Triangle Calculator
Calculate the area, perimeter, and all three angles of a triangle from its three side lengths (SSS).
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter the three side lengths of a triangle to calculate its area, perimeter, and all three angles.
Your result
14.697
Area
Perimeter18
Angle opposite side a44.415
Angle opposite side b57.122
Angle opposite side c78.463
AI explanation
Formula
Area via Heron's formula: √(s(s−a)(s−b)(s−c)), s = perimeter/2. Angles via the law of cosines.Worked example
5-6-7 triangle
| Field | Value |
|---|---|
| Side a | 5 |
| Side b | 6 |
| Side c | 7 |
| Area | 14.6969 |
| Perimeter | 18 |
| Angle opposite side a | 44.4153 |
| Angle opposite side b | 57.1217 |
| Angle opposite side c | 78.463 |
Assumptions
- The three side lengths must satisfy the triangle inequality (each side shorter than the sum of the other two) or no such triangle exists.
- For a right triangle specifically (one 90° angle), the Right Triangle Calculator gives a more direct solve from just the two legs.
Frequently asked questions
What is Heron's formula?
It calculates a triangle's area purely from its three side lengths, without needing to know any angle or height directly: Area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter (half the perimeter).
What is the law of cosines?
It generalizes the Pythagorean theorem to any triangle, relating one side's length to the other two sides and the angle between them — used here to work out each angle from the three known side lengths.
What if my three side lengths don't form a valid triangle?
If any one side is longer than or equal to the sum of the other two, no triangle can be formed — this calculator rejects that combination (the "triangle inequality").