Obtuse Triangle Calculator

Background.

An obtuse triangle has one angle wider than a right angle, and that one fact changes how the whole shape behaves. Its longest side lies opposite the wide angle. Two of its three heights land outside the triangle, so working out the area as half base times height can mean extending the base line. Even the centre of the circle through its corners sits outside it. Knowing which kind of triangle you have is often the first step in a geometry problem, and the three side lengths settle it without a protractor.

The test is a short extension of Pythagoras. Take the longest side, call it c, and compare its square with the squares of the other two added together. If a² + b² equals c², the angle opposite c is exactly 90°. If the sum is larger, every angle is below 90° and the triangle is acute. If the sum is smaller, the angle opposite c has opened past 90° and the triangle is obtuse. The law of cosines shows why: c² = a² + b² − 2ab cos C, and cos C turns negative precisely when C passes 90°.

The same three numbers give the triangle's other name, based on its sides: equilateral when all three match, isosceles when two do, scalene when none do. Both names are reported together, as in scalene obtuse or isosceles right, along with the perimeter.

Three lengths form a triangle only if the two shorter ones add up to more than the longest, and anything else is refused. The comparisons are exact, which suits textbook values; with sides you have measured, a nearly right triangle will usually come out as narrowly acute or narrowly obtuse.

What is obtuse triangle calculator?

An obtuse triangle is a triangle with one interior angle greater than 90°. Because the three angles add up to 180°, it can have only one such angle, and the other two must be acute. In terms of sides, a triangle is obtuse exactly when the square of its longest side is greater than the sum of the squares of the other two. By side type it can be scalene or isosceles, but never equilateral, since every angle of an equilateral triangle is 60°.

How to use this calculator.

1. 01Enter the three side lengths, in any order and all in the same unit. The sides are sorted automatically, so you do not need to put the longest in side c.
2. 02If the entry is refused, check the triangle inequality: the two shorter sides must add up to more than the longest. Lengths of 2, 3 and 5 lie flat and cannot enclose an area.
3. 03Read the classification, which pairs a side type (equilateral, isosceles or scalene) with an angle type (acute, right or obtuse), and the perimeter in your unit.
4. 04With measured rather than exact sides, treat a result near the boundary with care. A corner meant to be square that measures 3.01, 4 and 5 is reported as acute, because 3.01² + 4² = 25.0601 is just over 25.

The formula.

The three sides are sorted so that c is the longest. If a + b ≤ c the input is refused, because the lengths cannot close into a triangle. The angle type comes from comparing a² + b² with c²: equal means right, greater means acute, smaller means obtuse. This follows from the law of cosines, c² = a² + b² − 2ab cos C, because the cosine of the angle opposite c is negative only when that angle is more than 90°. Only the largest angle needs checking, since it is always the one opposite the longest side. The side type is settled separately by checking which lengths are exactly equal, and the perimeter is a + b + c. No angles are reported; if you want the obtuse angle itself, it is C = arccos((a² + b² − c²) ÷ 2ab).

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.