What is a triangle calculator?
A triangle calculator helps you quickly find the area, perimeter, and angles of a triangle based on known values. Choose from four calculation modes: three sides (SSS), base and height, two sides and an included angle (SAS), or two angles and a side (AAS).
How to calculate the area of a triangle?
The area of a triangle can be calculated in several ways depending on the available data:
- Base and height: A = ½ × base × height
- Heron's formula (three sides): A = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
- Two sides and included angle (SAS): A = ½ × a × b × sin(C)
What are the triangle formulas?
The key triangle formulas include:
- Perimeter: P = a + b + c
- Law of cosines: c² = a² + b² − 2ab × cos(C)
- Law of sines: a/sin(A) = b/sin(B) = c/sin(C)
- Angle sum: A + B + C = 180°
Triangle calculation examples
Consider a triangle with sides a = 3, b = 4, c = 5. This is a right triangle. The semi-perimeter s = (3+4+5)/2 = 6. Area by Heron's formula: A = √(6×3×2×1) = √36 = 6. Perimeter P = 12. Angles: A ≈ 36.87°, B ≈ 53.13°, C = 90°.
Another example: a triangle with base 10 and height 5. Area A = ½ × 10 × 5 = 25.
When to use a triangle calculator?
A triangle calculator is useful for students solving geometry problems, architects and engineers designing structures, surveyors calculating land areas, and anyone who needs to quickly determine triangle properties from partial measurements.
What are the types of triangles?
Triangles are classified by their sides and angles:
- Equilateral – all sides and angles are equal (60°)
- Isosceles – two sides are equal
- Scalene – all sides are different
- Right – one angle equals 90°
- Acute – all angles are less than 90°
- Obtuse – one angle is greater than 90°