter the three side lengths in any order. The page sorts them itself, so side c does not need to be the longest.
2. 02Use one unit for all three. Mixing centimetres with metres still produces a classification, but of a different triangle.
3. 03Type the lengths as precisely as you know them. Equality is tested exactly, so 5 and 5.0 count as equal while 5 and 5.001 do not.
4. 04Read the classification, side type first and angle type second, and the perimeter, which is in the same unit as the sides.

The formula.

Sort the sides so that a ≤ b ≤ c. First comes the triangle inequality: a + b must be greater than c, or no triangle exists. Then a² + b² is compared with c². The law of cosines shows why this works. It says c² = a² + b² − 2ab·cos C, where C is the angle opposite the longest side, so a² + b² − c² equals 2ab·cos C. That is positive when C is under 90°, zero when C is exactly 90° and negative when C is over 90°. Because 2ab is always positive, the sign of a² + b² − c² alone decides acute, right or obtuse, with no need to calculate any angle. The side label comes from separate equality checks between the three lengths and does not affect the angle test. The perimeter is a + b + c.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.