Triangle Calculator

Triangle Formulas

Area Formulas

Given base and height: Area = 0.5 × base × height. Given three sides (Heron's formula): Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. Given two sides and included angle: Area = 0.5 × a × b × sin(C).

Pythagoras' Theorem

For a right triangle: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle). This gives c = √(a² + b²). This theorem is the basis for countless engineering, construction, and navigation calculations.

Special Triangles

Equilateral (all sides equal): all angles = 60°. Isosceles (two equal sides): two equal angles. Right triangle: one angle = 90°. The 3:4:5 right triangle (and its multiples) is frequently used in construction to establish right angles.