Scalene Triangle Calculator

Background.

A scalene triangle is the ordinary case: three sides of different lengths, and with them three different angles. Pick any three lengths at random that can close into a triangle and you will almost always get one. Equal sides are the special case, and a triangle with even two of them has a line of symmetry that a scalene one lacks.

That lack of symmetry is what makes scalene triangles a little more work. In an isosceles triangle the altitude from the apex also bisects the base and the apex angle; in a scalene triangle the altitudes, medians and angle bisectors from each corner are all different lines with different lengths. The order of the sides still tells you a lot, though. The longest side always faces the largest angle and the shortest side the smallest, so the three angles of a scalene triangle line up in the same order as its sides.

A scalene triangle can be acute, right or obtuse, and the side lengths alone decide which. Square the two shorter sides and add them; if the total equals the square of the longest side, the largest angle is exactly 90°. The best-known example, 3, 4, 5, is scalene, and so is every right triangle with whole-number sides, because a right triangle with two equal legs has a hypotenuse of leg × √2, which is never a whole number when the legs are.

The checks here are exact. Lengths of 5 and 5.0001 count as different, so a triangle measured with a tape and found to be scalene by a fraction of a millimetre may be isosceles in intent. Three lengths that cannot close up into a triangle at all are refused.

What is scalene triangle calculator?

A scalene triangle is one whose three sides all have different lengths. Because the angle opposite a side grows with that side, its three interior angles are also all different, and it has no line of symmetry. Classifying a triangle from its sides combines two independent labels: scalene, isosceles or equilateral by how many sides match, and acute, right or obtuse by the size of its largest angle, which the side lengths fix completely.

How to use this calculator.

1. 01Enter the three side lengths as sides a, b and c in any order and in any one unit; the page sorts them itself.
2. 02If you measured a physical object, enter the lengths at the precision you actually measured. Extra digits from a calculator can turn an intended isosceles or right triangle into a scalene or acute one.
3. 03Read the classification, which gives both the side label and the angle label, for example scalene obtuse triangle.
4. 04Read the perimeter, the sum of the three sides in the same unit you entered. If the page refuses the lengths, the two shorter sides do not add up to more than the longest.

The formula.

The sides are first sorted so that c is the longest. A triangle exists only if a + b > c; when a + b equals or falls short of c, the lengths collapse into a line or cannot meet, and the page stops there. The side label counts matches: all three equal is equilateral, exactly two equal is isosceles, none equal is scalene. The angle label compares a² + b² with c², which is the law of cosines applied to the largest angle C: c² = a² + b² − 2ab cos C. If a² + b² = c², cos C is zero and C is 90°; if a² + b² is larger, C is acute and so are the other two; if smaller, C is obtuse. The perimeter, reported alongside, is simply the three sides added together.

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.