What this calculator does
A scalene triangle has three sides that are all different lengths, and as a result all three angles are different too. It is the least symmetric of the triangle types, unlike an isosceles triangle with two matching sides or an equilateral triangle with three.
This scalene triangle calculator takes three side lengths, works out the area with Heron’s formula, the three angles, and the perimeter, and then confirms whether the triangle you entered is actually scalene, in case two of the sides happen to match.
The formula
Heron’s formula finds the area from the half-perimeter s = (a+b+c)/2, as area = √(s(s−a)(s−b)(s−c)). The three angles then come from the law of cosines applied to each side in turn. A triangle is scalene only if all three sides are different; if any two match, it is isosceles instead, or equilateral if all three match.
| Term | Meaning |
|---|---|
| a, b, c | The three side lengths of the triangle, all different in a genuinely scalene triangle. |
| s | Half-perimeter, used inside Heron’s formula: (a + b + c) / 2. |
| Scalene | A triangle with no two sides, and therefore no two angles, equal. |
The inputs explained
| Field | What to enter |
|---|---|
| Side a | The length of the first side. |
| Side b | The length of the second side. |
| Side c | The length of the third side. |
When to use it
A surveyed plot with no matching sides
A block of land or triangular panel measured on site rarely has two sides come out exactly equal, so it is scalene by default, and this calculator gives its area and angles from the three measured sides alone.
Checking what is a scalene triangle from a set of measurements
Given three numbers, whether they actually describe a scalene triangle, as opposed to an isosceles one with two equal sides, is confirmed directly rather than left to eyeball.
Working a scalene triangle angles problem
A geometry question giving three unequal sides and asking for the angles is solved here without separately applying the law of cosines three times by hand.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Scalene triangle formula: area across a range of third sides
Two sides fixed at 5 and 7, with the third side varying across the range a valid triangle allows.
| Side c | Area | Is this triangle scalene? |
|---|---|---|
| 3 | 6.495 | Yes, all three sides are different lengths |
| 6 | 14.697 | Yes, all three sides are different lengths |
| 8 | 17.321 | Yes, all three sides are different lengths |
| 9 | 17.412 | Yes, all three sides are different lengths |
| 11 | 12.969 | Yes, all three sides are different lengths |
When does a triangle stop being scalene?
Two equal sides of 6 held fixed, with the third side a varying, to show the calculator correctly flag when the triangle is no longer scalene.
| Side a | Area | Is this triangle scalene? | Triangle shape by angle |
|---|---|---|---|
| 2 | 5.916 | No, this triangle has two or more equal sides | Acute |
| 4 | 11.314 | No, this triangle has two or more equal sides | Acute |
| 6 | 15.588 | No, this triangle has two or more equal sides | Acute |
| 8 | 17.889 | No, this triangle has two or more equal sides | Acute |
| 10 | 16.583 | No, this triangle has two or more equal sides | Obtuse |
Questions
What is a scalene triangle?
A scalene triangle is a triangle where all three sides are different lengths, and consequently all three angles are different as well. It has no line of symmetry.
What is a scalene triangle formula for area?
The same Heron’s formula used for any triangle: find the half-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)). No special adjustment is needed for a scalene triangle.
How can you tell if a triangle is scalene just from its angles?
If all three angles are different, the triangle is scalene. If exactly two angles match, it is isosceles, and if all three match at 60° each, it is equilateral.
Is a right-angled triangle ever scalene?
Yes. A right-angled triangle is scalene whenever its two legs are different lengths, which is true for most right triangles; a right isosceles triangle, with two equal legs, is the exception.
For a triangle with two equal sides instead, see the isosceles triangle calculator. For every measurement of any triangle from three known sides, see the triangle from three sides calculator.