Triangle Calculator

Calculate triangle properties using different methods: SSS (3 sides), SAS (2 sides + included angle), or base + height. Returns: area (via Heron's formula or trigonometry), perimeter, all three angles (via Law of Cosines). Used in geometry homework, engineering, surveying, architecture, navigation.

Details

Heron's formula (3 sides):

s = (a+b+c)/2 (semi-perimeter)

Area = √(s(s-a)(s-b)(s-c))

Law of Cosines: c² = a² + b² – 2ab·cos(C)

SAS Area: ½·a·b·sin(C)

Tips

• Triangle inequality: any two sides sum > third side
• Sum of angles always = 180°
• Equilateral: all sides equal, all angles 60°
• Right triangle: Pythagorean theorem: a²+b²=c²
• Isosceles: two equal sides + two equal angles

FAQs

Invalid triangle error?

Sides violate triangle inequality. Two sides must sum > third. Example: 3, 4, 9 is invalid (3+4<9).

How accurate?

Calculator uses double-precision floating point — 15 significant digits. Plenty for any practical use.

Different from Pythagoras?

Pythagoras only for right triangles. This tool handles any triangle. Heron's formula works for all triangles given 3 sides.