Pythagorean Theorem
Free Pythagorean Theorem for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations. Free math tool.
Formula
a² + b² = c²
The square of the hypotenuse (c) equals the sum of squares of the legs (a and b).
Worked Examples
Example 1: Standard 3-4-5
Problem:a=3, b=4
Solution:c = √(3² + 4²) = √(9 + 16) = √25 = 5
Result:5
Example 2: Large Triangle
Problem:a=5, b=12
Solution:c = √(25 + 144) = √169 = 13
Result:13
Frequently Asked Questions
Does this theorem work for all triangles?
No, the Pythagorean Theorem ONLY applies to right-angled triangles (triangles containing one 90° angle).
What is a Pythagorean Triple?
A set of three whole numbers that satisfy the equation a² + b² = c². Common examples include 3-4-5, 5-12-13, and 8-15-17.
What is the Converse of the Pythagorean Theorem?
It states that if the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a squared + b squared = c squared). It only applies to right triangles and is fundamental to geometry and trigonometry.