Pythagorean Theorem Calculator
Enter the two legs of a right triangle to calculate the hypotenuse, using a² + b² = c².
Last updated: September 5, 2026
Frequently asked questions
What is the Pythagorean theorem?
a² + b² = c², where a and b are the two shorter sides (legs) of a right triangle and c is the hypotenuse (the longest side, opposite the right angle). It only applies to right triangles.
How do I find a missing leg instead of the hypotenuse?
Rearrange the formula: a = √(c² − b²), or b = √(c² − a²). Subtract the known leg's square from the hypotenuse's square, then take the square root.
What's a common example of the Pythagorean theorem, like 3-4-5?
3-4-5 is the most common "Pythagorean triple" - a set of whole numbers that satisfy a² + b² = c² exactly: 3² + 4² = 9 + 16 = 25 = 5². Other common triples include 5-12-13 and 8-15-17, useful for quickly checking if a corner is truly square without a calculator.
Is a 'pythagoras theorem calculator' or 'pythagorean theorem calc' different from this tool?
No - "Pythagoras" and "Pythagorean" both refer to the same theorem and mathematician, and "calc" is just short for calculator. All of these searches want the same thing: a² + b² = c², which this calculator solves for you.
Can the Pythagorean theorem be used for non-right triangles?
Not directly - a² + b² = c² only holds exactly when the triangle has a 90° angle. For any other triangle, you need the law of cosines instead, which adds a correction term (−2ab·cos(C)) to account for the non-right angle.
What is the hypotenuse of a right triangle with legs 6 and 8?
10 - c = √(6² + 8²) = √(36 + 64) = √100 = 10, another well-known Pythagorean triple (a doubled 3-4-5).
Does it matter which leg I label 'a' and which I label 'b'?
No - a and b are interchangeable in the formula since addition is commutative (a² + b² gives the same result regardless of order). Only the hypotenuse c has a fixed role as the longest side, opposite the right angle.