Triangle Calculator
Inputs
Enter parameters to calculate Area, Perimeter, and missing sides/angles.
Understanding Triangles
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Identifying the properties of a triangle (sides, angles, area) is fundamental in trigonometry and construction.
Common Formulas
Area (Base & Height)
The most common formula, used when the base and vertical height are known.
Area = ½ × base × heightArea (Heron's Formula)
Used when all three side lengths (a, b, c) are known. First, calculate the semi-perimeter (s).
s = (a + b + c) / 2Area = √[s(s-a)(s-b)(s-c)]Law of Cosines (for Side c)
Used in SAS (Side-Angle-Side) cases.
c² = a² + b² - 2ab cos(C)Types of Triangles
- Equilateral: All 3 sides are equal. All angles are 60°.
- Isosceles: 2 sides are equal. The angles opposite those sides are equal.
- Scalene: No sides are equal. No angles are equal.
- Right Angled: Has one 90° angle. Follows a² + b² = c².
Frequently Asked Questions
What if the SSS inputs don't make a triangle?
For three sides to form a triangle, they must satisfy the Triangle Inequality Theorem: the sum of any two sides must be greater than the third side (a + b > c).
How do I find angles?
If you know all 3 sides, the calculator uses the Law of Cosines to reverse-calculate each angle.
Can I solve if I only have 3 angles?
No, you need at least one side length to determine the size of the triangle. Three angles (AAA) only proves similarity, not congruence (size).