Scalene triangle check
Enter three unequal sides to find the perimeter, area, and all interior angles.
Sides: 5, 6, 7
Perimeter = 18, area ≈ 14.70, angles sum to 180°
Triangle Calculator
Use this triangle calculator to find the area, perimeter, angles and other properties of a triangle by entering the three sides.
Triangle Calculator
Enter the three sides of a triangle, then click Calculate to find its properties.
Result
What is a Triangle?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
The three angles of a triangle always sum to 180 degrees. The sum of the lengths of any two sides must be greater than the length of the remaining side.
Triangle Properties
- Perimeter: The perimeter of a triangle is the sum of the lengths of its three sides: P = a + b + c.
- Area: The area can be calculated using Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter: s = (a + b + c)/2.
- Angles: The angles of a triangle can be calculated using the Law of Cosines. For example, angle C can be found using: cos(C) = (a² + b² - c²)/(2ab).
Types of Triangles
- Equilateral Triangle: A triangle with all sides equal and all angles equal (60°).
- Isosceles Triangle: A triangle with two sides equal and two angles equal.
- Scalene Triangle: A triangle with no sides equal and no angles equal.
- Right Triangle: A triangle with one angle equal to 90°.
- Acute Triangle: A triangle with all angles less than 90°.
- Obtuse Triangle: A triangle with one angle greater than 90°.
How to Use the Triangle Calculator
- Enter the length of side a.
- Enter the length of side b.
- Enter the length of side c.
- Click 'Calculate' to see the results and step-by-step solution.
The three side lengths must satisfy the triangle inequality: the sum of any two sides must be greater than the third side.
Applications of Triangle Calculations
- Architecture and construction for designing roof trusses and structural elements.
- Land surveying and mapping to calculate areas and distances.
- Navigation and GPS systems for determining positions and distances.
- Computer graphics and game development for rendering 3D objects.
Triangle Examples
Right triangle verification
A classic 3-4-5 triangle shows how area and angles are derived from side lengths.
Sides: 3, 4, 5
Perimeter = 12, area = 6, one angle = 90°
Near-equilateral triangle
Compare how close a triangle is to equilateral by reviewing the angle output.
Sides: 8, 8, 7
Angles are close to 60°, showing near symmetry
Surveying layout
Use three measured sides from a land plot to estimate enclosed area.
Sides: 15, 18, 21
Heron's formula gives the area directly from side lengths
Triangle Calculator FAQ
What formula does this calculator use for triangle area?
It uses Heron's formula, which calculates area from the three sides after first finding the semi-perimeter.
Can I calculate angles from only the three side lengths?
Yes. The calculator uses the Law of Cosines to compute each interior angle from the side lengths.
Why does the calculator reject some side combinations?
Those values do not satisfy the triangle inequality. If any two sides do not add up to more than the third side, a valid triangle cannot exist.
Is this calculator only for right triangles?
No. It works for any valid triangle, including scalene, isosceles, equilateral, acute, obtuse, and right triangles.