Math & Conversion
Pythagorean Theorem Calculator (a² + b² = c²)
Solve for any side of a right triangle given the other two.
What this calculates
The Pythagorean theorem relates the legs (a, b) of a right triangle to the hypotenuse (c): a² + b² = c². Given any two sides, the third is determined. This calculator solves all three cases.
Formula & how it works
c = √(a² + b²) when finding hypotenuse. a = √(c² − b²) when finding a leg. Requires c > a and c > b for leg-finding case.
Worked example
Legs 3 and 4 → hypotenuse 5. Hypotenuse 13 with leg 5 → other leg 12.
Frequently asked questions
Only works for right triangles?
Yes. For other triangles use the law of cosines.
What if I get an error solving a leg?
Means hypotenuse ≤ the known leg — invalid right triangle.
Pythagorean triples?
Integer sets like (3,4,5), (5,12,13), (8,15,17). Generated by m² − n², 2mn, m² + n² for m > n > 0.