The Pythagorean theorem states that in a right triangle, a² + b² = c², where a and b are the two shorter sides and c is the hypotenuse (the side opposite the right angle).
Named after the ancient Greek mathematician Pythagoras, this theorem only applies to right triangles — triangles with one 90-degree angle.
If you know the length of two sides of a right triangle, you can find the third. For example, a triangle with legs of 3 and 4 units has a hypotenuse of 5 units, since 3² + 4² = 9 + 16 = 25, and √25 = 5. This "3-4-5" triangle is a common example used to check if a corner is truly square, in construction and carpentry.
The theorem also underlies the distance formula used in coordinate geometry, GPS calculations, and computer graphics.
Last reviewed: September 2026