Pythagorean Theorem Calculator
Solve for any missing side of a right triangle using a^2 + b^2 = c^2. Enter any two sides to get the third, plus area and perimeter.
Right triangle sides
Enter any two sides. Leave the side you want to solve for blank. Sides a and b are the legs; c is the hypotenuse (longest side).
Hypotenuse c =
5
Area
6
Perimeter
12
Triangle
Frequently Asked Questions about the Pythagorean Theorem Calculator
What is the Pythagorean theorem formula?
In any right triangle, a squared plus b squared equals c squared, where a and b are the legs and c is the hypotenuse (the side opposite the right angle). Rearranged: c = sqrt(a^2 + b^2), a = sqrt(c^2 - b^2), b = sqrt(c^2 - a^2).
What is the Pythagorean theorem used for in real life?
Construction (squaring corners with the 3-4-5 rule), navigation and GPS distance, surveying, screen and TV diagonals, roof pitch, ladder safety angles, and computing straight-line distances in 2D coordinate systems.
What is a 3-4-5 triangle?
The simplest integer right triangle: legs of 3 and 4 give a hypotenuse of 5 because 3^2 + 4^2 = 9 + 16 = 25 = 5^2. Builders use this to confirm a right angle without a square.
What are Pythagorean triples?
Sets of three positive integers (a, b, c) that satisfy a^2 + b^2 = c^2. Common examples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29). Any multiple of a triple (like 6, 8, 10) is also a triple.
Does the Pythagorean theorem work for non-right triangles?
No. It only holds for right triangles. For other triangles, use the Law of Cosines: c^2 = a^2 + b^2 - 2ab cos(C), which reduces to the Pythagorean theorem when C = 90 degrees.