Pythagorean Theorem Calculator
Fill in any two sides of a right triangle and leave the third empty. The calculator rearranges the theorem for whichever side is missing.
How it works
How the Pythagorean Theorem Calculator works
the part a result on its own leaves out
What the theorem says
In a right triangle, the square built on the hypotenuse has exactly the same area as the two squares on the legs combined. That is a statement about areas, which is why the sides are squared.
Only right triangles
The relationship holds only when one angle is 90°. For any other triangle the law of cosines applies, and it reduces to Pythagoras exactly when the angle is a right angle.
Common mistakes
Common mistakes with the pythagorean theorem
the errors that actually show up, not every possible slip
Treating a leg as the hypotenuse
c is always the side opposite the right angle, and always the longest. Putting a leg in the c box gives a negative square and no real answer.
Forgetting the square root
a² + b² gives c², not c. Stopping one line early is the most common slip in this calculation.
Adding before squaring
(6 + 8)² is 196, but 6² + 8² is 100. The squaring happens first, to each side separately.
Questions
Asked often enough to answer here
answers that change how you work
What are Pythagorean triples?
Whole-number side sets like 3-4-5, 5-12-13 and 8-15-17. Any multiple of a triple is also a triple, which is why 6-8-10 works.
Can I use it to check for a right angle?
Yes. If a² + b² equals c² for the three sides, the triangle is right-angled. If the sum is larger the angle is acute, if smaller it is obtuse.
Why is the answer often irrational?
Because most sums of two squares are not perfect squares. √13 is exact; 3.6056 is rounded.
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