Triangle Calculator
Calculate the area, perimeter, angles, and side lengths of any triangle using SSS, SAS, ASA, or right triangle formulas step-by-step.
Triangle Property Solver
Enter known values to find missing properties
Choose which properties of the triangle you currently know
Triangle Properties
Area, perimeter, angles, and side lengths
Select your known values and click Calculate to find the area, perimeter, angles, and missing sides.
Essential Triangle Formulas
Common mathematical formulas used to calculate the properties of any triangle.
| Formula Name | Equation / Expression | Description |
|---|---|---|
| Area (Base/Height) | A = 0.5 × b × h | Half the product of base and corresponding height |
| Heron’s Formula | A = √(s(s-a)(s-b)(s-c)) | Area from three sides, where s is the semi-perimeter |
| Pythagorean Theorem | a² + b² = c² | Relates the legs and hypotenuse of a right triangle |
| Law of Sines | a/sin(A) = b/sin(B) = c/sin(C) | Relates sides to the sines of their opposite angles |
| Law of Cosines | c² = a² + b² – 2ab·cos(C) | Generalizes Pythagorean theorem for any triangle |
| Perimeter | P = a + b + c | Sum of all three side lengths |
Triangle Calculator FAQ
Everything you need to know about calculating triangle properties and solving for missing values.
The most common formula is Area = 0.5 × base × height. If you know all three sides but not the height, you can use Heron’s Formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2. This calculator automatically applies the correct formula based on your inputs.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides: a² + b² = c². It is only applicable to right triangles and is used to find a missing side length when the other two are known.
To find a missing side, you need at least three known properties (including at least one side). If it’s a right triangle, use the Pythagorean theorem. For any other triangle, use the Law of Cosines (if you have SAS or SSS) or the Law of Sines (if you have ASA, AAS, or SSA).
Triangles are classified by their sides and angles. By sides: Equilateral (3 equal sides), Isosceles (2 equal sides), and Scalene (no equal sides). By angles: Acute (all angles < 90°), Right (one angle = 90°), and Obtuse (one angle > 90°).
The sum of all interior angles in any triangle is always 180 degrees. If you know two angles, simply subtract their sum from 180 to find the third. If you only know the sides, you can use the Law of Cosines to find the angles: cos(A) = (b² + c² – a²) / 2bc.
No, a triangle cannot have two right angles in Euclidean (flat) geometry. Since the sum of all three interior angles must be exactly 180°, having two 90° angles would leave 0° for the third angle, which is impossible. A triangle can only have at most one right angle.