What Is a Triangle Calculator?
This triangle calculator finds the area, perimeter, all three angles, and triangle type from three known side lengths, using Heron's Formula and the Law of Cosines.
How to Use the Triangle Calculator
- Enter the lengths of all three sides.
- View the area, perimeter, all three angles, and triangle classification instantly.
Triangle Formulas
Worked Example
Semi-perimeter: s = (5+6+7)/2 = 9
Area = √[9(9−5)(9−6)(9−7)] = √(9×4×3×2) = √216 ≈ 14.70
This is a scalene, acute triangle (all sides and angles different, all angles under 90°).
Understanding Your Results
The calculator uses Heron's Formula to find area directly from the three side lengths (no height measurement needed), and the Law of Cosines to find each angle. Triangle Type classifies the shape both by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
Triangle Classification Reference
| Type | Definition |
|---|---|
| Equilateral | All three sides equal |
| Isosceles | Exactly two sides equal |
| Scalene | All sides different lengths |
| Acute | All angles less than 90° |
| Right | One angle exactly 90° |
| Obtuse | One angle greater than 90° |
Common Mistakes to Avoid
- Entering side lengths that can't form a valid triangle (any side must be shorter than the sum of the other two).
- Confusing Heron's Formula (needs three sides) with the basic ½ × base × height formula (needs a base and perpendicular height).
- Rounding angle calculations too early, which can compound small errors.
Frequently Asked Questions
It calculates a triangle's area directly from its three side lengths, without needing to know the height — useful when height isn't easily measured.
The triangle inequality theorem states that the sum of any two sides must be greater than the third side; if this fails, the sides cannot form a triangle.
Use the Law of Cosines: cos(A) = (b² + c² − a²) / (2bc), then take the inverse cosine to find angle A. Repeat for the other angles.
An acute triangle has all angles under 90°, a right triangle has exactly one 90° angle, and an obtuse triangle has one angle greater than 90°.
Yes — in standard Euclidean (flat) geometry, the three interior angles of any triangle always sum to exactly 180°.