Triangle calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Semi-perimeter s = (a + b + c) ÷ 2 = 6.
- Heron's formula: area = √(s(s − a)(s − b)(s − c)) = 6.
- Angles from the law of cosines: A = 36.869898°, B = 53.130102°, C = 90°.
| Inputs | Answer |
|---|---|
| Side a: 3; Side b: 4; Side c: 5 | A triangle with sides 3, 4 and 5 has area 6 (scalene, right). |
| Side a: 7; Side b: 8; Side c: 9 | A triangle with sides 7, 8 and 9 has area 26.832816 (scalene, acute). |
| Side a: 6; Side b: 6; Side c: 6 | A triangle with sides 6, 6 and 6 has area 15.588457 (equilateral, acute). |
| Side a: 2; Side b: 2; Side c: 3.9 | A triangle with sides 2, 2 and 3.9 has area 0.866599 (isosceles, obtuse). |
How to use it
With the three sides known, Heron's formula gives the area: s = (a + b + c) ÷ 2 and area = √(s(s − a)(s − b)(s − c)). The angles come from the law of cosines, and the type follows from the sides (equilateral, isosceles, scalene) and the largest angle (acute, right, obtuse).
The three sides must satisfy the triangle inequality: each side shorter than the other two together. If they do not, no triangle exists and the calculator says so.
Frequently asked questions
What is the area of a triangle with sides 3, 4 and 5?
6. It is a right triangle.
What is Heron's formula?
Area = √(s(s − a)(s − b)(s − c)) where s is half the perimeter.
When can three lengths form a triangle?
When each length is shorter than the sum of the other two.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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