Pythagorean Theorem Calculator
The right-triangle workhorse: a² + b² = c². Tell the tool which side you're missing — the hypotenuse or one leg — and it returns the length plus the exact steps. Handy for the classic 3-4-5 squaring trick on a job site, or finding a room's diagonal.
What Are You Solving For?
The Pythagorean Formula
For a right triangle with legs a and b and hypotenuse c:
a² + b² = c² → c = √(a² + b²) → a = √(c² − b²)
It only applies to right triangles (one 90° angle). For non-right triangles you'd need the law of cosines instead. The theorem is the basis for the distance formula in coordinate geometry and shows up constantly in area and layout work.
Worked Example: The 3-4-5 Triangle
Legs of 3 and 4: c = √(3² + 4²) = √(9 + 16) = √25 = 5. That 3-4-5 relationship is why builders use it to check a corner is square — a triangle with those side lengths is guaranteed right-angled. Going the other way, if the diagonal (hypotenuse) is 5 and one side is 4, the other side is √(25 − 16) = 3.
Frequently Asked Questions
What is the Pythagorean theorem?
a² + b² = c² — the hypotenuse squared equals the sum of the legs squared.
How do I find the hypotenuse?
c = √(a² + b²). For 3 and 4, c = 5.
How do I find a missing leg?
a = √(c² − b²). With c = 5, b = 4, a = 3.
Where is it used in real life?
Squaring foundations (3-4-5 rule), TV/room diagonals, straight-line distances, navigation.