Pythagorean Theorem Calculator

What this tool does

Enter any two of a right triangle’s three sides to solve for the missing one using the Pythagorean theorem, or switch to check mode to test whether three given side lengths actually form a right triangle. Every answer includes the substituted formula as working.

The Pythagorean theorem, a² + b² = c², connects the two legs and the hypotenuse of any right triangle. This calculator handles both directions of that relationship: solving for whichever side you are missing, and checking whether three sides you already have actually describe a right angle at all.

Pick the mode that matches your question — find the hypotenuse, find a leg, or verify a right triangle — and the required inputs appear while everything else stays hidden, keeping the form uncluttered.

How to use Pythagorean Theorem Calculator

1. Choose what you want to do: find the hypotenuse, find a leg, or check a triangle.
2. When solving, enter the two known sides into the fields that appear.
3. When checking, enter all three side lengths in any order.
4. Read the result, shown with the substituted formula underneath.
5. For the check mode, note the verdict — right, acute or obtuse-angled — based on comparing the squares.
6. Adjust any value and the answer updates immediately.

Tips for better results

• The hypotenuse is always the longest side and sits opposite the right angle; make sure you are not entering it as a leg by mistake.
• When solving for a leg, the hypotenuse you provide must be longer than the known leg, or no real triangle exists.
• In check mode, the three sides do not need to be entered in any particular order — the tool automatically treats the longest as the candidate hypotenuse.
• A triangle can fail the right-angle check yet still be a valid triangle; the tool reports it as acute or obtuse instead of throwing an error.

Common use cases

• Finding the diagonal distance across a rectangular room, screen or plot of land.
• Checking whether a carpentry or construction corner is actually square using the 3-4-5 rule or measured sides.
• Solving physics or engineering problems involving right-triangle components of a vector.
• Verifying a triangle from a geometry problem is right-angled before applying right-triangle-only formulas.

Common mistakes to avoid

• Entering the hypotenuse into a leg field when solving for the other leg, which the tool catches and reports as an error.
• Assuming any triangle with an integer-looking set of sides is automatically a right triangle without actually checking a² + b² against c².
• Rounding intermediate leg or hypotenuse values before the final answer, which can shift a true right triangle just over the floating-point tolerance used by the checker.
• Forgetting that three lengths that fail the triangle inequality (two shorter sides not exceeding the longest) cannot form any triangle, right-angled or otherwise.