Pythagorean Theorem Calculator (a² + b² = c²)
Solve right triangle hypotenuse and leg lengths with radical square root steps, perimeter, area, and acute angles.
Calculated Results
Frequently Asked Questions
What is the Pythagorean theorem formula?
The Pythagorean theorem states that in any right triangle (90-degree angle), the square of the hypotenuse is equal to the sum of the squares of the other two legs: a² + b² = c², where c is the hypotenuse opposite the right angle.
What are the most common Pythagorean triples?
Pythagorean triples are whole integer solutions: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), and (9, 40, 41). Any integer multiple of these (e.g. 6-8-10 or 30-40-50) is also a valid right triangle.
How do carpenters use the 3-4-5 rule to square corners?
Carpenters measure 3 feet along one wall, 4 feet along the perpendicular wall, and adjust the angle until the diagonal distance between the two marks measures exactly 5 feet, ensuring a perfectly square 90-degree corner.
Can the Pythagorean theorem be used for 3D distance?
Yes! In three-dimensional space, the distance formula is an extension of Pythagoras: d = √(x² + y² + z²).