NumberTally Pythagorean Theorem Calculator
Enter any two sides of a right triangle and this calculator solves the missing one — leg or hypotenuse — with the full step-by-step working, a labeled triangle diagram, and a validity check. Free, no sign-up.
Advanced options
Enter three positive numbers to test whether they form a Pythagorean triple (x² + y² = z²).
a² + b² = c²
In a right triangle, the two legs (a, b) meet at the 90° corner, and the hypotenuse (c) sits opposite it — always the longest side. The theorem says the squares of the legs add up to the square of the hypotenuse. To find a missing leg, rearrange: a = √(c² − b²).
Pythagorean triples
Some whole-number sets fit perfectly: 3-4-5, 5-12-13, 8-15-17, 7-24-25 — and any multiple of a triple is a triple (6-8-10, 9-12-15). The triple checker above tests your own three numbers.
Frequently Asked Questions
What is the Pythagorean theorem?
In a right triangle, a² + b² = c², where c is the hypotenuse. It relates all three sides, so any two determine the third.
How do you find the hypotenuse of a right triangle?
c = √(a² + b²). With legs 3 and 4: c = √(9 + 16) = √25 = 5.
How do you find a missing leg?
Subtract: a = √(c² − b²). With hypotenuse 5 and leg 4: a = √(25 − 16) = √9 = 3. The hypotenuse must be longer than the known leg, or there's no real answer.
Does the Pythagorean theorem work on any triangle?
No — only right triangles (one 90° angle). For other triangles you need the Law of Cosines: c² = a² + b² − 2ab·cos(C).
What are Pythagorean triples used for?
Builders use 3-4-5 to check square corners; the triple guarantees a right angle without measuring one. Multiples like 6-8-10 work for larger layouts.