Triangle Calculator
Pythagoras had a whole cult about triangles. We're just a website. Less intense.
In right triangle mode, sides a and b are the legs. The hypotenuse (c) is calculated automatically.
About This Calculator
How It Works
Enter what you know about a triangle — sides, angles, or a combination — and this calculator solves for the unknowns using the appropriate formula: the Pythagorean theorem for right triangles, the law of cosines or law of sines for oblique triangles, and Heron's formula for area when all three sides are known. The goal is to require as little input as possible to give you as much output as possible.
The Formula
Pythagorean: a² + b² = c². Law of cosines: c² = a² + b² - 2ab×cos(C). Area = 0.5 × base × height. Heron's formula for all three sides.
When to Use This
Triangle calculations come up in construction (roof pitches, staircase angles, diagonal bracing), navigation, land surveying, design, and any geometry coursework. If you know two sides of a right triangle, you can find the third. If you know all three sides, you can find all angles. This calculator handles the trigonometry so you don't have to.
Example
Right triangle with legs 3 and 4: hypotenuse = √(9+16) = √25 = 5. The classic 3-4-5 triangle. Pythagoras would be so proud.
Did You Know?
Pythagoras reportedly had a philosophical cult called the Pythagoreans who believed numbers had personalities. They kept mathematical discoveries secret and thought odd numbers were masculine and even numbers feminine. Geometry was intense back then.